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Contract negotiation, incomplete contracting, and asymmetric information : (essays in managerial accounting… Xie, Jia-Zheng James 1991

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CONTRACT NEGOTIATION, INCOMPLETE CONTRACTING, AND ASYMMETRIC INFORMATION (ESSAYS IN MANAGERIAL ACCOUNTING RESEARCH) BY JIA-ZHENG (JAMES) XIE B . S c , SHANGHAI EDUCATION UNIVERSITY, 1963 M . S c , SHANGHAI JIAO-TONG UNIVERSITY, 1982 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n THE FACULTY OF GRADUATE STUDIES FACULTY OF COMMERCE AND BUSINESS ADMINISTRATION THE UNIVERSITY OF BRITISH COLUMBIA We a c c e p t t h i s t h e s i s as c o n f o r m i n g to the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA March 1991 © JIA-ZHENG (JAMES) X I E , 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of British Columbia Vancouver, Canada DE-6 (2/88) Abstract This thesis contributes to the managerial accounting research literature. The methodology used is basically analytical modelling. Part I focuses on voluntary financial accounting disclosure. Following a detailed survey of the existing literature, an analytical model of an entry game with continua of types is provided to advance the results of prior research. By ex-plicitly considering both a potential entrant and potential investors, this model incorporates two opposing forces that may influence an incumbent's decision to disclose or withhold private information. Various equilibria are characterized and discussed. Part II of the thesis focuses on firms' con-tractual relationships. The analyses extend traditional agency theory analysis to situations in which complete contracting is costly. Two models related to incomplete contracting are offered. One model analyzes the influence of contracting costs on a firm's contracting strategy in the context of the firm's internal transfer of goods and services. The results of this analysis provide insights and a new basis for the research of the transfer pricing issue. The second model deals with the incentive issues within organizations. The analysis focuses on the situations in which verifiable performance measures are unavailable. In the model, two kinds of incentives, namely, high-powered and low-powered incentives, are analyzed. We find that contract renewal based on observable (but non-verifiable information) can provide useful low-powered incentives in an hierarchical organization in which employees build up human capital. This may provide useful insights into managerial accounting system design. ii T A B L E O F C O N T E N T S Abstract ii Table of Contents iii List of Tables vi List of Figures vii Acknowledgement ix Chapter 1 Introduction to the Thesis 1 References 7 Part I Voluntary Disclosure of Private Information 8 Chapter 2 Discretionary Disclosure Research in the 1980s: A Survey 9 Section 2.1 Introduction 10 Section 2.2 Key Dimensions for Classification of ana-lytical Models 11 Section 2.3 Two-player Disclosure Models 17 Section 2.4 Oligopolistic Models 27 Section 2.5 Three-player Disclosure Models 45 Section 2.6 Signalling Models 56 Section 2.7 Empirical and Behavioral Research on Voluntary Disclosure 68 Tables 77 References 82 Chapter 3 Voluntary Financial Disclosure in an Entry Game with Continua of Types 87 Section 3.1 Introduction 88 Section 3.2 The Basic Model 94 Section 3.3 I's Strategy Choice 102 Section 3.4 Full Disclosure Equilibria 109 Section 3.5 Partial Disclosure Equilibria 120 Section 3.6 Multiple Equilibria and Their Refinements 132 Section 3.7 Concluding Remarks 138 Tables 141 Figures 142 iii Appendix 3.A Payoffs in a Cournot Equilibrium Entry Game with Demand Uncer-tainty 152 Appendix 3. B Proofs 156 Appendix 3.C Notations Used in the Chapter 185 References 187 Part II Incomplete Contracting 188 Chapter 4 Introduction to Part II 189 References 200 Chapter 5 Incomplete Contracting for Economizing Contract-ing Costs 201 Section 5.1 Introduction 202 Section 5.2 Contracting Costs 206 Section 5.3 Basic Model Elements 213 Section 5.4 Contracting with Verifiable Information 217 Section 5.5 Contracting with Unverifiable Information 227 Section 5.6 Contracting with Large Ex Post Bargaining Costs 244 Section 5.7 Transfer Pricing for Economizing Contract-ing Costs 252 Section 5.8 Conclusions 262 Figures 264 Appendix 5 Proofs 272 References 277 Chapter 6 Contract Negotiation and Long-Term Incentives in Organizations 278 Section 6.1 Introduction 279 Section 6.2 Performance Measures and Human Assets 286 Section 6.3 Model and Analysis 291 Section 6.4 Implication for Managerial Accounting Sys-tem Design 339 Tables 346 iv Appendix 6 Proofs 347 References 358 v List of Tables Table No. Title Page1 2-1 Two-player Disclosure Models 17(77) 2-2 Oligopolistic Models 29(78) 2-3 Ex ante & Ex post Equilibrium Strategies 42(79) 2-4 Three-player Disclosure Models 45(80) 2-5 Signalling Models 60(81) 3-1 Sequence of Events in the Entry Game 95(141) 6-1 Comparison of Incentives 333(346) 1Page that the table i s inserted (Page that the table appears). vi List of Figures Figure No. Title Page2 3-1 Expected Outcomes 97(142) 3-2 Expected End-of-Period Wealth under Full Dis-closure 105(143) 3-3 Disclosure Versus Non-Disclosure (E's Breakeven Point is Common Knowledge) 107(144) 3-4 Capital Requirement/Entry Cost Conditions under which Full Disclosure Equilibria Exist (E's Breakeven Point is Uniformly Distributed) 117(145) 3-5 Capital Requirement/Entry Cost Conditions under which Partial Disclosure Equilibria Exist (E's Breakeven Point is Uniformly Distributed) 126(146) 3-6 Capital Requirement/Entry Cost Conditions under which Partial Disclosure Equilibria Exist (Variable Entry Cost/ Breakeven Point is Common Knowledge) 129(147) 3-7 Capital Requirement/Entry Cost Conditions under which Partial Disclosure Equilibria Exist (Fixed Entry Cost/ Breakeven Point is Common Knowledge) 130(148) 3-8 End-of-Period Cash Flow Curve and Contract Curve 177(149) 3-9 FD contract Curves with Different Parameter Values 178(150) 3-10 Comparison of Equilibria 184(151) 5-1 Positive and Nagative Gain Regions without Contracting Costs 219(264) 5-2 Trading Region of a Null Contract with Ex Post Bargaining Costs 225(265) 5-3 Regions Divided by Ex Ante Prices 229(266) 5-4 Regions with Marginal Adjustments 232(267) 5-5 Ex Ante Prices Corresponding to Different Governance Strutures 241 (268) 5-6 Different Parameter Categories 243(269) 2Page that the figure i s inserted (Page that the figure appears). vii 5-7 Suboptimal Dual Pricing Contract 251 (270) 5- 8 Optimal Dual Pricing Contract 252(271) 6- 1 Event Sequence for One-Period Model 300(300) 6-2 Event Sequence for Two-Period Model 312(312) viii Acknowledgement I am most grateful to my thesis supervisor Gerald A. Feltham for his illuminating guidance and continuing encouragement. I also wish to thank the members of my thesis committee, Alan Kraus and Paul Fischer for their comments and suggestions. I have also benefited from the discussions with Jack Hughes, Peter Cheng, and seminar participants at the University of British Columbia. My special thanks also go to Patricia Hughes and Stephen Sefcik for their help during my Ph.D program, to my classmates Lucie Courteau and Jane Saly for helpful discussions, to my colleagues at the University of Alberta, particularly to Dean Jean-Louis Malouin, to Michael Gibbins, James Newton, and David Cooper for their kind support, to Professor Hon-Shiang Lau and Amy Lau in Oklahoma State University, and Professor Jie-Ren Pan in Shanghai Jiao-Tong University for their precious help when I was in my motherland, to my wife Xiao-Fen Zou and my daughter Jing Xie, not only for their invaluable support and help, but also for their great patience and understanding. Financial support from CIDA (Canada International Development Agency) is gratefully acknowledged. Jia-Zheng (James) Xie ix Chapter 1 INTRODUCTION TO THE THESIS 1 This thesis contributes to the managerial accounting research l i t e r a t u r e . The analysis concentrates on two important elements of managerial accounting issues: i n f o r -mation and contracts. The thesis consists of s i x chap-t e r s . This chapter (Chapter 1) serves as an introduction to the whole th e s i s . The remaining f i v e chapters are grouped into two parts. Part I, which consists of Chapters 2 and 3, focuses on voluntary f i n a n c i a l accounting disclosure. As pointed out by Feltham [1984], i n the process of operating a firm, management i s l i k e l y to acquire considerable private information about the factors that a f f e c t the outcomes of the firm's a c t i v i t i e s . Some of that private information i s u l t i m a t e l y revealed by mandatory and voluntary public reports, and some may be revealed by observed management actions. To understand the information content of ac-counting reports and the reporting choices made by man-agement, we must understand the market forces that create incentives f o r management to acquire and then reveal or disguise p r i v a t e information. Therefore, a firm's behav-iour i n v o l u n t a r i l y d i s c l o s i n g i t s private information i s an important issue i n managerial and f i n a n c i a l accounting research. Many types of individuals are p o t e n t i a l l y interested i n management's private information. These include cur-2 r e n t a n d p o t e n t i a l i n v e s t o r s , c r e d i t o r s , s u p p l i e r s , e m p l o y e e s , c u s t o m e r s , c o m p e t i t o r s , a n d r e g u l a t o r s . M a n -a g e m e n t h a s a p r i m a r i l y c o o p e r a t i v e r e l a t i o n s h i p w i t h s o m e , b u t w i t h o t h e r s t h e r e l a t i o n s h i p i s p r i m a r i l y n o n - c o o p e r a t i v e . T h e r e f o r e , b o t h c o o p e r a t i v e a n d n o n - c o o p e r -a t i v e game t h e o r y p r o v i d e a n a l y s e s t h a t a r e r e l e v a n t t o u n d e r s t a n d i n g m a n a g e m e n t ' s c h o i c e s . F u r t h e r m o r e , s i n c e t h e r e a r e many i n d i v i d u a l s a n d f i r m s c o m p e t i n g f o r t h e e c o n o m y ' s r e s o u r c e s , a n a l y s e s t h a t e x p l i c i t l y r e c o g n i z e t h e i m p a c t o f c o m p e t i t i v e m a r k e t f o r c e s a r e p a r t i c u l a r l y r e l e v a n t . T h e a n a l y s i s i n P a r t I p u r s u e s t h e o b j e c t i v e s m e n -t i o n e d a b o v e . P a r t i c u l a r l y , we s u m m a r i z e a n d a d v a n c e p r i o r r e s e a r c h i n t h i s f i e l d . C h a p t e r 2 i s a d e t a i l e d s u r v e y o f t h e e x i s t i n g l i t e r a t u r e . I t a l s o s e r v e s a s a n i n t r o d u c t i o n t o P a r t I . C h a p t e r 3 a n a l y z e s a f o r m a l m o d e l t o e x t e n d t h e r e s u l t s o f p r i o r r e s e a r c h . O u r m o d e l d e p i c t s a n e n t r y game i n w h i c h t h e i n c u m b e n t i s c o n c e r n e d a b o u t b o t h t h e p o t e n t i a l e n t r y o f a n e n t r a n t a n d t h e v a l -u a t i o n o f h i s f i r m b y p o t e n t i a l i n v e s t o r s , who w i l l s u p p l y c a p i t a l f o r h i s i n v e s t m e n t i n h i s m a r k e t . T h e i n c u m b e n t h a s p r i v a t e i n f o r m a t i o n a b o u t t h e p r o f i t a b i l i t y o f t h e p r o d u c t m a r k e t a n d h e may b e u n c e r t a i n a b o u t t h e s e t o f b e l i e f s t h a t w i l l i n d u c e t h e e n t r a n t t o e n t e r h i s m a r k e t . By e x p l i c i t l y c o n s i d e r i n g b o t h a p o t e n t i a l e n t r a n t a n d 3 p o t e n t i a l i n v e s t o r s , o u r model i n c o r p o r a t e s two o p p o s i n g f o r c e s t h a t may i n f l u e n c e an incumbent's d e c i s i o n t o d i s c l o s e o r w i t h h o l d p r i v a t e i n f o r m a t i o n . V a r i o u s e q u i -l i b r i a a r e c h a r a c t e r i z e d and t h e i r n a t u r e i s d i s c u s s e d . Our r e s u l t s p r o v i d e p o s s i b l e e x p l a n a t i o n s f o r o b s e r v e d v o l u n t a r y d i s c l o s u r e c h o i c e s made by f i r m s . P a r t I I , w h i c h c o n s i s t s o f C h a p t e r s 4, 5 and 6, c o n t r i b u t e s t o o u r u n d e r s t a n d i n g o f t h e r o l e o f m a n a g e r i a l a c c o u n t i n g i n a f i r m ' s c o n t r a c t u a l r e l a t i o n s h i p s . The main p u r p o s e o f our a n a l y s i s i s t o e x t e n d t r a d i t i o n a l agency t h e o r y a n a l y s i s t o s i t u a t i o n s i n w h i c h complete c o n t r a c t i n g i s c o s t l y and, hence, c o n t r a c t s a r e f r e q u e n t l y i n c o m p l e t e . The b a s i c c o n c e r n o f agency t h e o r y i s w i t h t h e "con-t r o l and i n f o r m a t i o n r e l a t i o n s " m a n i f e s t e d i n t h e s e a r c h f o r t h e most p r e f e r r e d f e a s i b l e c o n t r a c t between t h e p r i n c i p a l and h i s agent. The agency c o n t r a c t d e l e g a t e s t o t h e agent t h e r e s p o n s i b i l i t y t o "manage" a p o r t i o n o f t h e f i r m ' s o p e r a t i o n s i n r e t u r n f o r compensation t h a t i s e f f e c t i v e l y a s h a r e o f t h e f i r m ' s outcome. Depending on t h e s h a r i n g r u l e , t h e a g e n t ' s compensation may be a f i x e d r e m u n e r a t i o n o r a n o n - t r i v i a l f u n c t i o n o f t h e outcome o r o t h e r i n f o r m a t i o n about h i s performance ( t h u s , i m p o s i n g c o mpensation r i s k on t h e a g e n t ) . The i n t e r e s t s o f t h e p r i n c i p a l and t h e agent a r e l i k e l y t o c o n f l i c t s i n c e t h e 4 a g e n t i s a s s u m e d t o m a x i m i z e h i s own u t i l i t y , a n d h i s c h o i c e s may n o t m a x i m i z e t h e p r i n c i p a l ' s n e t p r o f i t . T h u s , d e m a n d f o r i n f o r m a t i o n f o r c o n t r a c t i n g a n d m o n i t o r -i n g p u r p o s e s i s r a i s e d . A m a n a g e r i a l a c c o u n t i n g s y s t e m i s d e s i g n e d t o s u p p l y t h i s i n f o r m a t i o n . A g e n c y t h e o r y p r o v i d e s a f r a m e w o r k w i t h i n w h i c h t h e d i f f e r e n c e s b e t w e e n t h e o b j e c t i v e s o f t h e p r i n c i p a l a n d t h e a g e n t a r e i n c o r p o r a t e d a s a n i n t e g r a l p a r t o f t h e t h e o r y . I n t h i s w a y , m a n a g e r i a l a c c o u n t i n g r e s e a r c h c a n a n a l y z e t h e i m p o r t a n t m o t i v a t i o n a l a s p e c t s o f v a r i o u s t r a d i t i o n a l a c c o u n t i n g i s s u e s . I t s c o n s i d e r a b l e c a p a c i t y f o r p u t t i n g m a n a g e m e n t a c c o u n t i n g i n t o a b r o a d e r a n d m o r e c o h e r e n t c o n t e x t , f o r o f f e r i n g a m o r e r i g o r o u s r e p r e s e n t a -t i o n o f m a n a g e m e n t a c c o u n t i n g c o n c e p t s , a n d f o r c l a r i f y i n g i m p o r t a n t a n a l y t i c a l a s w e l l a s b e h a v i o r a l a s p e c t s o f m a n a g e m e n t a c c o u n t i n g i s s u e s , h a s g r e a t l y a d v a n c e d m a n a -g e r i a l a c c o u n t i n g r e s e a r c h i n t h e l a s t t w e n t y y e a r s . O n e k e y f e a t u r e o f t h e t r a d i t i o n a l a g e n c y t h e o r y i s i t s e m p h a s i s o n c o m p l e t e c o n t r a c t i n g . I n o t h e r w o r d s , i t i s a s s u m e d ( e i t h e r i m p l i c i t l y o r e x p l i c i t l y ) t h a t c o n -t r a c t i n g c o s t s a r e t r i v i a l . H e n c e , t h e r e s u l t s o f s u c h a n a l y s e s a r e v a l i d i n a p e r f e c t w o r l d w h e r e c o n t r a c t i n g i s c o s t l e s s , o r i n c a s e s i n w h i c h t h e i m p a c t o f c o n t r a c t i n g c o s t s i s t r i v i a l r e l a t i v e t o t r a n s a c t i o n g a i n s . H o w e v e r , t h e u s e f u l n e s s o f t h e s e r e s u l t s a r e l i m i t e d when we d e a l 5 w i t h c a s e s i n w h i c h t r a n s a c t i o n c o s t s p l a y a c r u c i a l r o l e . I n t h e s e c a s e s , c o m p l e t e c o n t r a c t i n g i s c o s t l y ( o r i m p o s s -i b l e ) a n d , h e n c e , c o n t r a c t s a r e a l w a y s i n c o m p l e t e . T h e r e -f o r e , i t i s u s e f u l t o e x t e n d a g e n c y t h e o r y t o i n c o r p o r a t e i n c o m p l e t e c o n t r a c t i n g t h e o r y a n d p r a c t i c e . T h e a n a l y s e s i n P a r t I I p r o v i d e t h i s t y p e o f e x t e n s i o n . C h a p t e r 4 i s a b r i e f i n t r o d u c t i o n t o i n c o m p l e t e c o n t r a c t i n g r e s e a r c h . C h a p t e r 5 a n a l y z e s a m o d e l i n w h i c h c o n t r a c t i n g c o s t s a r e e x p l i c i t l y c o n s i d e r e d i n t h e c o n t e x t o f i n t e r n a l t r a n s f e r s o f g o o d s a n d s e r v i c e s . O u r r e s u l t s show t h a t c o n t r a c t i n g c o s t s c a n h a v e a s i g n i f i c a n t i m p a c t o n c o n t r a c t i n g s t r a t e g y . C o n t r a c t e f f i c i e n c y c a n b e m o r e p r e c i s e l y d e f i n e d when t h e c o n t r a c t i n g c o s t s a r e e x p l i c i t -l y c o n s i d e r e d . T h i s e f f i c i e n c y i s r e a c h e d t h r o u g h t h e m a x i m i z a t i o n o f t h e n e t t r a d i n g g a i n , t a k i n g c o n t r a c t i n g c o s t s i n t o a c c o u n t . P a r t i c u l a r l y , when t h e t r a d i n g g a i n i s c o n s t a n t among v a r i o u s c o n t r a c t i n g s t r a t e g i e s , t h e n t h i s e f f i c i e n c y c a n b e r e a c h e d b y m i n i m i z i n g c o n t r a c t i n g c o s t s . O u r a n a l y s i s a l s o p r o v i d e s i n s i g h t s i n t o m a n a g e r -i a l a c c o u n t i n g r e s e a r c h b y r e l a t i n g o u r r e s u l t s t o t h e t r a n s f e r p r i c i n g p o l i c i e s u s e d b y f i r m s . T h i s g i v e s i n s i g h t s i n t o e x i s t i n g t r a n s f e r p r i c i n g p r a c t i c e a n d p r o v i d e s a new b a s i s f o r a n a l y z i n g a f i r m ' s t r a n s f e r p r i c i n g p o l i c i e s . C h a p t e r 6 c o n s i d e r s a n o t h e r m o d e l d e a l i n g w i t h i n c e n -6 t i v e issues within organizations where v e r i f i a b l e perform-ance measures are unavailable. Our model analyzes two kinds of incentives, high-powered and low-powered (see the chapters f o r a detailed explanation). The former can be observed e i t h e r i n the market or i n an organization, while the l a t t e r p r i marily e x i s t i n h i e r a r c h i c a l organizations. Most employees i n a firm are industrious not because they have contingent contracts, but because the contract renewal process provides low-powered incentives i n long-term employment r e l a t i o n s . Our r e s u l t s may provide insights into managerial accounting system design. The common ground of the analyses i n t h i s thesis i s how economic agents deal with uncertainties and informa-t i o n asymmetries i n exchange (of c a p i t a l , goods, and ser v i c e s ) . Information and contracting are two fundamen-t a l aspects of t h i s common problem. They are intimately connected, and sometimes, d i f f i c u l t to separate. There-fore, our analyses can be viewed as a theory for trans-actions from an accountants' perspective. R e f e r e n c e s 1 Feltham, G. A. [1984] "Financial Accounting Research: Contributions of Information Economics and Agency Theory." i n Modern Accounting Research: History. Survey, and Guide, ed. R. Mattessich, CGA Research Monograph 7, pp.179-207. 7 PARTI VOLUNTARY DISCLOSURE OF PRIVATE INFORMATION 8 Chapter 2 DISCRETIONARY DISCLOSURE RESEARCH IN THE 1980s: A SURVEY 9 2.1 Introduction The decade of the 1980s represents a period during which accounting researchers paid more attention to firms' voluntary accounting disclosure than ever before. This represents a s i g n i f i c a n t contribution f o r the following reasons. F i r s t , unless we understand firms' incentives to withhold t h e i r private information, we w i l l not have a s o l i d base f o r mandatory accounting d i s c l o s u r e regula-t i o n s . Firms' voluntary disclosures may reveal a l l the information required by these regulations. Second, pre-d i c t i n g managers' behavior i n deciding when to withhold or di s c l o s e information can be useful i n evaluating the consequences of al t e r n a t i v e mandatory reporting pro-cedures . This chapter reviews the advances i n t h i s important accounting research area i n the l a s t decade. Our survey covers a number of published a n a l y t i c a l and empirical papers and also a few unpublished working papers. We believe t h i s chapter has value f o r the following reasons. F i r s t , i t provides a summary of the main r e s u l t s of the extant l i t e r a t u r e . Second, we provide a c l e a r c l a s s i f i c a -t i o n of a l l the a n a l y t i c a l models. This c l a s s i f i c a t i o n e x h i b i t s the s i m i l a r i t i e s and differences among various models along several key dimensions. This may a s s i s t future research, p a r t i c u l a r l y , when one attempts to b u i l d 10 new models. Third, the survey r a i s e s some questions about issues which may stimulate future research. This chapter i s organized as follows. Section 2.2 discusses the key dimensions along which various models d i f f e r . Sections 2.3 to 2.5 summarize two-player, oligop-o l i s t i c , and three-player disclosure models, respectively. Section 2.6 summarizes a few s i g n a l l i n g models that close-l y r e l a t e to disclosure models. Section 2.7 i d e n t i f i e s some re l a t e d empirical work. 2 . 2 Key Dimensions of A n a l y t i c a l Models A n a l y t i c a l models of d i s c r e t i o n a r y information d i s -closure d i f f e r along several key dimensions. The d i f f e r -ences mainly r e s u l t from various assumptions and model structures. F i r s t , models d i f f e r as to the number of players e x p l i c i t l y modelled. The simplest models have only two players, usually a firm versus i t s f i n a n c i a l market or i t s p o t e n t i a l r i v a l , or sometimes, a s e l l e r versus a buyer. We s h a l l r e f e r to t h i s group as two-player models. Recently, a few papers have analyzed more complicated models with three players — a firm, a finan-c i a l market, and an opponent. We s h a l l r e f e r to these papers as containing three-player models. There i s an-other set of papers, mostly i n the economics l i t e r a t u r e , that deal with the same issue i n a s e t t i n g of o l i g o p o l i s -t i c games. Most of these papers assume that a f i n i t e number of firms (sometimes only two) compete i n a product market playing Cournot or Bertrand games with asymmetric information. We s h a l l r e f e r to these papers as containing o l i g o p o l i s t i c models. The second c r u c i a l difference among models r e s u l t s from differences i n assumptions about the cost associated with information transfer. T y p i c a l l y , there are two d i f -ferent assumptions about t h i s cost. F i r s t , some models assume that the informed player(s) can make v e r i f i a b l e announcements regarding h i s private information, and the v e r i f i c a t i o n cost i s n e g l i g i b l e . In other words, i t i s possible f o r the informed player to communicate cr e d i b l y with the uninformed players at a reasonable cost l e v e l . Second, some models assume that the information possessed by the informed player i s u n v e r i f i a b l e , i . e . , the v e r i f i -c a t ion cost i s p r o h i b i t i v e l y high. Hence, t r u t h f u l i n f o r -mation t r a n s f e r through announcements i s impossible. The use of an i n d i r e c t mechanism, such as a contingent con-t r a c t or an exogenous co s t l y s i g n a l , i s necessary to con-v i n c i n g l y communicate players' private information to the uninformed players. We r e f e r to a model with the f i r s t assumption as a disclosure model, and to a model with the second assumption as a s i g n a l l i n g model. Since the argu-ments, techniques, and r e s u l t s i n these two kinds of 12 models are quite d i f f e r e n t , we examine them i n separate sections. The following dimensions mainly r e l a t e to disclosure models, but some of them also apply to s i g n a l l i n g models. Most di s c l o s u r e papers assume that the manager of the firm can only make t r u t h f u l announcements, i.e.., they cannot l i e . The motivation not to l i e i s not e x p l i c i t l y modelled. The j u s t i f i c a t i o n f o r t h i s assumption i s based on the following arguments: (i) the market can c o s t l e s s l y v e r i f y or audit any of manager's claims; ( i i ) there i s a threat of s i g n i f i c a n t penalties i f managers are "caught" misrepresenting t h e i r information; ( i i i ) a n t i t r u s t law and SEC regulations p r o h i b i t firms from making fraudulent disclosures; (iv) firms are concerned about t h e i r "reputa-t i o n s " . However, although firms cannot l i e , they can make incomplete disclosures. This i s the t h i r d dimension which r e l a t e s to d i f f e r e n t assumptions about the l i m i t a t i o n on firm's d i s c l o s u r e strategy choices. We define "complete dis c l o s u r e " 1 as a strategy by which a firm d i s c l o s e s a l l the information i t holds at the moment of disclosure. I f complete dis c l o s u r e i s required, then the manager has only 'Some papers c a l l "complete" and "incomplete" d i s -closure as " f u l l " and " p a r t i a l " disclosure, respectively. We would l i k e to save these terms for the types of equi-l i b r i a that appear i n the subsequent discussion. 13 two choices: e i t h e r to t e l l a l l he 2 knows or to keep s i l e n t . In contrast, i f a manager can make an "incomplete disclosure", then he can choose to t r u t h f u l l y d i s c l o s e e i t h e r a part of h i s information or a noisy representation of that information. For example, when a manager observes (x,y) , he can dis c l o s e e i t h e r x, y, or u=y.+z, where z i s a zero mean disturbance. Fourth, models d i f f e r as to the assumed motivation of the managers. Most papers do not e x p l i c i t l y model manager incentives. Instead, they t y p i c a l l y assume that the man-ager i s exogenously motivated to maximize e i t h e r the cur-rent market value of the firm, or i t s expected end-of-period cash flows to the i n i t i a l equity holders (we w i l l r e f e r to t h i s as the expected payoff). Some models have included both objectives, e i t h e r by taking a weighted average of the two (Miller/Rock [1985]), or by t r e a t i n g the objective of the manager as private information (Don-ton [1990]). The reasons f o r these objectives are t y p i -c a l l y not discussed (except i n Myers/Majluf [1984]). F i f t h , i n those models i n which the managers maximize the firm's expected payoffs, some completely ignore the c a p i t a l market to focus e n t i r e l y on the product market, usually i n a stochastic o l i g o p o l i s t i c s e t t i n g . On the 2In t h i s d i s s e r t a t i o n , the pronoun "he" represents e i t h e r "he" or "she". 14 other hand, others assume that the manager must obtain funds from the c a p i t a l market and i s therefore i n d i r e c t l y concerned with the firm's current market value. Sixth, models d i f f e r as to whether disclosure can have a d i r e c t impact on the firm's end-of-period cash flow. Information i s termed proprietary i f i t can have a d i r e c t impact, and non-proprietary i f i t does not. As Dye [1985a] points out, the former c l a s s includes not only information whose disclosure could a l t e r a firm's future operating cash flows due to actions by competitors, but also information whose disclosure could generate regula-tory actions, create p o t e n t i a l l e g a l l i a b i l i t i e s , reduce consumer demand for i t s products, induce labour unions or other suppliers to renegotiate contracts, or cause revisi o n s i n the firm's c r e d i t standing. The information i s , i n the t r a d i t i o n a l sense, s t r a t e g i c a l l y valuable. The non-proprietary information includes information, such as annual earnings' forecasts, whose release would a f f e c t the pr i c e s of the firms' stocks, but not the d i s t r i b u t i o n of the firms' future cash flows. Obviously, the characteriz-ation i s a s i m p l i f i c a t i o n to ease the analysis. S p e c i f i -c a l l y , what constitutes non-proprietary information must be defined i n reference to a p a r t i c u l a r set of expecta-tions about a p a r t i c u l a r firm's future earnings. Seventh, models i n which the information i s p r o p r i -15 etary d i f f e r as to how disclosure (or non-disclosure) impacts on the firm's end-of-period cash flows. In some models, the impact takes the form of a cost that i s incurred i f , and only i f , disclosure takes place, indepen-dent of the information disclosed. Other models assume that the impact depends on the actions of an "opponent". The opponent can be a competitor or p o t e n t i a l entrant i n the firm's product market, a labour union, or a regulatory agency such as those concerned with taxation or u t i l i t y rates. The key difference i n t h i s dimension i s whether the d i s c l o s u r e cost i s exogenously given or endogenously derived. Eighth, models d i f f e r as to whether managers always have p r i v a t e information. I f there i s a p o s i t i v e prob-a b i l i t y of "no information", then "non-disclosure" can be the r e s u l t of ei t h e r "no information" or non-disclosure by an informed manager. This assumes, of course, that the manager cannot communicate that he lacks information. Ninth, models d i f f e r as to whether the set of poss-i b l e p r i v a t e signals i s binary ("good" versus "bad") or a continuum. F i n a l l y , models d i f f e r as to whether managers v o l u n t a r i l y choose (and commit to) a disclosure p o l i c y p r i o r to re c e i v i n g t h e i r private information, or they choose to d i s c l o s e or not di s c l o s e t h e i r p r i v a t e informa-t i o n a f t e r they know t h e i r information. 16 We organize the a n a l y t i c a l papers we w i l l summarize into four sections. Each section contains a table which exhi b i t s the main c h a r a c t e r i s t i c s of the models i n i t s c l a s s using the related dimensions discussed above. Sec-ti o n s 2.3 through 2.5 summarize three groups of disclosure papers. Section 2.6 summarizes a few r e l a t e d s i g n a l l i n g models. 2.3 Two-Player Disclosure Models Table 2-1 exhibits the main c h a r a c t e r i s t i c s of the papers i n t h i s c l a s s . Insert Table 2-1 here Grossman and Hart [1980] i s one of the e a r l i e s t papers dealing with the voluntary disclosure issue. They model a s e l l e r and a buyer of an item. The s e l l e r knows p r i v a t e l y the q u a l i t y of the item. They assume l y i n g i s i l l e g a l and there are no transaction or d i s c l o s u r e costs. Based on an adverse s e l e c t i o n argument, they conclude that i t w i l l always be i n the s e l l e r ' s i n t e r e s t to d i s c l o s e the q u a l i t y of the item v o l u n t a r i l y . The only equilibrium f o r t h e i r model i s a f u l l d i s c l o s u r e equilibrium. The i n t u -i t i o n underlying t h i s r e s u l t i s that when the s e l l e r with-holds information, the buyer's suspicions about the qual-i t y of the item are so great that they discount i t s qual-17 i t y to the point that the s e l l e r i s always better served to d i s c l o s e what he knows. Such a sin g l e threat gives incentive to the s e l l e r to d i s c l o s e except when h i s item has the lowest q u a l i t y i n the market. Milgrom [1981] includes a persuasion game which i s s i m i l a r to Grossman/Hart [1980]. The differences follows. F i r s t , Milgrom assumes that the s e l l e r ' s s i g n a l may be multi-dimensional and he may conceal any dimension of h i s s i g n a l . Second, Milgrom uses sequential equilibrium con-cept, which i s a more r e s t r i c t i v e concept than a Nash equilibrium. However, since the basic assumptions about the d i s c l o s u r e cost are the same as Grossman/Hart, Milgrom reaches the same conclusion that i n every sequential equi-librium, the s e l l e r uses a strategy of f u l l d isclosure. Jovanovic [1982], l i k e Grossman/Hart [1980], examines the disclosure of the q u a l i t y of an item. The two players i n the model are, again, a s e l l e r and a buyer. The ques-t i o n investigated i s whether the free market o f f e r s s e l l e r s enough incentives to d i s c l o s e information about the q u a l i t y of t h e i r product. Jovanovic i s the f i r s t to consider the impact of an exogenous cost f o r credibly and t r u t h f u l l y d i s c l o s i n g information. This cost ensures a p a r t i a l d isclosure equilibrium with one threshold value. The paper in t e r p r e t s the model i n two ways. In the f i r s t , information and i t s disclosure y i e l d only p r i v a t e gains — 18 they only lead to a r e d i s t r i b u t i o n of income among s e l l e r s . In the second, information r a i s e s welfare because i t r e s u l t s i n goods being traded from people who value them l e s s to people who value them more. The paper concludes that, whether information i s of purely p r i v a t e value or not, more than the s o c i a l l y optimal amount of d i s c l o s u r e takes place. Hence, i n a world where f a l s e claims cannot occur, the free market o f f e r s ample incen-t i v e s f o r disclosure. The f i r s t paper published i n an accounting journal on t h i s t o p i c i s Verrecchia [1983]. A c r u c i a l contribution of t h i s paper i s i t s introduction of an exogenous p r o p r i -etary cost — the cost associated with d i s c l o s i n g informa-t i o n which may be proprietary i n nature, and therefore may be p o t e n t i a l l y damaging. The existence of t h i s cost induces uncertainty about the manager's pr i v a t e informa-t i o n when information i s withheld. Investors are unsure whether a p a r t i c u l a r non-disclosure occurs because: (i) the managers' private information i s "bad news"; or ( i i ) the information i s "good news", but not s u f f i c i e n t l y good news to warrant incurring the proprietary cost. The mar-ket's i n a b i l i t y to unambiguously in t e r p r e t non-disclosure as "bad news" i s s u f f i c i e n t to support a p a r t i a l d i s c l o s -ure equilibrium with one threshold l e v e l . Below t h i s threshold l e v e l the manager withholds h i s p r i v a t e informa-19 t i o n — a r e s u l t consistent with Jovanovic's [1982] f i n d -ing. Verrecchia also shows that as the proprietary cost increases, the threshold l e v e l of disclosure increases, i . e . , the manager 1s incentive to withhold information increases and he discloses l e s s information. This implies, i n turn, that more competition r e s u l t s i n l e s s voluntary disclosure. Verrecchia [1990] studies the same model as Verrec-chia [1983] but focuses on how the q u a l i t y of information a v a i l a b l e to a manager a f f e c t s h i s incentives to d i s c l o s e or withhold that information i n the presence of external p a r t i e s who have r a t i o n a l expectations about h i s motiv-ation. The q u a l i t y of the manager's information about the uncertain l i q u i d a t i n g value of the r i s k y asset i s repre-sented by the p r e c i s i o n of the zero mean normal d i s t r i b -uted random noise. Under the assumption that the market pr i c e s the r i s k y asset at i t s expected value, the paper has following conclusions. F i r s t , the threshold l e v e l of d i s c l o s u r e decreases as the q u a l i t y of manager's informa-t i o n increases, and increases as the q u a l i t y of p r i o r b e l i e f s increases. Second, the p r o b a b i l i t y of disclosure increases as the manager's information increases, and f a l l s as the q u a l i t y of p r i o r b e l i e f s increases. These r e s u l t s are consistent with Jung/Kwon [1988], Dye [1985a] o f f e r s two d i f f e r e n t models to support a 20 p a r t i a l d isclosure equilibrium. The f i r s t model depends on the assumption that the market i s unsure whether the manager i s endowed with private information. Hence, i f a manager withholds information, the investors cannot d i s -cern whether he has received information but chosen not to release i t , or he has not received information. Of course, the manager i s assumed to be incapable of making a cr e d i b l e announcement that he has not received new i n f o r -mation. These assumptions r e s u l t i n a p a r t i a l disclosure equilibrium s i m i l a r to that of Verrecchia [1983]. The threshold l e v e l of disclosure decreases as the p r o b a b i l i t y that manager receives information increases. When t h i s p r o b a b i l i t y approaches one, a f u l l d isclosure p o l i c y r e s u l t s . A t e c h n i c a l error i n Dye's analysis i s corrected by Jung/Kwon [1988]. The l a t t e r reexamines Dye's [1985a] model with the following amendment. In the absence of disclosure, they allow outside investors to revise t h e i r b e l i e f that managers have received no information, i . e . , they use p o s t e r i o r p r o b a b i l i t i e s instead of the uncondi-t i o n a l p r o b a b i l i t i e s used i n Dye [1985a]. This correction enables them to resolve the problem of p o t e n t i a l m u l t i -p l i c i t y of p a r t i a l disclosure p o l i c i e s and, thereby, e s t a b l i s h i t s uniqueness. They also provide two r e s u l t s i n a comparative s t a t i c s analysis. F i r s t , the threshold l e v e l decreases as the p r o b a b i l i t y that the manager has received information increases. I f one believes t h i s p r o b a b i l i t y increases as time elapses, then t h i s may explain why worse news i s released l a t e r . Secondly, the threshold value increases as the market's p r i o r b e l i e f becomes worse, i n the sense of stochastic dominance. Hence, i f one believes that, p r i o r to information d i s c l o s -ure by the manager, investors independently acquire i n f o r -mation about the firm's value, then t h i s a c q u i s i t i o n may t r i g g e r the release of private information which had previously been suppressed due to i t s unfavourableness but has now become favourable compared to the information that the market has independently acquired. The second model i n Dye [1985a] assumes that managers possess non-proprietary private information and there i s a moral hazard problem between the manager and the firm's shareholders. Although the disclosure of a manager's information, by d e f i n i t i o n , w i l l not a l t e r the firm's earnings, i t may a l t e r the manager's compensation since the optimal agency contract depends on the firm's stock p r i c e , which w i l l be affected by the firm's disclosure. Dye analyzes the optimal contracts and finds that investors and the manager always weakly prefer contracts which encourage the manager not to d i s c l o s e h i s informa-t i o n . The adverse e f f e c t s that disclosure may have on both the owners and the manager of a firm r e s u l t from the fa c t that the manager's contract depends on the firm's stock p r i c e . I f the manager discloses h i s information, then the stock p r i c e contains more information about the firm's earnings, but i t may not contain more information about the manager's actions. In addition, information that i s u s e f u l f o r forecasting net income may be detrimen-t a l f o r contracting purposes. Therefore, p o l i c i e s which encourage management disclosure of private information may produce superior forecasts of the firm's earnings, but i n f e r i o r measures of the manager's actions. In summary, disclosures may exacerbate agency problems between the manager and the shareholders. Dye [1985b] focuses on the r e l a t i o n between mandatory reports and voluntary disclosure. The analysis of t h i s issue depends c r i t i c a l l y on the firm's motivation f o r choosing among f i n a n c i a l reporting techniques. One key assumption of t h i s paper i s that a firm's choice among reporting requirements i s influenced by how that choice a l t e r s i t s a b i l i t y to protect i t s proprietary information. To endogenize the proprietary cost of the firm's d i s c l o s -ure, Dye models an entry game with two players: a firm and i t s r i v a l . The dissemination of the established firm's operating information w i l l a s s i s t r i v a l s i n determining whether to enter the firm's market. I f entry occurs, the 23 firm's future earnings w i l l be reduced. The analysis of t h i s entry game shows that, i n equilibrium, the estab-l i s h e d firm i s better o f f with more d i s c r e t i o n i n the choice of accounting techniques. I f voluntary supplemen-tary disclosures are considered, the firm i s always weakly better o f f with l e s s d e t a i l e d reporting requirements. Dye concludes that, by imposing more d e t a i l e d reporting r e -quirements, accounting boards do not necessarily increase investors' knowledge of the firms' future earnings pros-pects. This r e s u l t can occur f o r ei t h e r of two reasons. F i r s t , mandatory and voluntary disclosures are sometimes substitutes, so that the "amount" of information produced by "more d e t a i l e d " mandatory reports may be o f f s e t by a reduction i n voluntary disclosures. Second, firms may be able to reveal information by t h e i r choice among account-ing techniques, so that the mandatory use of a "more det a i l e d " , but uniform, accounting procedure may remove t h i s p o t e n t i a l source of information. Dye also provides conditions under which more d e t a i l e d reporting require-ments increase the amount of information p u b l i c l y revealed about firms. Dye [1986] analyzes disclosure p o l i c i e s adopted by managers endowed with both proprietary and non-proprietary information. This model explains s e l e c t i v e disclosure of managerial information and the e f f e c t s of changes i n f i -nancial reporting requirements on firms' voluntary d i s -closure p o l i c i e s . I t establishes that increasing manda-tory reporting requirements can increase the incentives fo r voluntary disclosure. To derive t h i s r e s u l t , Dye assumes the manager observes non-proprietary s i g n a l x and proprietary s i g n a l y. Disclosure of y incurs cost c. Disclosure of x alone, although i t i s non-proprietary, s t i l l incurs cost c since i t may reveal something about y. Under t h i s cost structure, the optimal strategy of the manager has the following c h a r a c t e r i s t i c s . F i r s t , with p o s i t i v e p r o b a b i l i t y , the non-proprietary information i s not disclosed. Second, a p o l i c y of absolutely no d i s c l o s -ure i s t y p i c a l l y not c r e d i b l e except where c and c are s u f f i c i e n t l y large. Third, f o r each r e a l i z a t i o n of x, no disclosure i s preferred to f u l l d i s c l o s u r e f o r a y that i s l e s s than some threshold value. The reverse i s true f o r other values of y. Fourth, good news i s more l i k e l y to be disclosed or p a r t i a l l y d i s c l o s e d than bad news. F i n a l l y , the payoffs of no, p a r t i a l , and f u l l d i s c l o s u r e p o l i c i e s depend on the value of (x,y). I t i s possible f o r each of these p o l i c i e s to be optimal. The i n t u i t i o n f o r these r e s u l t s i s that disclosure of non-proprietary information may p a r t i a l l y reveal manager's proprietary information. Hence, disc l o s u r e of good news may assuage investors' concerns regarding the firm's future earnings prospects while, at the same time, worsening these prospects by divulging proprietary information. Summary of Two-Player Models One obvious merit of a two-player model i s i t s sim-p l i c i t y . By focusing on one dimension of .the r e l a t i o n between the firm and i t s environment, the analyses of these models derive r e l a t i v e l y simple dis c l o s u r e s t r a t -egies. Most of the papers i n t h i s group consider a game played by a firm and i t s investors. Both the manager and the investors of the firm are assumed to be r a t i o n a l . Under various p r e - s p e c i f i e d rules, the equilibrium of the game induces d i f f e r e n t disclosure strategies. The models we summarized i n t h i s section have shown that a firm's d i s c l o s u r e strategy may be influenced by various factors such as the market perception about the firm's p r i v a t e information, the costs incurred i n information release, the q u a l i t y of manager's private information, the manag-er's incentive contract, and a l t e r n a t i v e communication channels. Depending on the combination of factors con-sidered i n the model, the firm may choose f u l l , p a r t i a l , or non-disclosure strategies. A p a r t i a l d i s c l o s u r e equi-l i b r i u m derived i n these models usually consists of a s i n g l e threshold l e v e l . The manager di s c l o s e s h i s private s i g n a l i f i t i s above t h i s l e v e l , and withholds i f i t i s below. In the extreme cases, the threshold l e v e l goes to i n f i n i t y , e i t h e r p o s i t i v e or negative, r e s u l t i n g i n a f u l l or non-disclosure equilibrium, respectively. The key element i n d e r i v i n g a p a r t i a l disclosure equilibrium i s the market's i n a b i l i t y to i n f e r manager's privat e informa-t i o n p r e c i s e l y when the manager does not d i s c l o s e . We can view a two-player model as a p a r t i a l analysis of the e n t i r e problem. While t h i s i s an important step i n obtaining a more complete understanding of the whole prob-lem, a firm's environment i s l i k e l y to be so complex that i t s management w i l l face multi-dimensional influences. The manager's decisions must involve tradeoffs among the various considerations. Hence, a simple two-player model i s not s u f f i c i e n t to obtain a f u l l picture of the d i s c l o s -ure problem and, thus, more complicated models are required i n further research. 2 . 4 O l i g o p o l i s t i c Models Table 2-2 exhibits the main c h a r a c t e r i s t i c s of the papers summarized i n t h i s section. The table shows that there i s a s i g n i f i c a n t d i s t i n c t i o n between the models i n t h i s group and those i n the l a s t section. That i s , almost a l l the o l i g o p o l i s t i c models deal with voluntary d i s c l o s -ure p o l i c y instead of voluntary signal d i s c l o s u r e . Hence, i n t h i s section, the central question i s whether firms have incentive to commit to a p o l i c y to pool t h e i r private information, i . e . , to commit to d i s c l o s i n g t h e i r informa-t i o n . The strong assumption that firms can commit to a disclosure p o l i c y through a commitment mechanism such as a trade association or mandated disclosure r u l e s (enforced by auditors) i s made by a l l papers i n t h i s category. For example, Kirby [1988] and others have suggested that trade associations may be a mechanism fo r committing to a given l e v e l of disclosure (although t h i s does not preclude a d d i t i o n a l voluntary d i s c l o s u r e ) . Feltham/Gigler/Hughes [1990] examine line-of-business reporting and assume that one commits to a given l e v e l of audited information through "consistency" of reporting p r a c t i c e by the firm, and assume that voluntary disclosure i s not credible. The v i a b i l i t y of t h i s assumption i s an open question. For example, Darrough [1990] comments that even i f firms prefer to commit ex ante to pooling information, t h e i r preferences regarding the disclosure of t h e i r information a f t e r they receive t h e i r s i g n a l may d i f f e r . The firms which receive unfavourable signals might attempt to add as much noise as possible i f there i s any room for choosing the l e v e l of information d e t a i l ( i . e . , the degree of aggregation). These firms may f a i l to comply with t h e i r commitment, and i t may be c o s t l y to monitor and to penal-28 i z e firms f o r such opportunistic behaviour. Insert Table 2-2 here Novshek/Sonnenschein [1982] i s one of the e a r l i e s t papers that deal with information a c q u i s i t i o n and release i n a competitive market. They assume a l i n e a r demand function i n a Cournot duopoly model. There i s uncertainty about the value of the quantity intercept. Firm i inde-pendently acquires n. information signals and allows m,- of these s i g n a l s to be used i n a common pool to be made "availa b l e " to both firms. Under the notion of f u l f i l l e d expectations (or Bayesian Nash equilibrium), they show that the equilibrium expected p r o f i t f o r firm i i s : (i) increasing i n n {; ( i i ) increasing i n n. when there i s some pooling but unaffected by mj i f there i s no pooling; ( i i i ) decreasing i n m? i f firm j retains some private i n -formation, but unaffected by mi i f firm j places a l l of i t s information i n the common pool (mj=nj); (iv) increas-ing i n m.} i f n^nj or 2mj>n1.-nj. The l a s t conclusion can be interpreted as a s i t u a t i o n i n which the opposing firm controls more information, or i n which the firm's c o n t r i -bution to the pool i s r e l a t i v e l y large. In addition, they conclude that i f firms can contract to pool information, then, when n^=n2, no pooling and f u l l pooling are weakly undominated. When n 1 and n 2 are not equal, both of the above e q u i l i b r i a are again undominated. F u l l pooling leads to the highest t o t a l p r o f i t , but no pooling leads to the highest p r o f i t f or the firm with " c o n t r o l " over more observations. Clarke [1983] investigates the incentives f o r firms to share p r i v a t e information about cost or. demand i n a stochastic market. For a n-firm o l i g o p o l i s t i c model, the paper shows that i n a f u l l Bayes-Cournot equilibrium, there i s no mutual incentive f o r a l l firms i n an industry to share information. However, i f cooperative quantity s e t t i n g i s possible, then there i s always an incentive to share — as long as a sui t a b l e p r o f i t d i s t r i b u t i o n can be negotiated among the conspirators. Technically, Clarke assumes uncertain market variables may be parameterized by normal d i s t r i b u t i o n s so that the precise c o n d i t i o n a l expectations that characterize the equilibrium can be e x p l i c i t l y computed. Vives [1984] analyzes two types of duopoly informa-t i o n e q u i l i b r i a , Cournot and Bertrand. He allows the incentives f o r information sharing and i t s welfare conse-quences to depend on the type of competition, the nature of the goods (substitutes or complements), and the degree of product d i f f e r e n t i a t i o n . The uncertainty comes from an unknown common pri c e intercept of a l i n e a r demand func-t i o n . Firm i ' s signal s, i s an independent and unbiased estimate of the intercept. I f there i s no sharing of private signals, then the firms have independent informa-t i o n . On the other hand, they have correlated information i f they pool t h e i r signals. The paper focuses on s e l f -enforcing pooling agreements. In the f i r s t stage of a two-stage game, firms commit t h e i r disclosure p o l i c i e s to an agency p r i o r to the market data c o l l e c t i o n . At the second stage market research i s conducted, the agency sends the pooled signals to the firms, and a Bayesian game i s played. I t shows that the two-stage game has a unique subgame perfect equilibrium i n dominant stra t e g i e s at the f i r s t stage. With substitutes i t involves no pooling of information i n Cournot competition and complete pooling i n Bertrand competition. With complements the r e s u l t s reverse. The i n t u i t i o n behind these r e s u l t s follows. When the goods are substitutes with Cournot competition, an increase i n the pr e c i s i o n of the r i v a l ' s information and an increase i n the c o r r e l a t i o n of the signals have adverse e f f e c t s on the expected p r o f i t of the firm. Therefore, not to share any information i s a dominant strategy. On the other hand, i n Bertrand competition the two factors mentioned above have p o s i t i v e e f f e c t s on the expected p r o f i t of the firm. Hence, to put everything i n the common pool i s a dominant strategy. When the goods are complements a l l above arguments are reversed. F r i e d [1984] examines the nature of the equilibrium s o l u t i o n to the duopoly problem under various incomplete information structures and incentives f o r information production and disclosure. The paper focuses on the game i n which duopolists face the choice of making t h e i r cost functions known to t h e i r opponents. At the f i r s t stage of a two-stage game, firms make information production and disclo s u r e decisions which are assumed to be enforceable and known. At the second stage, firms make quantity out-put decisions based upon the information a v a i l a b l e to them as a consequence of the f i r s t stage decision. The r e s u l t s of the analysis are: (i) that i t w i l l be i n the best i n t e r e s t of each duopolist to produce information about himself; ( i i ) that both firms are better o f f when they d i s c l o s e as opposed to the case where only one of them or neither of them di s c l o s e s ; ( i i i ) that a firm i s better o f f d i s c l o s i n g even i f the competitor does not reciprocate; (iv) that i f one firm cannot obtain i t s own cost function, the other firm might be better o f f d i s c l o s i n g h i s own cost function; (v) that i n an environment that does not permit disclosure, one firm might be better o f f i f the other firm goes ahead and produces information. These r e s u l t s can be explained by decomposing the information d i s c l o s e d into two components: " f i r m - s p e c i f i c " and "common" cost i n f o r -mation. Once the firms know t h e i r own cost functions, the only information l e f t to d i s c l o s e i s " f i r m - s p e c i f i c " . Thus the e f f e c t of any disclosure w i l l be confined to a " c o l l u s i v e " one, since i t s sole purpose w i l l be to allow the opponents to make the necessary and mutually benefi-c i a l "counter" adjustments. Thus, even u n i l a t e r a l d i s -closure would be i n the best i n t e r e s t of the duopolist. L i [1985] studies the incentives f o r information sharing among firms i n an o l i g o p o l i s t i c industry. The uncertainty i s about either the demand function or the i n d i v i d u a l cost functions. The paper assumes that the pr i v a t e information that firms receive has equal accuracy and obeys a l i n e a r conditional expectation property. D i f f e r e n t uncertainties, as mentioned above, are studied separately i n two models that are a l l two-stage games. Sim i l a r to those i n Vives [1984] and F r i e d [1984]. The paper derives pure-strategy Nash e q u i l i b r i a which are subgame-perfect under a symmetric information structure where firms receive private signals with equal p r e c i s i o n . The r e s u l t s show that there i s a systematic difference between the incentives to share common demand and private cost information. No information sharing i s the unique equilibrium when an o l i g o p o l i s t faces stochastic demand that i s common to a l l the firms. Conversely, complete information sharing i s the unique equilibrium when the private costs are uncertain. These differences are due to 33 the d i s t i n c t nature of the information: whether i t has "private" value or "common" value. Knowledge of the demand has "common" value, while knowledge of the costs has "private" value. Gal-Or [1985] addresses the same issue as the other papers summarized above. Her model i s very s i m i l a r to Novshek/Sonnenschein [1982] and Clarke [1983]. The p r i n -c i p a l novelty of t h i s paper i s that (i) competitors have av a i l a b l e a continuum of incomplete revelation strategies, s i m i l a r to L i [1985], and ( i i ) various degrees of i n i t i a l c o r r e l a t i o n among private signals are allowed and are the focus of t h i s analysis. The conclusion i s that i n an oligopoly where firms observe signals about l i n e a r sto-ch a s t i c demand, private information i s never revealed i f firms behave as Nash competitors i n s e t t i n g output l e v e l s . This r e s u l t i s derived regardless of the degree of i n i t i a l c o r r e l a t i o n among signa l s . This implies that no informa-t i o n sharing i s the unique equilibrium regardless of whether firms can make inferences about the signals observed by others. Gal-Or [1986] pursues the same objective as Vives [1984], i . e . , to examine how incentives f o r two duopolists to share information hornestly depends on the nature of competition (Cournot or Bertrand), and the information structure. However, i n Gal-Or [1986] the uncertainty i s about unknown private costs. The analysis of Cournot e q u i l i b r i a i s s i m i l a r to Fried [1984], but the analysis of Bertrand e q u i l i b r i a shows that when the information i s about unknown costs, firms have no incentives to pool information. With unknown private costs, the paper shows that sharing i s a dominant strategy with Cournot competi-t i o n , and concealing i s a dominant strategy with Bertrand competition. The i n t u i t i o n behind the r e s u l t s i s that the pooling of p r i v a t e information about unknown costs has two e f f e c t s on the firm. On the one hand, more accurate i n -formation about the r i v a l ' s cost i s a v a i l a b l e , and the str a t e g i e s can be more accurately chosen so that the firm and i t s competitor's l i k e l i h o o d of mistakenly over-produc-ing or under-producing i s reduced. This has an unambigu-ous p o s i t i v e e f f e c t on the payoff of the firm. On the other hand, the pooling of the information reduces the c o r r e l a t i o n among the decision rules to expand or contract output. This may have a p o s i t i v e or negative e f f e c t depending upon the slope of the reaction functions of the firms. I f they are downward sloping (Cournot competition) reduced c o r r e l a t i o n has a p o s i t i v e e f f e c t , and i f they are upward sloping (Bertrand competition) reduced c o r r e l a t i o n has a negative e f f e c t . Gal-Or [1986] extends F r i e d [1984]'s r e s u l t to the si t u a t i o n s i n which each duopolist observes i t s own costs 35 with noise and may send noisy signals to i t s r i v a l . One key assumption of the paper i s that firms must commit themselves to a f i x e d amount of garbling p r i o r to learning t h e i r s i g n a l s . That i s , firms are allowed to reveal t h e i r private information incompletely ( p a r t i a l l y ) but the accu-racy must be reported ex ante. Hence, i t i s c r u c i a l that the transmission of the information i s conducted by an "outside agency". The r e s u l t s of t h i s and p r i o r papers imply that an industry w i l l have incentive to create an "association" that c o l l e c t s and p u b l i c i z e s information depending on the nature of competition i n the industry and the nature of the information structure. I f firms compete i n quantity the "association" w i l l c o l l e c t and p u b l i c i z e information about a parameter of the model that i s d i f f e r -ent f o r each firm. I f they compete i n p r i c e i t w i l l c o l -l e c t and p u b l i c i z e information about a parameter of the model that i s common to a l l firms. Shapiro [1986] independently and concurrently studies the same issue as Fried [1984] and Gal-Or [1986], which deal with the case of private information about costs. Shapiro analyzes oligopoly information exchange and firms' decisions to j o i n a trade association that exchanges the cost information. His model includes the case of p o s i t i v e c o r r e l a t i o n between the firms' r e a l i z e d costs. In addi-t i o n , i t provides a complete analysis of the welfare e f f e c t s of information exchange. As i n a l l other papers i n t h i s category, i t assumes that the firms can v e r i f y each other's reports, and firms can commit to the d i s c l o s -ure p o l i c y chosen before the a r r i v a l of private informa-t i o n . Technically, i t assumes a l i n e a r demand function, a l i n e a r i t y property f o r the conditional expectations, and i d e n t i c a l d i s t r i b u t i o n of costs. The r e s u l t s can be sum-marized as follows. The o l i g o p o l i s t s a l l prefer an indus-t r y wide cost sharing agreement to no cost sharing, and s t r i c t l y so i f the c o r r e l a t i o n c o e f f i c i e n t i s s t r i c t l y l e s s than one. Such a cost sharing agreement also raises expected welfare, but i t reduces expected consumer sur-plus. These conclusions hold i n both symmetric and asym-metric s i t u a t i o n s . The paper also shows that complete information sharing i s the unique c o a l i t i o n a l outcome i n the core of the membership game, where the firms c o r r e c t l y a n t i c i p a t e the expected p r o f i t s they w i l l earn f o r any given pattern of information exchange. Kirby [1988] reexamines Clarke's [1983] Cournot o l i g o p o l i s t i c model but uses a quadratic cost function. In contrast to much of the t h e o r e t i c a l work on the incen-t i v e s of Cournot o l i g o p o l i s t s not to share information about market demand, she shows that firms may be better o f f sharing information than keeping i t p r i v a t e . Further-more, she shows that sharing information may constitute a Nash equilibrium and always improves expected consumer surplus. The information-sharing arrangements examined i n t h i s paper are d i f f e r e n t from Novshek/Sonnenschein [1982], Gal-Or [1985], and L i [1985], where firms independently s e l e c t the amount of t h e i r private information to be shared, and yet a l l receive the r e s u l t i n g aggregate. Kirby assumes the same rul e as i n Clarke [1983], where the trade association gathers the private signals of i n d i v i d -ual firms, aggregates the signals, and then disseminates the aggregate sig n a l to each of the p a r t i c i p a t i n g firms. The key r e s u l t i s that the benefit from sharing informa-t i o n depends upon the shape of the cost function. I f the quadratic cost c o e f f i c i e n t d i s s u f f i c i e n t l y large, i . e . , the cost function i s s u f f i c i e n t l y convex, then information sharing i s Pareto preferred to a s e t t i n g of private i n f o r -mation and forms a Nash equilibrium. The i n t u i t i o n i s that as d increases, marginal cost also increases, and "errors" i n production become very c o s t l y . Hence, the value from sharing information increases. Dontoh [1990] models a (n+l)-firm oligopoly i n which one of these firms i s endowed with private information about the stochastic demand parameter. The informed f i r -m's incentive to d i s c l o s e information depends upon i t s manager's objectives; there are two types of firms, both of which are consistent with the value maximization c r i -38 t e r i o n . Type A firms maximize current market value, while type B firms maximize end-of-period payoff with no concern for how they are valued by market currently. The model assumes a firm's type i s private information, i . e . , the market cannot i d e n t i f y whether a firm i s type A or type B. I f an informed firm i s type A, then i t has. incentive to di s c l o s e good news but withhold bad news. For an informed type B firm, the disclosure behavior i s reversed, i . e . , i t disclos e s bad news but withholds good news. Since the market cannot i d e n t i f y a firm's type, when the information i s withheld, the market i s also incapable of unambiguously i n f e r r i n g whether the information i s good or bad news. This, as i n Verrecchia [1983] and Dye [1985a], i s s u f f i -c i e n t to support a p a r t i a l equilibrium. I t i s noteworthy that i n t h i s model, a firm's type has no influence e i t h e r on any uninformed firm's strategy i n the f i r s t stage of the game, or on a l l firms' output decision i n the second stage. Hughes/Kao [1990] study the e q u i l i b r i a that emerge under d i f f e r e n t disclosure regimes, thereby leading to predictions of how outputs, p r o f i t s and l e v e l s of invest-ment i n R&D vary across those regimes. In t h e i r model, R&D i s defined as an a c t i v i t y which r e s u l t s i n an uncer-t a i n reduction i n the marginal costs of producing a con-sumption good. The actual marginal costs are d i r e c t l y 39 observable only to the firm. They investigate the nature of o l i g o p o l i s t i c e q u i l i b r i a when firms p u b l i c l y report both R&D spending and the r e a l i z a t i o n of t h e i r marginal costs, compared with the benchmark regime i n which firms report R&D spending only. In the symmetric case where firms are i d e n t i c a l p r i o r to marginal cost, r e a l i z a t i o n s , they f i n d that i f managers are r i s k neutral, then the equilibrium expected p r o f i t i s higher under f u l l d i s c l o s -ure than under p a r t i a l disclosure. However, equilibrium l e v e l s of R&D spending are the same under both regimes. I f managers are r i s k averse and t h e i r compensation i s proportional to p r o f i t s , then the equilibrium l e v e l s of R&D spending are greater under the benchmark regime than under f u l l d i sclosure. This i s because the r i s k under f u l l d i s c l o s u r e can only be ameliorated by reducing R&D, whereas under p a r t i a l disclosure the output decisions also a f f o r d an opportunity f o r r i s k reduction. Introducing asymmetries i n cost uncertainty and the r i s k preferences of firm managers modify the r e s u l t s described above, but not i n a major way. Given r i s k n e u t r a l i t y , the l e v e l s of equilibrium R&D spending are unaffected by an asymmetry i n cost uncertainty, and are ordered s i m i l a r l y across d i s -closure regimes under both symmetric and asymmetric r i s k preferences. Furthermore, under the benchmark regime, a firm with a r i s k neutral manager enjoys an advantage over 40 a firm with a r i s k averse manager. The paper does not consider welfare issues, nor the e f f i c i e n c y of R&D d e c i -sions. Darrough [1990] analyzes the incentives of firms i n a duopoly market to d i s c l o s e private information, and exam-ines how disclosure incentives are influenced by the nature of competition and private information. Both Cournot and Bertrand competition are investigated when firms receive private information e i t h e r on demand or on costs. The f i r s t part of the paper u n i f i e s the extant r e s u l t s i n the p r i o r l i t e r a t u r e about the incentive to d i s c l o s e v o l u n t a r i l y i n an ex ante sense: firms s e l e c t a d i s c l o s u r e p o l i c y before they receive a s i g n a l on the uncertainty parameter. The second part considers whether firms have incentives to d i s c l o s e t h e i r p r i v a t e signals v o l u n t a r i l y a f t e r they receive these s i g n a l s . In t h i s ex post case, firms are endowed with priva t e information before they make disclosure decisions. By combining these two parts, the paper interprets how market structures a f f e c t voluntary disclosure incentives. I t also o f f e r s predictions about the type of e q u i l i b r i a that p r e v a i l i n d i f f e r e n t market settings. The r e s u l t s of part 1 and 2 are best shown i n Tables 2-3(1) and 2-3(2), which are quoted from the paper. 41 Insert Table 2-3 here Based on the r e s u l t s mentioned above, i n Bertrand competi-t i o n with demand uncertainty and Cournot competition with cost uncertainty, firms would be w i l l i n g to commit ex ante to the most accurate disclosure. They might e l e c t to do so by way of trade associations or by committing to a mandated disclosure p o l i c y . Ex post, those firms with unfavourable signals f i n d themselves with "bad luck". Had they known the r e a l i z a t i o n , they would have acted d i f f e r -ently. I f firms do not ex ante commit to a disclosure p o l i c y , they t r y to hide unfavourable s i g n a l s . However, t h e i r e f f o r t w i l l l i k e l y be f u t i l e because a r a t i o n a l market w i l l i n t e r p r e t the sig n a l of "No d i s c l o s u r e " as one with unfavourable news, thereby s t a r t i n g the unravelling process. On the other hand, i f the ex ante consensus i s no disclosure, those firms with favorable signals may t r y to " s i g n a l " t h e i r information through other means of voluntary disclosure. Whether perfect r e v e l a t i o n ensues depends upon what additional factors are considered i n the model. Summary of O l i g o p o l i s t i c Models This c l a s s of papers focuses on the incentives f o r firms to d i s c l o s e private information i n a competitive 42 environment. A l l the papers assume the information can be c o s t l e s s l y v e r i f i e d i f disclosed. The models usually are a n-firm oligopoly or i t s s i m p l i f i c a t i o n — a two-firm duopoly. Manager's objective i s always to maximize the expected p r o f i t of h i s firm. The incentives used to induce managers to pursue t h i s objective are usually not considered. Most papers determine an optimal voluntary disclosure p o l i c y , i . e . , firms can commit ex ante to t h e i r information sharing strategy before they observe t h e i r s i g n a l s . Almost a l l models have continuous s i g n a l v a r i -ables. The r e s u l t s show that the incentives to pool information depend on many fac t o r s . The most important ones are: the competitive environment (Cournot or Ber-trand) , the type of uncertainty (demand or c o s t ) , the nature of the products (substitutes or complements), and the form of the cost functions ( l i n e a r or quadratic). The optimal information sharing p o l i c i e s may induce f u l l shar-ing, no sharing, or p a r t i a l sharing. The i n t u i t i o n behind the r e s u l t s i s the twofold influence of information pool-ing on firms' p r o f i t s . On the one hand, more accurate information about the r i v a l i s a v a i l a b l e , and the s t r a t -egies can be more accurately chosen so that the l i k e l i h o o d that some firms under-produce or over-produce can be reduced. On the other hand, the pooling of information may increase or reduce the c o r r e l a t i o n among the decision 43 rules about the production quantities. The l a t t e r may have p o s i t i v e or negative e f f e c t s on firms' p r o f i t s de-pending on the various factors described above. Most oligopoly disclosure models consider only a sing l e r e l a t i o n between a firm and i t s environment: compe-t i t i o n i n the product market. Such a model can be viewed as e s s e n t i a l l y a two-player model i n which the r i v a l s i n the product market replace the investors i n the f i n a n c i a l market as the second player. The analysis of these models provide important contributions to our understanding of disclosure choice, but the contribution i s at best a p a r t i a l analysis of the larger problem with a diverse set of players. Many topics i n t h i s area have not been exploited. For instance, most papers assume a l i n e a r cost function to enhance the t r a c t a b i l i t y . However, as Kirby [1988] shows i n her model, a quadratic cost function may reverse a l l the r e s u l t s derived from a l i n e a r cost function model i f other elements of the model are not changed. Whether t h i s i s true i n other models i s s t i l l an open question. Also, most papers assume firms can commit to t h e i r strategies ex ante. As pointed by Darrough [1990], the a b i l i t y of an oligopoly to enforce such commitment i s doubtful. For example, i f a firm commits ex ante to a non-disclosure p o l i c y , but ex post the firm receives a s i g n a l which i t would l i k e to d i s c l o s e , there i s l i t t l e an association can do to p r o h i b i t the firm from v o l u n t a r i l y d i s c l o s i n g i t s information by some i n d i r e c t means. Hence, i t i s import-ant to consider both ex ante and ex post incentives. The research i n t h i s aspect of disclosure choice has j u s t started. 2.5 Three-Player Disclosure Models Table 2-4 presents the main c h a r a c t e r i s t i c s of the papers summarized i n t h i s section. As indicated by the t i t l e of t h i s section, the models i n t h i s group consider games i n which three players i n t e r a c t with each other. Insert Table 2-4 here Bhattacharya/Ritter [1983] i s the f i r s t paper to consider the behavior of an informed firm facing c o n f l i c t -ing e f f e c t s of i t s private information release. An asym-me t r i c a l l y informed agent i s motivated to communicate i t s p r i v a t e l y known "good news" to the f i n a n c i a l market but can do so only through channels or signals which d i r e c t l y convey information to competing agents. The private information i s valuable i n the research of both the informed firm and i t s competitors. Hence, the informed firm faces a tradeoff between (i) reducing the value of i t s informational advantage, and ( i i ) obtaining c a p i t a l at 45 t e r m s t h a t r e f l e c t g o o d news a b o u t i t s i n n o v a t i o n p r o s -p e c t s , t h u s l o w e r i n g t h e o w n e r s h i p d i l u t i o n s u f f e r e d b y t h e e x i s t i n g o w n e r s o f t h e " r e s e a r c h t e c h n o l o g y " . I n t h i s w a y , t h e m o d e l c o n n e c t s t h e i n f l u e n c e o f i n f o r m a t i o n r e l e a s e o n p r o d u c t m a r k e t c o m p e t i t i o n w i t h i t s i n f l u e n c e o n f i n a n c i a l m a r k e t v a l u a t i o n . T h e p r o p r i e t a r y c o s t o f d i s c l o s u r e i s , t h e r e f o r e , e n d o g e n i z e d i n t h e m o d e l . T h e r e a r e N f i r m s e n g a g e d i n a n R&D " r a c e " f o r a p a t e n t a b l e i n v e n t i o n , w h i c h h a s known p r i v a t e v a l u e V . T h i s v a l u e a c c r u e s o n l y t o t h e f i r s t f i r m t o s u c c e e d . S i n c e a l l u n i n f o r m e d e n t r a n t s c a n b e v i e w e d a s o n e o p p o n e n t o f t h e i n f o r m e d f i r m , t h e w h o l e game c a n b e v i e w e d a s h a v i n g t h r e e p l a y e r s , w i t h t h e f i n a n c i a l m a r k e t a s t h e t h i r d p l a y e r . 3 T h e m o d e l a l l o w s t h e i n f o r m e d f i r m t o d e c i d e t h e d i s c l o s u r e l e v e l a f t e r t h e f i r m r e c e i v e s i t s p r i v a t e i n f o r m a t i o n . H e n c e , t h e m o d e l i s a t y p i c a l v o l u n t a r y s i g n a l i n c o m p l e t e d i s c l o s u r e s e t t i n g . T h e c o s t o f d i s -c l o s u r e i s e n d o g e n o u s l y d e t e r m i n e d b y t h e n u m b e r o f e n t r a n t s , w h i c h i s a f u n c t i o n o f t h e p r i v a t e i n f o r m a t i o n a n d i t s d i s c l o s u r e l e v e l . A l l f i r m s m u s t o b t a i n c a p i t a l f r o m t h e c a p i t a l m a r k e t t h r o u g h e q u i t y i s s u e s . O t h e r 3 T h e m a r k e t i n t h i s m o d e l i s n o t a f u l l y a c t i v e p l a y e r i n t h e game i n t h a t i t d o e s n o t p l a y s t r a t e g i c a l l y . I n s t e a d , t h e m a r k e t i s q u i t e p a s s i v e a n d i s o n l y m o d e l l e d t o t h e e x t e n t o f c o n s i d e r i n g how i t f o r m s b e l i e f s a b o u t t h e f i r m ' s c a s h f l o w s . T h i s p o i n t i s common t o a l l p a p e r s i n t h i s c l a s s , i n c l u d i n g t h e m o d e l i n C h a p t e r 3 . 46 f i n a n c i a l means are not considered. Disclosure by the informed firm a f f e c t s the terms at which i t can obtain c a p i t a l . In making i t s disclosure decision, the informed firm also considers the adverse a f f e c t that the disclosure has on i t s conjectured i n t r i n s i c value. This value repre-sents i t s b e l i e f regarding the discounted .expected value of i t s invention payoff as a function of i t s disclosure, taking the impact of such dis c l o s u r e on the number and t e s t i n g rate of i t s competitors into account. The equi-librium provides p a r t i a l d isclosure, with the c h a r a c t e r i s -t i c that the proportion of p r i v a t e knowledge disclosed declines as the private knowledge increases. Lanen/Verrecchia [1987] analyze how the use of man-agement accounting information to make operating decisions can imprecisely communicate that information when d i r e c t (precise) disclosure i s c o s t l y . Their model consists of three players: the owner of a firm, the supplier of the technology, and an external party who p o t e n t i a l l y evalu-ates the firm's prospects. 4 Their analysis focuses on the owner's tradeoff between an e f f i c i e n t operating d e c i -sion and the disclosure of proprietary information. 4The r o l e of the supplier i s not e x p l i c i t l y modelled. The supplier merely serves as a player to whom the owner can commit to a replacement standard, which i s an important determinant i n the way i n which the retention-replacement decision i s viewed by external investors. 47 S p e c i f i c a l l y , they consider how proprietary data, that i s generated by the firm's i n t e r n a l accounting system i n making a production decision, are imperfectly i n f e r r e d by outsiders who observe the outcome of the decision process. They i d e n t i f y conditions under which optimal management decision making i s altered by the existence of t h i s poten-t i a l i n d i r e c t communication a l t e r n a t i v e to disc l o s u r e . This implies that when operating decisions depend on private information, the operating decision made may deviate from the e f f i c i e n t decision from an outsider's perspective. Thus, t h e i r analysis o f f e r s one r a t i o n a l e f o r firms pursuing p o l i c i e s such as re t a i n i n g managers of below-average competence or obsolete technologies. When the r o l e of the replacement decision as a communication mechanism i s considered, these p o l i c i e s may i n f a c t be optimal. Darrough/Stoughton [1990] i s a three-player model about an entry game. The basic idea of the model i s s i m i l a r to Bhattacharya/Ritter [1983]. The difference i s that i n the current paper, the opponent i s a p o t e n t i a l entrant. The informed firm trades o f f between the bene-f i t s and costs of the disclosure. The benefits of d i s -c l o s i n g good news come from a higher f i n a n c i a l market evaluation. The proprietary cost i s due to the f a c t that the d i s c l o s u r e could compromise the incumbent's competi-48 t i v e p o s i t i o n by providing s t r a t e g i c information to poten-t i a l competitors. The game modelled consists of two stages. At the f i r s t stage, the incumbent firm, as a monopolist i n i t s industry, r a i s e s k units of c a p i t a l from the f i n a n c i a l market by s e l l i n g a portion of the firm. The terms of financing are influenced by the disclosure strategy, and the po t e n t i a l entrant's decision. I f entry takes place, the second stage i s a duopoly game. Other-wise, the incumbent i s s t i l l i n i t s monopoly p o s i t i o n . The p r i v a t e s i g n a l i s binary, i . e . , good news versus bad news. Under a condition which amounts to entry deterrence being more important than f i n a n c i a l valuation, they have i d e n t i f i e d three e q u i l i b r i a of t h e i r disclosure-entry game: (i) a disclosure equilibrium i n which the incumbent disclos e s both good and bad news, which occurs when the p r i o r b e l i e f i s o p t i m i s t i c or the entry cost i s r e l a t i v e l y low; ( i i ) a non-disclosure equilibrium i n which the incum-bent d i s c l o s e s no information, which occurs when the p r i o r b e l i e f i s r e l a t i v e l y p e s s i m i s t i c or the entry cost i s r e l a t i v e l y high; and ( i i i ) a p a r t i a l disclosure e q u i l i b -rium i n which only unfavourable bad news i s disclosed. An implication of the model i s that competition, through threat of entry, encourages voluntary disclosure — a r e s u l t that d i f f e r s from Verrecchia's [1983] conclusion. This i s because Darrough/Stoughton deal with pre-entry competition. In t h e i r s e t t i n g , when entry costs are low, entry i s more l i k e l y to occur so that the motive fo r entry deterrence becomes dominant fo r an incumbent with good news. This w i l l r e s u l t i n a f u l l disclosure equilibrium. While Verrecchia [1983] deals with post-entry competition, and d i s c l o s u r e always serves to reduce the informed firm's competitive advantage. Thus, stronger competition w i l l r e s u l t i n l e s s voluntary disclosure. Wagenhofer [1990] analyzes a model s i m i l a r to Dar-rough/Stoughton [1990] but with a continuum of private s i g n a l s . Knowledge of t h i s signal i s valuable to both the f i n a n c i a l market and an opponent. The opponent decides to take a b e n e f i c i a l action only i f the signal i s s u f f i c i e n t -l y favourable. This action imposes proprietary costs on the d i s c l o s i n g firm. The firm does not r a i s e c a p i t a l from the c a p i t a l market, but i s assumed to maximize i t s current market p r i c e . With an a d d i t i o n a l assumption that the firm's market p r i c e i s equal to the value of the s i g n a l , the paper derives the following equilibrium r e s u l t s : (i) a sequential equilibrium with f u l l disclosure always e x i s t s ; ( i i ) a p a r t i a l d isclosure equilibrium with two non-dis-closure i n t e r v a l s may e x i s t ; and ( i i i ) f u l l non-disclosure i s never a part of a sequential equilibrium. In addition, the paper points out that multiple e q u i l i b r i a may e x i s t . Chapter 3 of t h i s d i s s e r t a t i o n pursues the same t o p i c 50 t as t h e o t h e r papers i n t h i s c a t e g o r y . 5 The b a s i c model i s v e r y s i m i l a r t o Wagenhofer [1990] except t h a t i n t h e l a t t e r model t h e incumbent r e q u i r e s no funds from t h e c a p i t a l market and t h e manager seeks t o maximize t h e c u r r e n t market v a l u e o f t h e f i r m , w h i l e i n t h e former model t h e amount o f c a p i t a l r a i s e d from t h e c a p i t a l market i s an i m p o r t a n t parameter and t h e manager seeks t o m a x i -mize t h e e x p e c t e d e n d - o f - p e r i o d p a y o f f . A key f e a t u r e t h a t d i s t i n g u i s h e s t h e a n a l y s i s i n C h a p t e r 3 from o t h e r d i s c l o s u r e p a p e r s i s t h a t i t i n t r o d u c e s p r i v a t e e n t r a n t i n f o r m a t i o n . T h a t i s , t h e model i n C h a p t e r 3 a l l o w s f o r t h e p o s s i b i l i t y t h a t t h e incumbent may n o t know t h e e n -t r a n t ' s b r e a k - e v e n p o i n t and , t h e r e f o r e , does n o t know what b e l i e f s w i l l i n d u c e t h e e n t r a n t t o e n t e r . The major impact o f t h i s change i s t o e l i m i n a t e e q u i l i b r i a i n which t h e incumbent f i r m p a r t i a l l y d i s c l o s e s h i s i n f o r m a t i o n and t h e e n t r a n t p l a y s a mixed s t r a t e g y . In t h e model i n which t h e e n t r a n t has p r i v a t e i n f o r m a t i o n , t h e e n t r a n t p l a y s a p u r e s t r a t e g y , whether t h e incumbent d i s c l o s e s h i s p r i v a t e i n f o r m a t i o n o r n o t . The model i n C h a p t e r 3 e x p r e s s e s b o t h t h e monopo-l i s t ' s and t h e d u o p o l i s t s ' p r o f i t s as l i n e a r f u n c t i o n s o f t h e i n c u m b e n t ' s i n f o r m a t i o n . However, i t a l s o demon-5 T h e a n a l y s i s i n C h a p t e r 3 i s a more e x t e n s i v e p r e s -e n t a t i o n o f the a n a l y s i s c o n t a i n e d i n F e l t h a m / X i e [1991] . 51 s t r a t e s t h a t t h i s i s c o n s i s t e n t w i t h s t a n d a r d d u o p o l y m o d e l s i n w h i c h f i r m s h a v e q u a d r a t i c p r o f i t f u n c t i o n s . T h e d i s t r i b u t i o n s u s e d t o d e s c r i b e t h e i n c u m b e n t ' s i n f o r -m a t i o n a n d t h e e n t r a n t ' s b r e a k - e v e n p o i n t a r e q u i t e g e n -e r a l , b u t t h e p a p e r f o c u s e s o n t w o e x t r e m e c a s e s : common k n o w l e d g e v e r s u s a u n i f o r m d i s t r i b u t i o n a b o u t t h e e n -t r a n t ' s b r e a k - e v e n p o i n t . B a s e d o n t h e s e a s s u m p t i o n s , t h e a n a l y s i s e x p l i c i t l y s o l v e s f o r a l l p o s s i b l e e q u i l i b r i a . T h e r e s u l t s show t h a t p a r t i a l d i s c l o s u r e e q u i l i b r i a e x i s t when t h e f i r m h a s a r e l a t i v e l y b a l a n c e d c o n c e r n f o r t h e r e s p o n s e s o f b o t h m a r k e t s . T h e m o s t i n t e r e s t i n g a s p e c t o f t h e i r r e s u l t s i s t h a t t h e r e a r e t w o p o s s i b l e p a r t i a l d i s c l o s u r e e q u i l i b r i a . P D - L e q u i l i b r i a a r e c h a r a c t e r i z e d b y a c a p i t a l m a r k e t i n w h i c h t h e n o n - d i s c l o s u r e f i r m s h a v e a l o w e r m a r k e t v a l u e t h a n a l l d i s c l o s u r e f i r m s . P D - H e q u i l i b r i a , o n t h e o t h e r h a n d , a r e c h a r a c t e r i z e d b y a c a p i t a l m a r k e t i n w h i c h some d i s c l o s u r e f i r m s h a v e l o w e r m a r k e t v a l u e s t h a n t h e n o n - d i s c l o s u r e f i r m s . S i n c e t h e e q u i l i b r i a a p p l y o n a f i r m - b y - f i r m b a s i s , t h i s r e s u l t i m p l i e s t h a t , i n e q u i l i b r i u m , we w o u l d e x p e c t t o o b s e r v e f i r m s t h a t c h o o s e t o w i t h h o l d i n f o r m a t i o n e v e n t h o u g h i t s r e l e a s e w o u l d i n c r e a s e t h e i r m a r k e t v a l u e , w h i l e o t h e r f i r m s d i s c l o s e i n f o r m a t i o n e v e n t h o u g h w i t h h o l d i n g i t w o u l d i n c r e a s e t h e i r m a r k e t v a l u e . C h a p t e r 3 i s t h e f i r s t a n a l y s i s t o i d e n t i f y s i t u -52 a t i o n s i n which a f u l l d i s c l o s u r e e q u i l i b r i u m does no t e x i s t , and o n l y a p a r t i a l e q u i l i b r i u m p r e v a i l s . I n a d d i -t i o n , i t shows t h a t when f u l l and p a r t i a l d i s c l o s u r e e q u i l i b r i a c o e x i s t , t h e f u l l d i s c l o s u r e e q u i l i b r i u m w i l l n o t be s t a b l e under a s u i t a b l e r e f i n e m e n t c r i t e r i o n . T h i s i m p l i e s t h a t , under c e r t a i n c o n d i t i o n s , w i t h h o l d i n g i n f o r -m a t i o n may be t h e o n l y e q u i l i b r i u m s t r a t e g y — a r e s u l t c o n s i s t e n t w i t h e m p i r i c a l o b s e r v a t i o n s . Summary o f T h r e e - P l a y e r Models O b v i o u s l y , t h r e e - p a y e r models a r e more advanced t h a n most t w o - p l a y e r o r o l i g o p o l y mode l s . W i t h r e g a r d t o t h e scope o f a n a l y s i s , a t h r e e - p l a y e r model c o n s i d e r s two d i m e n s i o n s o f t h e impact o f d i s c l o s u r e w h i l e t h e o t h e r models u s u a l l y c o n s i d e r o n l y one d i m e n s i o n . The r e s u l t i n g e q u i l i b r i a f o r such a model a r e more complex , as i n t u -i t i v e l y would be t h e case i n t h e r e a l w o r l d . These models show t h a t f i r m s may w i t h h o l d b o t h good news and bad news. The market v a l u e o f t h e n o n - d i s c l o s i n g f i r m s may be h i g h e r o r lower t h a n d i s c l o s i n g f i r m s . The key f a c t o r i n t h e e x i s t e n c e o f v a r i o u s e q u i l i b r i a i s t h e r e l a t i v e importance t o t h e i n f o r m e d f i r m o f d i v e r s e i n f l u e n c e s o f d i s c l o s i n g i n f o r m a t i o n . The f i r m must t r a d e o f f among m u l t i - d i m e n -s i o n a l b e n e f i t s and c o s t s from i t s d i s c l o s u r e s t r a t e g i e s . V e r r e c c h i a ' s [1990b] comments about D a r r o u g h / S t o u g h -53 t o n [1990] may a p p l y t o most papers i n t h i s c a t e g o r y . The i n n o v a t i o n sugges ted i n a t h r e e - p l a y e r model i s t h a t the p r o p r i e t a r y c o s t s a r i s i n g i n a d i s c r e t i o n a r y d i s c l o s u r e e q u i l i b r i u m can be endogen ized by a p p e a l i n g t o t h e n o t i o n o f an e n t r y game among f i r m s i n a p r o d u c t market whose degree o f p r o d u c t d i f f e r e n t i a t i o n i s exogenous ly s p e c -i f i e d . T h i s s u g g e s t i o n i s n o v e l i n t h a t i t c o u p l e s two u n r e l a t e d a r e a s o f r e s e a r c h , namely , d i s c r e t i o n a r y d i s -c l o s u r e by f i n a n c i a l managers and e n t r y games among f i r m s , t o produce e q u i l i b r i a where p r o p r i e t a r y c o s t s o c c u r n a t -u r a l l y . However, t h e e x t e n t o f e n d o g e n e i t y i s l i m i t e d , because i n a l l t h e s e models exogenous c o s t s must e x i s t t o p r e c l u d e f u l l d i s c l o s u r e . F o r example , t h e need t o r a i s e an amount k o f c a p i t a l t o produce i n t h e p r o d u c t market i s j u s t such a c o s t . V e r r e c c h i a a l s o r a i s e s t h e f o l l o w i n g c o n c e r n s . F i r s t , t h e s t r u c t u r e o f t h e game i s such t h a t t h e p o s s i -b i l i t y o f f u l l d i s c l o s u r e i s n e v e r e l i m i n a t e d a n d , i n f a c t , i s s u p p o r t e d by a v a r i e t y o f c r i t e r i a . T h i s i s q u i t e t r u e i n Darrough /Soughton [1990] and Wagenhofer [1990] , b u t p a r t i a l l y s o l v e d i n C h a p t e r 3 s i n c e i t i d e n t -i f i e s s i t u a t i o n s i n which t h e r e i s no f u l l d i s c l o s u r e e q u i l i b r i u m . F u r t h e r m o r e , i f a p a r t i a l d i s c l o s u r e e q u i -l i b r i u m e x i s t s , f u l l d i s c l o s u r e does no t s u r v i v e t h e G r o s s m a n / P e r r y s t a b i l i t y c r i t e r i o n . However, even i n 54 C h a p t e r 3 , a f u l l d i s c l o s u r e e q u i l i b r i u m i s s t i l l s u s -t a i n e d i n many s i t u a t i o n s . Second, the e n t r y game may g i v e e x a g g e r a t e d b e n e f i t t o d i s c l o s i n g "bad news" i n two ways: (1) i t exaggera te s t h e u s e f u l n e s s o f "bad news" as a s i g n a l t o d i s c o u r a g e market e n t r a n t s by s u g g e s t i n g t h a t common i n f o r m a t i o n l i k e s a l e s d a t a , would n o t a l r e a d y be known by p o t e n t i a l c o m p e t i t o r s i n the absence o f d i s c l o s -u r e ; (2) i t exaggera te s t h e p o s i t i v e impact o f d i s c l o s i n g "bad news" by i g n o r i n g t h e c o s t s t o managers a s s o c i a t e d w i t h a t t e m p t s t o t e r m i n a t e t h e i r t e n u r e i n t h e wake o f "bad news", e i t h e r e x t e r n a l l y i n t h e form o f h o s t i l e t a k e o v e r s o r i n t e r n a l l y i n t h e form o f s h a r e h o l d e r d i s a p -p r o v a l . The e n t r y game exaggera te s e n t r y from w i t h o u t b u t i g n o r e s e n t r y from w i t h i n . I n a d d i t i o n t o t h e above comments, t h e f o l l o w i n g two p o i n t s a r e n o t e w o r t h y . F i r s t , t h e m u l t i p l i c i t y o f e q u i -l i b r i a i s an u n s o l v e d prob lem i n g e n e r a l . T h e r e may be a need t o d e v e l o p m u l t i - p e r i o d mode l s , o r t o i n d u c e o t h e r arguments , s u c h as r e p u t a t i o n , t o d e a l w i t h such p r o b l e m s . Second, B h a t t a c h a r y a / R i t t e r [1983] , D a r r o u g h / S toughton [1990] , and C h a p t e r 3 c o n s i d e r o n l y e q u i t y f i n a n c i n g . There a r e o t h e r f i n a n c i a l arrangements t h a t f i r m s can use t o r a i s e c a p i t a l . I n t e r e s t i n g i s s u e s o f c h o i c e o f f i n a n -c i a l s t r u c t u r e can a r i s e , s i n c e d i f f e r e n t f i n a n c i a l c o n -t r a c t s may i n v o l v e d i f f e r i n g d i s c l o s u r e " r e q u i r e m e n t s " . 55 F u t u r e r e s e a r c h may endogenize the c h o i c e o f f i n a n c i a l arrangement t o b u i l d more r e a l i s t i c mode l s . 2.6 S i g n a l l i n g Models As ment ioned i n S e c t i o n 2 . 2 , when t r u t h f u l i n f o r m a -t i o n t r a n s f e r t h r o u g h announcements i s i m p o s s i b l e , f i r m s may use i n d i r e c t communicat ion mechanisms t o " s i g n a l " t h e i r p r i v a t e i n f o r m a t i o n . The r e s e a r c h a l o n g t h i s l i n e forms a n o t h e r group o f p a p e r s under t h e t i t l e o f s i g -n a l l i n g m o d e l s . Both d i s c l o s u r e models and s i g n a l l i n g models f o c u s on f i r m s ' b e h a v i o r i n r e l e a s i n g p r i v a t e i n f o r m a t i o n . Hence , many s i g n a l l i n g p a p e r s a r e c l o s e l y r e l a t e d t o t h e d i s c l o s u r e models summarized i n t h e p r i o r s e c t i o n s . G e n e r a l l y , a s i g n a l l i n g model c o n s i s t s o f one o r more u n i n f o r m e d p l a y e r s and one o r more i n f o r m e d p l a y e r s . An u n i n f o r m e d p l a y e r might be an i n s u r e r , an i n v e s t o r , an employer , o r a cus tomer , whereas an i n f o r m e d p l a y e r m i g h t be an i n s u r e e , an e n t r e p r e n e u r , a manager, a w o r k e r , o r a s u p p l i e r . The asymmetr ic i n f o r m a t i o n may p e r t a i n t o t h e l i k e l i h o o d t h e i n s u r e e w i l l s u f f e r a l o s s , t h e p r o b a b i l i t y o v e r t h e p o t e n t i a l outcome from a f i r m ' s o p e r a t i o n s , t h e s k i l l o r p r o d u c t i v i t y o f t h e w o r k e r , o r t h e q u a l i t y o f a p r o d u c t t h a t i s b e i n g s o l d . Hence , t h e u n i n f o r m e d p l a y e r i s t y p i c a l l y a "buyer" and t h e i n f o r m e d p l a y e r i s a " s e l l e r " o f some "good". The s e l l e r knows 56 more about the " q u a l i t y " o f t h e "good" t h a n does the b u y e r . In each case t h e r e i s a range o f q u a l i t y l e v e l s , which a r e u s u a l l y r e f e r r e d t o as " types" . The key assump-t i o n o f s i g n a l l i n g models i s t h a t p r i v a t e i n f o r m a t i o n o f t h e i n f o r m e d p l a y e r r e g a r d i n g h i s t y p e cannot be d i r e c t l y and c r e d i b l y t r a n s f e r r e d t o t h e u n i n f o r m e d p l a y e r s . In o t h e r words , t h e c o s t s o f i n f o r m a t i o n t r a n s f e r o r v e r i f i -c a t i o n a r e p r o h i b i t i v e l y h i g h , so t h a t d i r e c t d i s c l o s u r e w i l l n o t work. However, t h e " p r i c e " which t h e s e l l e r can o b t a i n f o r h i s good w i l l be i n f l u e n c e d by t h e b u y e r ' s p e r c e p t i o n about the t y p e o f good b e i n g s o l d . The l a t t e r , i n t u r n , i s i n f l u e n c e d by t h e i n f o r m a t i o n t h e b u y e r r e c e i v e s . T h e r e a r e two ways t h e s e l l e r can i n d i r e c t l y " s i g n a l " h i s t y p e t o the b u y e r : e i t h e r t h r o u g h c o n t i n g e n t c o n t r a c t s o r exogenous c o s t l y s i g n a l s . These two ways o f s i g n a l l i n g a r e q u a l i t a t i v e l y d i f -f e r e n t , b u t a r e not c o m p l e t e l y d i s t i n c t o r s e p a r a t e . Sometimes, exogenous s i g n a l s may be i n c l u d e d i n a c o n t i n -gent c o n t r a c t . The fundamental p r i n c i p l e o f s i g n a l l i n g i s t h a t an a c t i o n t a k e n by a r e l a t i v e l y h i g h e r t y p e s e l l e r w i l l be more c o s t l y f o r a r e l a t i v e l y l ower t y p e s e l l e r a n d , hence , t h e buyer can i d e n t i f y t h e t r u e t y p e o f the s e l l e r t h r o u g h t h e s e l l e r ' s a c t i o n . C o n t i n g e n t c o n t r a c t s have b o t h r i s k s h a r i n g and s i g n a l l i n g d i m e n s i o n s . T h a t i s , such a c o n t r a c t t r a n s f e r s 57 b o t h r i s k and i n f o r m a t i o n . S i g n a l l i n g models w i t h c o n t i n -gent c o n t r a c t s may d i f f e r i n s e v e r a l fundamental d i m e n -s i o n s . Some models assume c o m p e t i t i v e b u y e r s ; i . e . , t h e r e a r e a l a r g e number o f b u y e r s who w i l l p u r c h a s e t h e good a t a c o m p e t i t i v e p r i c e , based on the b u y e r s ' knowledge o f t h e q u a l i t y o f t h e good. In t h i s c a s e , t h e ne t t r a d i n g s u r -p l u s goes t o t a l l y t o t h e s e l l e r . A l t e r n a t i v e l y , some models assume a m o n o p o l i s t i c b u y e r ; i . e . , t h e r e i s a s i n g l e b u y e r who seeks t o o b t a i n the "goods" as c h e a p l y as p o s s i b l e , r e t a i n i n g a maximum share o f s u r p l u s f o r h i m -s e l f . He must pay t h e s u p p l i e r a p r i c e s u f f i c i e n t t o i n d u c e h im t o s e l l t h e good; t h a t " r e s e r v a t i o n " p r i c e i s t a k e n as a g i v e n . Models a l s o d i f f e r as t o "who moves f i r s t " . Some a n a l y s e s d e p i c t the market as f u n c t i o n i n g as i f each b u y e r o f f e r s a menu o f c o n t r a c t s t o t h e s u p p l i e r s , and each s u p p l i e r chooses t h e b e s t c o n t r a c t from among a l l t h o s e o f f e r e d . The b u y e r i s assumed t o commit t o t h e c o n t r a c t s he o f f e r s and he cannot change them a f t e r he has seen t h e s u p p l i e r s ' r e s p o n s e s . O t h e r a n a l y s e s assume t h a t each s u p p l i e r o f f e r s a s i n g l e c o n t r a c t t o t h e b u y e r s , who t h e n have some response t o make. F o r example , t h e c o n -t r a c t may s p e c i f y a p r i c e as w e l l as o t h e r terms such as w a r r a n t i e s , and t h e b u y e r m e r e l y a c c e p t s o r r e j e c t s t h e c o n t r a c t . Many b u y e r s may a c c e p t t h e same c o n t r a c t , o r t h e r e may be a s i n g l e good which goes t o t h e f i r s t b u y e r 58 who a c c e p t s i t . A l t e r n a t i v e l y , t h e s e l l e r may o f f e r a c o n t r a c t w i t h o u t s p e c i f y i n g a p r i c e and t h e n a c c e p t t h e b e s t p r i c e t h a t i s o f f e r e d . S i g n a l l i n g models w i t h exogenous c o s t l y s i g n a l s d i f f e r m a i n l y as t o t h e d i m e n s i o n s o f t h e p r i v a t e i n f o r m a -t i o n and t h e t y p e s o f s i g n a l s u s e d . E a r l y p a p e r s assume t h a t t h i s i n f o r m a t i o n i s r e p r e s e n t e d by one parameter so one s i g n a l can f u l f i l l t h e s i g n a l l i n g t a s k . L a t e r work assumes two d imens ions o f t h e p r i v a t e i n f o r m a t i o n , so two s i g n a l s a r e n e c e s s a r y t o do t h e j o b . These s i g n a l s a r e assumed, as p o i n t e d above , t o be c o s t l y and t h e c o s t s a r e n e g a t i v e l y c o r r e l a t e d w i t h t h e t y p e . T h e r e a r e a l a r g e number o f p a p e r s i n v o l v i n g s i g -n a l l i n g . A complete s u r v e y o f t h i s c a t e g o r y i s no t t h e o b j e c t i v e o f t h i s c h a p t e r . We p r i m a r i l y f o c u s on t h o s e p a p e r s t h a t d e a l w i t h t h e i s s u e s o f o b t a i n i n g o f c a p i t a l from and s h a r i n g r i s k s w i t h t h e c a p i t a l m a r k e t , o r com-m u n i c a t i n g i n f o r m a t i o n t o c o m p e t i t o r s i n a p r o d u c t m a r k e t . These p a p e r s a r e c l o s e l y r e l a t e d t o v o l u n t a r y d i s c l o s u r e r e s e a r c h because they p r o v i d e an a l t e r n a t i v e way f o r f i r m s t o communicate w i t h t h e m a r k e t . T a b l e 2-5 e x h i b i t s t h e main c h a r a c t e r i s t i c s o f some i m p o r t a n t p a p e r s t h a t a r e s e l e c t e d based on t h e above c r i t e r i a . The f o l l o w i n g i s a summary o f t h e s e p a p e r s . 59 I n s e r t T a b l e 2-5 h e r e The i n f l u e n c e s o f i n f o r m a t i o n asymmetry on markets i n which b u y e r s a r e i m p e r f e c t l y in formed about t h e q u a l i t y o f a c o l l e c t i o n o f d i f f e r e n t i a t e d p r o d u c t s t h a t appear on the s u p p l y s i d e o f the market were a n a l y z e d f i r s t by A k e r l o f [1970] . Assuming t h a t t h e a s y m m e t r i c a l i n f o r m a t i o n p e r -s i s t s , A k e r l o f c o n c l u d e s t h a t h i g h q u a l i t y s e l l e r s may wi thdraw t h e i r p r o d u c t s from t h e market because t h e i r p r o d u c t s cannot be d i s t i n g u i s h e d and t h e r e f o r e a r e p r i c e d a c c o r d i n g t o t h e a v e r a g e . Spence [1973] [1976] d e a l s w i t h t h e o t h e r a s p e c t o f t h e same i s s u e . He a n a l y z e s e f f o r t s by s e l l e r s t o " t e l l " b u y e r s about the p r o d u c t s , and t h e r e f o r e , t o change t h e i n i t i a l asymmetr ic i n f o r m a t i o n a l s t r u c t u r e o f t h e m a r k e t . Spence d e f i n e s these d i f f e r e n t i a t i n g a c t i v i t i e s , as t h e y p e r t a i n t o i n f o r m a t i o n , as s i g n a l l i n g from t h e s e l l e r ' s p o i n t o f v i e w . I t a l s o can be r e f e r r e d t o as s c r e e n i n g from t h e b u y e r s ' s t a n d p o i n t . Spence [1973] c l a i m s t h a t e d u c a t i o n can s i g n a l p r o d u c t i v e p o t e n t i a l i f i t s c o s t s a r e n e g a t i v e l y c o r r e l a t e d w i t h t h a t p o t e n t i a l . T h e r e f o r e , i n g e n e r a l , b e t t e r workers w i l l a c q u i r e more e d u c a t i o n . A k e r l o f and Spence*s i n s i g h t f u l f i n d i n g s were advanced by a s e r i e s o f e x c e l l e n t p a p e r s . R o t h s c h i l d / S t i g l i t z [1976] p r o v i d e s a s e m i n a l a n a l y s i s o f i n s u r a n c e 60 m a r k e t s . J a f f e e / R u s s e l l [1976] use s i g n a l l i n g game t o a n a l y z e a l o a n market . S a l o p / S a l o p [1976] f o c u s on t h e l a b o r m a r k e t , a n a l y z i n g the i n f l u e n c e o f u n o b s e r v a b l e employees ' c h a r a c t e r i s t i c s — t h e p r o b a b i l i t y o f q u i t t i n g t h e j o b . A k e r l o f [1976] p r e s e n t s f o u r examples about t h e use o f exogenous s i g n a l s ( i n d i c a t o r s ) t o p r e d i c t t h e b e h a v i o r o f economy and i n d i v i d u a l s t o r e s o l v e i n f o r m a t i o n asymmetry p r o b l e m s . F o l l o w i n g t h e above a n t e c e d e n t s , L e l a n d / P y l e [1977] a n a l y z e s i g n a l l i n g i n f i n a n c i a l m a r k e t s . In f i n a n c i a l m a r k e t s , i n f o r m a t i o n a l asymmetr ies a r e p a r t i c u l a r l y p r o -nounced . I t i s commonly r e c o g n i z e d t h a t e n t r e p r e n e u r s p o s s e s s " i n s i d e r " i n f o r m a t i o n about t h e i r own p r o j e c t s f o r which t h e y seek f i n a n c i n g . I n t h e i r p a p e r t h i s i n f o r m a -t i o n i s m o d e l l e d as p r i v a t e knowledge about t h e expec ted v a l u e o f t h e r i s k y p r o j e c t . I t i s a l s o assumed t h a t t h e r e i s no c r e d i b l e way t h e e n t r e p r e n e u r can convey t h i s i n f o r -m a t i o n d i r e c t l y t o o t h e r p o t e n t i a l s h a r e h o l d e r s . However, t h e p o t e n t i a l s h a r e h o l d e r s w i l l r e spond t o a s i g n a l by t h e e n t r e p r e n e u r r e g a r d i n g h i s e v a l u a t i o n o f t h e e x p e c t e d v a l u e i f t h e y know t h a t i t i s i n t h e s e l f - i n t e r e s t o f t h e e n t r e p r e n e u r t o send t r u e s i g n a l s . The s i g n a l a n a l y z e d i s t h e r e t a i n e d ownership o f t h e e n t r e p r e n e u r . The market p e r c e i v e s t h e expec ted v a l u e o f t h e p r o j e c t t o be a f u n c -t i o n o f t h e s i g n a l , and the e q u i l i b r i u m v a l u a t i o n f u n c t i o n i s e x p l i c i t l y d e r i v e d . The p r o p e r t i e s o f t h i s f u n c t i o n show t h a t t h e g r e a t e r the e n t r e p r e n e u r ' s w i l l i n g n e s s t o t a k e a p e r s o n a l s t a k e i n t h e p r o j e c t , t h e more i n v e s t o r s a r e w i l l i n g t o pay f o r t h e i r s h a r e o f i t . These c o n -c l u s i o n s have been s u p p o r t e d by e m p i r i c a l o b s e r v a t i o n s . M i l g r o m / R o b e r t s [1982] use a s i g n a l l i n g model t o e x p l a i n l i m i t p r i c i n g . They model an e n t r y game i n which n e i t h e r t h e e s t a b l i s h e d f i r m n o r t h e p o t e n t i a l e n t r a n t i s p e r f e c t l y in formed as t o t h e o t h e r f i r m ' s u n i t c o s t . i n such a s i t u a t i o n , t h e p r e - e n t r y p r i c e may become a s i g n a l r e g a r d i n g t h e e s t a b l i s h e d f i r m ' s c o s t s , wh ich i n t u r n a r e a d e t e r m i n a n t o f t h e p o s t - e n t r y p r i c e and p r o f i t s f o r t h e e n t r a n t . T h u s , t h e r e l a t i o n s h i p t h a t a l ower p r i c e (by s i g n a l l i n g lower c o s t s ) t e n d s t o d i s c o u r a g e e n t r y emerges endogenous ly i n e q u i l i b r i u m . Hence, l i m i t - p r i c i n g can be_ an e q u i l i b r i u m b e h a v i o r , w i t h t h e e s t a b l i s h e d f i r m a t -t e m p t i n g t o i n f l u e n c e t h e e n t r y d e c i s i o n by c h a r g i n g a p r e - e n t r y p r i c e which i s below t h e s i m p l e monopoly l e v e l . However, s i n c e t h e e n t r a n t w i l l , i n e q u i l i b r i u m , r e c o g n i z e t h e i n c e n t i v e s f o r l i m i t - p r i c i n g , i t s e x p e c t a t i o n s o f t h e p r o f i t a b i l i t y o f e n t r y w i l l no t be c o n s i s t e n t l y b i a s e d by t h e e s t a b l i s h e d f i r m ' s b e h a v i o r . T h e n , depend ing on t h e p a r t i c u l a r e q u i l i b r i u m t h a t i s e s t a b l i s h e d and t h e parame-t e r s o f t h e mode l , the p r o b a b i l i t y o f e n t r y may f a l l s h o r t o f , e q u a l t o , o r even exceed what i t would be i f t h e r e 62 were comple te i n f o r m a t i o n , and thus no l i m i t p r i c i n g . M y e r s / M a j l u f [1984] d e v e l o p an e q u i l i b r i u m model i n which a manager ' s i s s u e - i n v e s t d e c i s i o n may s i g n a l h i s p r i v a t e i n f o r m a t i o n about t h e f i r m ' s v a l u e . The model c o n s i d e r s a f i r m t h a t has a s s e t s - i n - p l a c e w i t h a v a l u a b l e r e a l i n v e s t m e n t o p p o r t u n i t y . The f i r m has t o i s s u e common s h a r e s t o r a i s e p a r t o r a l l t h e c a s h r e q u i r e d t o u n d e r t a k e t h e i n v e s t m e n t p r o j e c t . I f managers have i n s i d e r i n f o r m a -t i o n t h e r e must be some c a s e s i n which t h a t i n f o r m a t i o n i s so f a v o r a b l e t h a t management, i f i t a c t s i n t h e i n t e r e s t o f t h e o l d s h a r e h o l d e r s , w i l l r e f u s e t o i s s u e s h a r e s even i f i t means p a s s i n g up a good inves tment o p p o r t u n i t y . I n v e s t o r s , aware o f t h e i r r e l a t i v e i g n o r a n c e , w i l l r e a s o n t h a t a d e c i s i o n not t o i s s u e s h a r e s s i g n a l s "good news". The news conveyed by an i s s u e i s bad o r a t l e a s t l e s s good . T h i s a f f e c t s t h e p r i c e i n v e s t o r s a r e w i l l i n g t o pay f o r t h e i s s u e , which i n t u r n , a f f e c t s t h e i s s u e - i n v e s t d e c i s i o n . Under r e a s o n a b l e s i m p l i f y i n g a s s u m p t i o n s , t h e p a p e r s o l v e s t h e e q u i l i b r i u m s h a r e p r i c e c o n d i t i o n a l on t h e i s s u e - i n v e s t d e c i s i o n . Of c o u r s e , i t assumes r a t i o n a l i n v e s t o r s and a r a t i o n a l f i r m which bases i t s i s s u e - i n v e s t d e c i s i o n on t h e p r i c e i t f a c e s . The r e s u l t s c a n e x p l a i n s e v e r a l a s p e c t s o f c o r p o r a t e f i n a n c i n g b e h a v i o r , i n c l u d i n g t h e t endency t o r e l y on i n t e r n a l s o u r c e s o f funds and t o p r e f e r debt t o e q u i t y i f e x t e r n a l f i n a n c i n g i s r e q u i r e d . 63 M i l l e r / R o c k [1985] extend the s t a n d a r d f i n a n c e model o f t h e f i r m ' s d i v i d e n d / i n v e s t m e n t / f i n a n c i n g d e c i s i o n s by a l l o w i n g t h e f i r m ' s managers t o know more t h a n o u t s i d e i n v e s t o r s about the t r u e s t a t e o f t h e f i r m ' s c u r r e n t e a r n i n g s . The e x t e n s i o n endogenizes t h e e f f e c t s o f d i v i -dend announcements, w h i c h , i n a w o r l d o f r a t i o n a l e x p e c t a -t i o n s , s e r v e as s i g n a l s f o r t h e market t o deduce t h e unobserved i n f o r m a t i o n about f i r m ' s c u r r e n t e a r n i n g s . The c o s t o f s i g n a l l i n g t h a t a t t r i b u t e t o t h e market by i n -c r e a s i n g d i v i d e n d s i s t h e foregone use o f t h e funds i n p r o d u c t i v e i n v e s t m e n t . T h i s c o s t o f s i g n a l l i n g any s p e c -i f i e d l e v e l o f e a r n i n g s w i l l be h i g h e r , t h e l ower t h e l e v e l o f e a r n i n g s a c t u a l l y a c h i e v e d . Trueman [1986] i s a s i g n a l l i n g model which t r i e s t o e x p l a i n why managers o f t e n r e l e a s e e a r n i n g s f o r e c a s t s p r i o r t o a c t u a l e a r n i n g s announcements. I t would appear t h a t managers s h o u l d a t b e s t be i n d i f f e r e n t t o such a r e l e a s e g i v e n t h a t t h e a c t u a l e a r n i n g w i l l be d i s c l o s e d a t a f u t u r e d a t e . The paper argues t h a t t h e f o r e c a s t r e l e a s e g i v e s i n v e s t o r s a more f a v o r a b l e assessment o f t h e manag-e r ' s a b i l i t y t o a n t i c i p a t e economic env ironment changes , and t o a d j u s t p r o d u c t i o n p l a n s a c c o r d i n g l y . Hence , i n t h i s mode l , a v o l u n t a r y f o r e c a s t r e l e a s e s e r v e s as a s i g n a l about t h e manager's t a l e n t , which i s , t h e r e b y t r a n s l a t e d i n t o a h i g h e r f i r m market v a l u e . I n o t h e r 64 words , the manager's m o t i v a t i o n t o r e l e a s e h i s e a r n i n g s f o r e c a s t stems not from h i s d e s i r e t o i n f o r m i n v e s t o r s about h i s r e v i s e d e x p e c t a t i o n f o r t h e p e r i o d ' s e a r n i n g s , b u t from h i s d e s i r e t o i n f o r m them t h a t he has r e c e i v e d new i n f o r m a t i o n about t h e p e r i o d ' s e a r n i n g s . T h i s means t h a t t h e manager w i l l be j u s t as w i l l i n g t o r e l e a s e bad news as he i s t o r e l e a s e good news. I n t u r n , t h i s i m p l i e s t h a t t h e average p r i c e change a t t h e t i m e o f f o r e c a s t r e l e a s e w i l l be p o s i t i v e . Hughes [1986] extends L e l a n d / P y l e • s [1977] model t o a b i v a r i a t e s i g n a l l i n g mode l . A t i s s u e i s t h e i n f o r m a t i o n asymmetry between i n v e s t o r s and t h e i s s u e r o f an i n i t i a l p u b l i c o f f e r i n g about t h e v a l u e o f t h e s e c u r i t y . To a v o i d market f a i l u r e , a s o l u t i o n i s p r o p o s e d i n w h i c h t h e i s s u e r makes a d i s c l o s u r e about f i r m v a l u e t h a t i s v e r i f i e d by an i n v e s t m e n t b a n k e r . The inves tment b a n k e r i m p l i c i t l y e n t e r s i n t o a c o n t i n g e n t c o n t r a c t w i t h i n v e s t o r s which imposes a p e n a l t y i f t h e ex p o s t o b s e r v a b l e c a s h f low i n d i c a t e s f r a u d u l e n t d i s c l o s u r e . The f e a t u r e o f t h e model i s t h a t t h e p r i v a t e i n f o r m a t i o n has two e l e m e n t s : t h e e x p e c t e d v a l u e and the v a r i a n c e o f t h e f u t u r e c a s h f l o w s . To s i g n a l b o t h e l ements , r e t a i n e d ownersh ip as one s i g n a l i s no t enough. Hence t h e second s i g n a l , d i r e c t d i s c l o s -u r e , i s u s e d t o complete t h e t a s k . The e q u i l i b r i u m i s s o l v e d under t h e assumpt ions o f e x p o n e n t i a l u t i l i t y , 65 normal d i s t r i b u t i o n , and an exogenous ly g i v e n d i s c l o s u r e c o s t f u n c t i o n . G r i n b l a t t / H w a n g [1988] p u r s u e t h e same i s s u e as Hughes [1986] except t h a t i n t h e i r mode l , t h e i s s u e r uses r e t a i n e d ownership and u n d e r p r i c i n g as two s i g n a l s t o communicate h i s p r i v a t e i n f o r m a t i o n about t h e mean and the v a r i a n c e . The e q u i l i b r i u m v a l u a t i o n f o r m u l a and u n d e r -p r i c i n g a r e s o l v e d assuming a m e a n / v a r i a n c e u t i l i t y f u n c -t i o n and b i v a r i a t e v a l u e o f t h e v a r i a n c e . G e r t n e r / G i b b o n s / S c h a r f s t e i n [1988] d e v e l o p a t h r e e -p l a y e r s i g n a l l i n g mode l , which a n a l y z e s an i n f o r m e d f i r m ' s c h o i c e o f f i n a n c i a l s t r u c t u r e when t h e f i n a n c i n g c o n t r a c t i s o b s e r v e d not o n l y by t h e c a p i t a l market b u t a l s o by a second un in formed p a r t y , such as a compet ing f i r m . The i n f o r m e d f i r m ' s g r o s s p r o f i t i s endogenous, because t h e second p a r t y ' s a c t i o n depends on t h e t r a n s a c t i o n i t o b s e r v e s between the in formed f i r m and t h e c a p i t a l m a r k e t . The main r e s u l t o f t h i s two-aud ience s i g n a l l i n g model i s t h a t t h e "reasonable" c a p i t a l - m a r k e t e q u i l i b r i a maximize t h e ex a n t e e x p e c t a t i o n o f t h e i n f o r m e d f i r m ' s endogenous g r o s s p r o d u c t - m a r k e t p r o f i t s . I n t h i s sense t h e c h a r a c t e r o f c a p i t a l - m a r k e t e q u i l i b r i u m i s d e t e r m i n e d by t h e s t r u c -t u r e o f t h e p r o d u c t - m a r k e t . T h u s , i t may be m i s l e a d i n g t o a n a l y z e t h e f i r m ' s a c t i v i t i e s i n t h e f i n a n c i a l market s e p a r a t e l y from i t s a c t i v i t i e s i n t h e p r o d u c t m a r k e t . In 66 a d d i t i o n , t h e p a p e r shows t h a t , g e n e r i c a l l y , e i t h e r a l l t h e r e a s o n a b l e e q u i l i b r i a a r e s e p a r a t i n g o r a l l t h e r e a -s o n a b l e e q u i l i b r i a a r e p o o l i n g . T h i s i s i n c o n t r a s t t o e a r l i e r work on t h e i n f o r m a t i o n c o n t e n t o f f i n a n c i a l s t r u c t u r e and t o more r e c e n t work on r e f i n e m e n t i n s i g -n a l l i n g games, b o t h o f which f o c u s on s e p a r a t i n g e q u i l i b -r i a . Hence t h e p a p e r c l a i m s t h a t f u l l d i s c l o s u r e need not be r e a s o n a b l e e q u i l i b r i u m b e h a v i o u r . Summary o f s i g n a l l i n g models The r e p r e s e n t a t i v e s i g n a l l i n g p a p e r s summarized above show t h e f o l l o w i n g . F i r s t , i n s t e a d o f t h e f o c u s i n most d i s c l o s u r e p a p e r s ( t h a t f i r m s may have i n c e n t i v e s t o w i t h h o l d t h e i r p r i v a t e i n f o r m a t i o n ) , s i g n a l l i n g p a p e r s focus on t h e f a c t t h a t f i r m s may have i n c e n t i v e s t o com-municate t h e i r p r i v a t e i n f o r m a t i o n t o r e l e v a n t p a r t i e s . I n t e r e s t i n g l y , one f i r m ' s i n c e n t i v e s t o r e v e a l i t s i n f o r -m a t i o n may be c r e a t e d by a n o t h e r f i r m ' s i n c e n t i v e s t o w i t h h o l d i n f o r m a t i o n . I n o r d e r t o s e p a r a t e a f i r m from a n o t h e r f i r m w i t h "bad c h a r a c t e r i s t i c s " , t h e f i r m has i n c e n t i v e s t o r e v e a l i n f o r m a t i o n about i t s t r u e s t a t e . Second , when c r e d i b l e d i s c l o s u r e i s i m p o s s i b l e , f i r m s may use i n d i r e c t ways t o s i g n a l t h e i r p r i v a t e i n f o r m a t i o n . T h u s , s i g n a l l i n g and d i s c l o s u r e a r e a l t e r n a t i v e methods f o r communicat ing p r i v a t e i n f o r m a t i o n . T h i r d , s i g n a l l i n g 67 i s c o s t l y . T h e r e f o r e , i f c r e d i b l e d i r e c t communicat ion i s c o s t l e s s , t h e n i t w i l l be used i n s t e a d o f c o s t l y s i g -n a l l i n g . However, i f c r e d i b l e d i r e c t communicat ion i s c o s t l y , t h e n s i g n a l l i n g and d i r e c t d i s c l o s u r e a r e a l t e r n a -t i v e c o s t l y communicat ion d e v i c e s . I n t h a t s e t t i n g , i d e n t i f y i n g t h e communicat ion d e v i c e u s e d . b y a p r i v a t e l y i n f o r m e d f i r m i s a m a t t e r o f i d e n t i f y i n g h i s e q u i l i b r i u m c h o i c e . 2.7 Empirical and Behavioral Research i n Voluntary Dis-closure D i r e c t t e s t s o f t h e r e s u l t s d e r i v e d from t h e a n a l y t i -c a l d i s c l o s u r e models a r e r a r e because o f t h e d i f f i c u l t y i n d e t e r m i n i n g when a manager i s w i t h h o l d i n g i n f o r m a t i o n . I n a d d i t i o n , even i f one b e l i e v e s t h a t a manager i s w i t h -h o l d i n g i n f o r m a t i o n , one cannot v e r i f y whether t h e u n d i s -c l o s e d i n f o r m a t i o n i s "good" news o r "bad" news i f t h e i n f o r m a t i o n i s n e v e r d i s c l o s e d . Hence, e m p i r i c a l a n a l y s e s o f managers ' b e h a v i o u r a r e l a r g e l y r e s t r i c t e d t o t h e e x a m i n a t i o n o f t h e t i m i n g o f t h e r e l e a s e mandated a c c o u n t -i n g r e p o r t s , and t h e e x a m i n a t i o n o f market r e a c t i o n t o "mis s ing" announcements t h a t were expec ted by t h e market based on t h e f i r m ' s t r a d i t i o n a l d i s c l o s u r e b e h a v i o r . The t h e o r e t i c a l j u s t i f i c a t i o n f o r a p o s s i b l e c o n n e c t i o n between w i t h h o l d i n g and d e l a y i n g d i s c l o s u r e o f i n f o r m a t i o n 68 i s p r o v i d e d by V e r r e c c h i a [1983] and Jung/Kwon [1988] , V e r r e c c h i a [1983] sugges t s a g e n e r a l i z a t i o n o f h i s model t o a l l o w t h e p r o p r i e t a r y c o s t t o be a f u n c t i o n o f t i m e . Jung/Kwon [1988] assume t h e p r o b a b i l i t y t h a t t h e manager has r e c e i v e d i n f o r m a t i o n i s an i n c r e a s i n g f u n c t i o n o f t i m e . T h u s , t h e manager's d e c i s i o n t o w i t h h o l d i n f o r m a -t i o n may change as t ime e l a p s e s . T h i s change r e s u l t s i n an o b s e r v a b l e d e l a y o f i n f o r m a t i o n d i s c l o s u r e . The p a p e r s t h a t examine t h e t i m i n g o f f i r m s ' d i s c l o s -u r e s a r e i m p o r t a n t t o v o l u n t a r y d i s c l o s u r e r e s e a r c h f o r t h e f o l l o w i n g r e a s o n s . F i r s t , i f f i r m s have i n c e n t i v e s t o w i t h h o l d i n f o r m a t i o n , b u t d i s c l o s u r e o f t h i s i n f o r m a t i o n i s mandated, t h e n we may o b s e r v e s y s t e m a t i c d e l a y s i n t h e f i r m s ' d i s c l o s u r e s . F o r example , f i r m s may w i t h h o l d "bad" news as l o n g as p o s s i b l e , u n t i l t h e due d a t e o f t h e r e -p o r t i n g r e q u i r e m e n t . Second , i f t h e d i s c l o s u r e i s h o t mandatory , t h e n an i n v e s t i g a t i o n o f t h e r e l a t i v e t i m i n g and q u a n t i t y o f "good news" v e r s u s "bad news" may r e v e a l something about f i r m s ' d i s c l o s u r e b e h a v i o r . T h i r d , exam-i n i n g t h e m a r k e t ' s r e a c t i o n t o t h e t i m i n g o f f i r m s ' r e -p o r t i n g may p r o v i d e e v i d e n c e o f t h e m a r k e t ' s p e r c e p t i o n o f f i r m s ' d i s c l o s u r e s t r a t e g i e s . F o r example , such an e x a m i n a t i o n may r e v e a l whether t h e market i n t e r p r e t s a " n o n - r e p o r t " as a s i g n a l o f f o r t h c o m i n g "bad" news. Pas tena and Ronen [1979] e m p i r i c a l l y t e s t t h e i m p l i -69 c a t i o n s o f t h e e x i s t e n c e o f a d i s i n c e n t i v e t o produce and d i s s e m i n a t e n e g a t i v e i n f o r m a t i o n . They do so by examining the e x t e n t o f d e l a y i n t h e r e l e a s e o f n e g a t i v e f o r e k n o w l -edge u n t i l t h e t ime such d i s c l o s u r e s a r e f o r c e d on manage-ment as a r e s u l t o f t h e a n n u a l a u d i t o r t h r o u g h o t h e r media u n c o n t r o l l e d by management. They d e f i n e i n f o r m a t i o n h a r d n e s s as t h e p r o b a b i l i t y o f imminent d i s c l o s u r e by s o u r c e s u n c o n t r o l l e d by management o r as a r e s u l t o f an a u d i t o r b o t h . The e m p i r i c a l r e s u l t s p r o v i d e s u p p o r t f o r t h e h y p o t h e s i s t h a t : ( i ) managers a c t as i f t h e y a t tempt t o d e l a y t h e d i s s e m i n a t i o n o f n e g a t i v e i n f o r m a t i o n , r e l a -t i v e t o p o s i t i v e i n f o r m a t i o n ; ( i i ) t h e y a c t as i f t h e y d i s c l o s e p r i m a r i l y s o f t p o s i t i v e i n f o r m a t i o n as c o n t r a s t e d w i t h s o f t n e g a t i v e i n f o r m a t i o n ; : a n d ( i i i ) t h e y d i s c l o s e n e g a t i v e i n f o r m a t i o n e s s e n t i a l l y o n l y a f t e r such i n f o r m a -t i o n becomes h a r d . They c o n c l u d e t h a t managers have s u f f i c i e n t d i s c r e t i o n o v e r t h e t i m i n g o f t h e g e n e r a t i o n and d i s s e m i n a t i o n o f n e g a t i v e i n f o r m a t i o n so t h a t t h e r e i s a p l a n n e d d e l a y o f n e g a t i v e s o f t i n f o r m a t i o n . K r o s s [1982] e x p l o r e s whether a l a t e r t h a n expec ted e a r n i n g s d i s c l o s u r e i s p e r c e i v e d as a s i g n o f bad news by t h e c a p i t a l m a r k e t . The t e s t i s conducted a f t e r a d e t e r -m i n a t i o n i s made f o r a sample o f f i r m s t h a t bad news i s r e p o r t e d l a t e r t h a n good news. I t f i n d s t h a t l a t e r e a r n -i n g s announcements have a h i g h e r p r o b a b i l i t y o f c o n t a i n i n g bad news t h a n do e a r l y announcements f o r t h e sample o f f i r m s t e s t e d . I t a l s o d i s c o v e r s t h a t t h e s h a r e s o f l a t e r e p o r t i n g f i r m s e a r n lower r e s i d u a l r e t u r n s t h a n e a r l y r e p o r t i n g f i r m s d u r i n g t h i s p e r i o d . These t i m e e f f e c t s a r e s t i l l e v i d e n t when news e f f e c t s a r e c o n t r o l l e d . P a t e l l and Wol f son [1982] documented s y s t e m a t i c p a t t e r n s i n t h e exac t t i m i n g o f announcements i n r e l a t i o n t o t h e h o u r s o f o p e r a t i o n o f t h e major s t o c k exchanges . They t e s t t h e "market wisdom" t h a t good news i s r e l e a s e d d u r i n g t r a d i n g w h i l e bad news i s h e l d u n t i l a f t e r t h e market c l o s e s . The s t a t i s t i c a l a n a l y s i s o f e a r n i n g s and d i v i d e n d announcements y i e l d s r e s u l t s t h a t a r e c o n s i s t e n t w i t h t h e c o n j e c t u r e t h a t t h e l i k e l i h o o d o f "bad news" d i s c l o s u r e s i n c r e a s e s a f t e r t h e c l o s e o f t r a d i n g f o r t h e d a y . The r e l a t i v e p r o p o r t i o n o f announcements o f i n c r e a s e d e a r n i n g s o r d i v i d e n d s was s i g n i f i c a n t l y h i g h e r d u r i n g t r a d i n g t h a n a f t e r t r a d i n g . The p r i c e changes were more l i k e l y t o be p o s i t i v e f o r d u r i n g - t r a d i n g r e l e a s e s , w h i l e t h e r e was a marked s h i f t toward n e g a t i v e p r i c e changes f o r a f t e r - t r a d i n g announcements. T h i s s t o c k p r i c e r e s p o n s e may c o n t r i b u t e t o an i n t e r p r e t a t i o n o f t h e s y s -t e m a t i c t i m i n g b e h a v i o r as an at tempt t o r e d u c e t h e p u b l i c exposure o f u n f a v o u r a b l e e v e n t s . G i v o l y and Palmon [1982] p r e s e n t e v i d e n c e on t h e t i m e l i n e s s o f annua l e a r n i n g s announcements i n t h e U n i t e d 71 S t a t e s . They a n a l y z e i t s p o s s i b l e d e t e r m i n a n t s and exam-i n e t h e r e l a t i o n s h i p between the i n f o r m a t i o n c o n t e n t o f t h e a c c o u n t i n g r e p o r t and i t s t i m e l i n e s s . S p e c i f i c a l l y , t h e y f i n d t h a t announcements c o n t a i n i n g bad news t e n d t o be d e l a y e d . I n v e s t i g a t i o n o f t h e r e l a t i o n s h i p between company c h a r a c t e r i s t i c s and t i m e l i n e s s i n d i c a t e s t h a t s i z e i s i n v e r s e l y r e l a t e d and c o m p l e x i t y o f t h e a u d i t i s d i -r e c t l y r e l a t e d t o the r e p o r t i n g d e l a y . However, t h e e x p l a n a t o r y power o f t h e s e v a r i a b l e s i s s m a l l . K r o s s and Schroeder [1984] examine b o t h t h e a s s o c i -a t i o n between q u a r t e r l y announcement t i m i n g ( e a r l y o r l a t e ) and t h e t y p e o f news (good o r bad) r e p o r t e d , and the r e l a t i o n s h i p between s t o c k r e t u r n s and t i m i n g around t h e e a r n i n g s announcement d a t e . The o b j e c t i v e i s t o de termine whether t h e a s s o c i a t i o n between announcement t i m i n g and s t o c k r e t u r n s p e r s i s t s a f t e r c o n t r o l l i n g f o r t h e s i g n and magnitude o f t h e e a r n i n g s f o r e c a s t e r r o r and f i r m s i z e . The r e s u l t s show t h a t e a r l y q u a r t e r l y e a r n i n g s announce-ments ( i ) c o n t a i n b e t t e r news, and ( i i ) were a s s o c i a t e d w i t h l a r g e abnormal r e t u r n s r e l a t i v e t o l a t e announce-ments . These r e s u l t s h o l d independent a l l c o n t r o l l a b l e e f f e c t s ment ioned above. Chambers and Penman [1984] p r o v i d e d e s c r i p t i v e e v i -dence on t h e r e l a t i o n s h i p between t i m e l i n e s s o f e a r n i n g s r e p o r t s and s t o c k p r i c e b e h a v i o u r s u r r o u n d i n g t h e i r 72 r e l e a s e . They f i n d some r e l a t i o n s h i p between t h e t ime l a g i n r e p o r t i n g and r e t u r n v a r i a b i l i t y a t t h e r e p o r t d a t e f o r r e p o r t s o f r e l a t i v e l y s m a l l f i r m s b e a r i n g good news. T i m e l y i n t e r i m r e p o r t s o f s m a l l f i r m s which b r i n g good news a r e a s s o c i a t e d w i t h h i g h e r p r i c e r e a c t i o n s t h a n a r e t h o s e w i t h l o n g e r t i m e l a g s . T h i s i s not o b s e r v e d f o r r e p o r t s r e v e a l i n g bad news o r r e p o r t s f o r r e l a t i v e l y l a r g e f i r m s . They a l s o f i n d t h a t when r e p o r t s a r e p u b l i s h e d e a r l i e r t h a n e x p e c t e d , t h e y t e n d t o have l a r g e r p r i c e e f f e c t s t h a n when t h e y a r e p u b l i s h e d on t i m e o r l a t e r t h a n e x p e c t e d . U n e x p e c t e d l y e a r l y r e p o r t s a r e c h a r a c t e r i z e d by good news, whereas u n e x p e c t e d l y l a t e r e p o r t s t e n d t o b e a r bad news. When f i r m s miss t h e i r expec ted r e p o r t i n g d a t e s , t h e market i n t e r p r e t s t h i s as bad news. Penman [1980] examines v o l u n t a r y f o r e c a s t d i s c l o s u r e t o p r o v i d e e v i d e n c e r e l e v a n t t o t h e f o l l o w i n g two i s s u e s . The f i r s t i s s u e d e a l s w i t h i n f o r m a t i o n c o n t e n t — do v o l u n t a r y e a r n i n g s f o r e c a s t s convey i n f o r m a t i o n t o i n v e s -t o r s about t h e f i r m s which p u b l i s h them? The second i s s u e d e a l s w i t h f u l l d i s c l o s u r e — does v o l u n t a r y f o r e c a s t d i s c l o s u r e r e s u l t i n t h e p u b l i c a t i o n o f o n l y a s u b s e t o f t h e e a r n i n g s f o r e c a s t i n f o r m a t i o n p o t e n t i a l l y a v a i l a b l e , and i f s o , what c h a r a c t e r i z e s t h a t subse t? The r e s u l t s o f t h e t e s t s w i t h r e s p e c t t o t h e i n f o r m a t i o n c o n t e n t i s s u e i n d i c a t e t h a t c o r p o r a t e e a r n i n g s f o r e c a s t s , on a v e r a g e , p o s s e s s i n f o r m a t i o n r e l e v a n t t o the v a l u a t i o n o f f i r m s . W i t h r e s p e c t t o the f u l l d i s c l o s u r e i s s u e , t h e t e s t s i n d i c a t e t h a t t h e r e t u r n s on sample s e c u r i t i e s o f f o r e -c a s t i n g f i r m s d u r i n g t h e f i s c a l y e a r i n which t h e f o r e c a s t i s made a r e , on a v e r a g e , h i g h e r t h a n t h o s e on t h e market as a who le , o t h e r t h i n g s b e i n g h e l d c o n s t a n t . I t appears t h a t f i r m s w i t h r e l a t i v e l y p o o r e a r n i n g s p r o s p e c t s and r e l a t i v e l y low s e c u r i t y r e t u r n s do no t r e v e a l t h e i r r e l a -t i v e p o s i t i o n t h r o u g h an e a r n i n g s f o r e c a s t . L e f t w i c h , W a t t s , and Zimmerman [1981] i n v e s t i g a t e t h e economic i n c e n t i v e s o f managers t o p r o v i d e i n t e r i m r e p o r t s v o l u n t a r i l y . They a n a l y z e why c o r p o r a t i o n s choose a p a r t i c u l a r r e p o r t i n g f r e q u e n c y f o r e x t e r n a l p u r p o s e s . They e x p l o r e whether t h e m o n i t o r i n g p r o c e s s a s s o c i a t e d w i t h i s s u i n g c a p i t a l t o p a r t i e s o u t s i d e t h e f i r m can e x p l a i n why managers exceed minimum r e p o r t i n g r e q u i r e -ments . T h e i r r e s u l t s sugges t t h a t r e p o r t i n g f r e q u e n c y i s c o n n e c t e d w i t h t h e c h o i c e o f S t o c k Exchange , f i r m ' s r e -p o r t i n g h i s t o r y , and f i r m ' s c a p i t a l s t r u c t u r e . However, t h e r e s u l t s a r e no t s t r o n g . I n t h e b e h a v i o u r a l a c c o u n t i n g r e s e a r c h l i t e r a t u r e , G i b b i n s , R i c h a r d s o n , and Waterhouse [1990] p r e s e n t i n t e r -v iew d a t a r e g a r d i n g v a r i o u s a s p e c t s o f f i r m d i s c l o s u r e . T h e i r i n f o r m a n t s v iewed t h e o u t p u t o f t h e d i s c l o s u r e p r o c e s s as a s e t o f components , i n c l u d i n g t h e p a r t i c u l a r i n f o r m a t i o n d i s c l o s e d and a v a r i e t y o f r e l a t e d management a c t i v i t i e s . T h i s s e t o f o u t p u t s i s i n f l u e n c e d by s e v e r a l v a r i a b l e s , w h i c h they c a t e g o r i z e as t h e f i r m ' s d i s c l o s u r e p o s i t i o n and i t s a n t e c e d e n t s , s p e c i f i c d i s c l o s u r e i s s u e s f a c e d by t h e f i r m , e x t e r n a l c o n s u l t a n t s and a d v i s o r s , and s t r u c t u r e . They t h e o r i z e t h a t f i r m s d e v e l o p a s t a b l e i n t e r n a l p r e f e r e n c e f o r the way i n which d i s c l o s u r e i s managed. Two d imens ions o f a f i r m ' s d i s c l o s u r e p o s i t i o n a r e i d e n t i f i e d — r i t u a l i s m and o p p o r t u n i s m . The former r e f e r s t o a s e t o f i n t e r n a l b e h a v i o r a l p a t t e r n s c h a r a c t e r -i z e d by a p r o p e n s i t y toward u n c r i t i c a l adherence t o p r e -s c r i b e d norms. The l a t t e r r e f e r s t o a p r o p e n s i t y t o seek f i r m - s p e c i f i c advantage i n t h e d i s c l o s u r e o f i n f o r m a t i o n . O p p o r t u n i s t i c d i s c l o s u r e b e h a v i o u r i n v o l v e s an a t tempt by t h e f i r m t o c l o s e l y manage t h e d i s c l o s u r e p r o c e s s , c r e a t -i n g and t a k i n g advantage o f o p p o r t u n i t i e s as t h e y a r r i v e . Summary o f E m p i r i c a l R e s u l t s : As shown by t h e above summary, e m p i r i c a l r e s e a r c h has p r o v i d e d o n l y i n d i r e c t e v i d e n c e w i t h r e s p e c t t o t h e r e s u l t s d e r i v e d from a n a l y t i c a l mode l s . The e m p i r i c a l r e s u l t s show t h a t managers w i t h h o l d some i n f o r m a t i o n and d i s c l o s e o t h e r s . In p a r t i c u l a r , t h e y can m a n i p u l a t e t h e t i m i n g o f d i s c l o s u r e s and t h e r e b y a f f e c t t h e impact o f t h e i n f o r m a t i o n r e l e a s e . On t h e o t h e r hand , e m p i r i c a l e v i -75 d e n c e s u g g e s t s t h a t t h e m a r k e t i s r a t i o n a l i n i n t e r p r e t i n g t h e o b s e r v e d d i s c l o s u r e d e c i s i o n o f f i r m s . When t h e m a r k e t e v a l u a t e s a n y i n f o r m a t i o n d i s c l o s e d , t i m e l i n e s s a n d o t h e r d i s c l o s u r e c h a r a c t e r i s t i c s a r e t a k e n i n t o a c c o u n t . T h e s e r e s u l t s a r e c o n s i s t e n t w i t h m o s t r e c e n t a n a l y t i c a l f i n d i n g s . H o w e v e r , t h e e m p i r i c a l r e s e a r c h t o d a t e h a s p r o v i d e d l i m i t e d i n f o r m a t i o n a b o u t t h e i s s u e . T h e r e i s a n o b v i o u s i m b a l a n c e b e t w e e n a n a l y t i c a l m o d e l l i n g a n d e m p i r i c a l i n v e s t i g a t i o n . 76 Tables T a b l e 2 - 1 : T w o - p l a y e r D i s c l o s u r e M o d e l s **************************************** P a p e r s (1) (2) (3) (4) (5) (6) (V) (8) (9) G r o s s m a n / H . [1980] T C D CMV — NDC — — DT V S D FD M i l g r o m [1981] T I D CMV - NDC — — C T V S D FD J o v a n o v i c [1982] T C D CMV - - E X C - C T V S D PD V e r r e c c h i a [1983] T C D CMV - - E X C - C T V S D PD D y e (1) [ 1 9 8 5 a ] T C D CMV - NDC ' - N P I C T V S D PD (2) [ 1 9 8 5 a ] T C D U - - ENC - C T V S D ND D y e [ 1 9 8 5 b ] T C D CMV - - ENC - C T V D P PD D y e [1986] T I D CMV - • - E X C - C T V S D A L L J u n g / K w o n [1988] T C D CMV - NDC - N P I C T V S D PD V e r r e c c h i a [1990] TCD CMV — - E X C — C T V S D PD * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * T r u t h f u l C o m p l e t e D i s c l o s u r e . T r u t h f u l I n c o m p l e t e D i s c l o s u r e , m a n a g e r m a x i m i z e s C u r r e n t M a r k e t V a l u e o f t h e f i r m . m a n a g e r m a x i m i z e s t h e E n d - o f - P e r i o d V a l u e o f t h e i n i t i a l s h a r e h o l d e r s ' e q u i t y i n t h e f i r m , m a n a g e r i s U t i l i t y m a x i m i z e r . m a n a g e r m u s t o b t a i n C a p i t a l M a r k e t F u n d s . No D i s c l o s u r e C o s t s ( n o n - p r o p r i e t a r y i n f o r m a t i o n ) . E x o g e n o u s C o s t s o f p r o p r i e t a r y i n f o r m a t i o n . E N d o g e n o u s C o s t s o f p r o p r i e t a r y i n f o r m a t i o n , p o s i t i v e p r o b a b i l i t y o f No P r i v a t e I n f o r m a t i o n . B i n a r y T y p e s . D i s c r e t e T y p e s . C o n t i n u u m T y p e s . V o l u n t a r y S i g n a l D i s c l o s u r e . V o l u n t a r y D i s c l o s u r e P o l i c y . F u l l D i s c l o s u r e e q u i l i b r i u m . N o n - D i s c l o s u r e e q u i l i b r i u m . P a r t i a l D i s c l o s u r e e q u i l i b r i u m . F D / N D / P D (1) T C D : T I D : (2) C M V : E P V : U : (3) C M F : (4) N D C : (5) E X C : E N C : (6) N P I : (7) B T : D T : C T : (8) V S D : V D P : (9) F D : N D : P D : A L L : 77 T a b l e 2 - 2 : O l i g o p o l i s t i c M o d e l s ******************************************* p a p e r s (1) (2) (3) (4) (5) (6) (7) (8) N o v s h e k / S . [1982] D C T I D CMV A C T V D P F P / N P C l a r k e [1983] 0 C T C D CMV A / C C T V D P NP V i v e s [1984] D C / B T I D CMV A C T V D P F P / N P F r i e d [1984] D C T C D CMV C C T V D P F P L i (1) [1985] 0 C T I D CMV A C T V D P NP (2) [1985] 0 C T C D CMV C C T V D P F P G a l - O r [1985] 0 C T I D CMV A C T V D P NP G a l - O r [1986] D C / B T I D CMV C C T V D P F P / N P S h a p i r o [1986] 0 C T C D CMV C C T V D P F P K i r b y [1988] 0 C T C D CMV A C T V D P F P D o n t o h [1990] 0 C T C D *** A / C C T V D P PD H u g h e s / K a o [1990] D C T C D CMV A C T V D P F D / P D D a r r o u g h [1990] D C / B T C D CMV A / C C T / B T *** F P / N P ****************************************************** (1) D : D u o p o l y m o d e l . O : O l i g o p o l y m o d e l . (2) C : C o u r n o t c o m p e t i t i o n g a m e . B : B e r t r a n d c o m p e t i t i o n g a m e . (3) T C D : T r u t h f u l C o m p l e t e D i s c l o s u r e . T I D : T r u t h f u l I n c o m p l e t e D i s c l o s u r e . (4) C M V : m a n a g e r m a x i m i z e s C u r r e n t M a r k e t V a l u e o f t h e f i r m . E P V : m a n a g e r m a x i m i z e s t h e E n d - o f - P e r i o d V a l u e o f t h e i n i t i a l s h a r e h o l d e r s 1 e q u i t y i n t h e f i r m . U : m a n a g e r i s U t i l i t y m a x i m i z e r . * * * : C M V / E P V (5) A : u n c e r t a i n i n t e r c e p t o f a l i n e a r d e m a n d . C : u n c e r t a i n c o n s t a n t m a r g i n a l C o s t . (6) B T : B i n a r y T y p e s . D T : D i s c r e t e T y p e s . C T : C o n t i n u u m T y p e s . (7) V S D : V o l u n t a r y S i g n a l D i s c l o s u r e . V D P : V o l u n t a r y D i s c l o s u r e P o l i c y . * * * : V S D / V D P (8) F D : F u l l D i s c l o s u r e e q u i l i b r i u m . N D : N o n - D i s c l o s u r e e q u i l i b r i u m . P D : P a r t i a l D i s c l o s u r e e q u i l i b r i u m . 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R o n e n [1979] "Some H y p o t h e s e s o n t h e P a t t e r n o f M a n a g e m e n t ' s I n f o r m a l D i s c l o s u r e s . " J o u r n a l o f  A c c o u n t i n g R e s e a r c h . V o l . 1 7 N o . 2 p p . 5 5 0 - 6 5 . P a t e l l , J . M . a n d M . A . W o l f s o n [1982] " G o o d N e w s , B a d N e w s , a n d t h e I n t r a d a y T i m i n g o f C o r p o r a t e D i s c l o s u r e s . " T h e  A c c o u n t i n g R e v i e w . V o l . L V I I N o . 3 p p . 5 0 9 - 2 7 . P e n m a n , S . H . [1980] " A n E m p i r i c a l I n v e s t i g a t i o n o f t h e V o l u n t a r y D i s c l o s u r e o f C o r p o r a t e E a r n i n g s F o r e c a s t s . " J o u r n a l o f A c c o u n t i n g R e s e a r c h . V o l . 1 8 N o . l p p . 1 3 2 - 6 0 . R o t h s c h i l d , M . a n d J . S t i g l i t z [1976] " E q u i l i b r i u m i n C o m -p e t i t i v e I n s u r a n c e M a r k e t s : A n E s s a y o n t h e E c o n o m i c s o f I m p e r f e c t I n f o r m a t i o n . " Q u a r t e r l y J o u r n a l o f E c o n o m i c s . V o l . 9 0 p p . 6 2 9 - 4 9 . S a l o p , J . a n d S . S a l o p [1976] " S e l f - s e l e c t i o n a n d T u r n o v e r i n t h e L a b o r M a r k e t . " Q u a r t e r l y J o u r n a l o f E c o n o m i c s f V o l . 9 0 p p . 6 1 9 - 2 7 . S h a p i r o , C . [1986] " E x c h a n g e o f C o s t I n f o r m a t i o n i n O l i g o p o l y . " R e v i e w o f E c o n o m i c S t u d i e s . V o l . L I I I p p . 4 3 3 -4 6 . S p e n c e , M . [ 1973 ] " J o b M a r k e t S i g n a l l i n g . " Q u a r t e r l y  J o u r n a l o f E c o n o m i c s , p p . 3 5 4 - 7 4 . S p e n c e , M . [ 1976 ] " I n f o r m a t i o n a l A s p e c t s o f M a r k e t S t r u c -t u r e : a n I n t r o d u c t i o n . " Q u a r t e r l y J o u r n a l o f E c o n o m i c s . V o l . 9 0 p p . 5 9 1 - 9 7 . T r u e m a n , B . [1986] "Why Do M a n a g e r s V o l u n t a r i l y R e l e a s e E a r n i n g s F o r e c a s t s ? " J o u r n a l o f A c c o u n t i n g a n d E c o n o m i c s . V o l . 8 p p . 5 3 - 7 1 . V e r r e c c h i a , R . E . [1983] " D i s c r e t i o n a r y D i s c l o s u r e . " J o u r - n a l o f A c c o u n t i n g a n d E c o n o m i c s . V o l . 5 p p . 1 7 9 - 9 4 . V e r r e c c h i a , R . E . [1986] " M a n a g e r i a l D i s c r e t i o n i n t h e C h o i c e Among F i n a n c i a l R e p o r t i n g A l t e r n a t i v e s . " J o u r n a l  o f A c c o u n t i n g a n d E c o n o m i c s . V o l . 8 p p . 1 7 5 - 9 5 . V e r r e c c h i a , R . E . [ 1990a ] " I n f o r m a t i o n Q u a l i t y a n d D i s c r e -t i o n a r y D i s c l o s u r e . " J o u r n a l o f A c c o u n t i n g a n d E c o n o m i c s . V o l . 1 2 p p . 3 6 5 - 8 0 . V e r r e c c h i a , R . E . [1990b] " E n d o g e n o u s P r o p r i e t a r y C o s t s T h r o u g h F i r m I n t e r d e p e n d e n c e . " J o u r n a l o f A c c o u n t i n g a n d 85 E c o n o m i c s . V o l . 1 2 p p . 2 4 5 - 5 0 . V i v e s , X . [ 1984 ] " D u o p o l y I n f o r m a t i o n E q u i l i b r i u m : C o u r n o t a n d B e r t r a n d . " J o u r n a l o f E c o n o m i c T h e o r y . V o l . 3 4 p p . 7 1 -9 4 . W a g e n h o f e r , A . [1990] " V o l u n t a r y D i s c l o s u r e w i t h a S t r a -t e g i c O p p o n e n t . " J o u r n a l o f A c c o u n t i n g a n d E c o n o m i c s . V o l . 1 2 p p . 3 4 1 - 6 3 . W a t t s , R . L . a n d J . L . Z i m m e r m a n [ 1 9 7 9 ] " T h e Demand f o r a n d S u p p l y o f A c c o u n t i n g T h e o r i e s : T h e M a r k e t f o r E x c u s e s . " T h e A c c o u n t i n g R e v i e w . V o l . L I V N o . 2 p p . 2 7 3 - 3 0 5 . 86 Chapter 3 VOLUNTARY FINANCIAL DISCLOSURE IN AN ENTRY GAME WITH CONTINUA OF TYPES 87 3 . 1 I n t r o d u c t i o n A s p a r t o f t h e management p r o c e s s , m a n a g e r s c o n s t a n t -l y a c q u i r e i n f o r m a t i o n a b o u t t h e i r f i r m ' s f u t u r e p r o f i t -a b i l i t y . T o t h e e x t e n t t h a t t h i s i n f o r m a t i o n i s n o t known b y o t h e r s , we r e f e r t o i t a s p r i v a t e m a n a g e m e n t i n f o r m a -t i o n . I f t h e f i r m ' s o w n e r s h i p i s p u b l i c l y t r a d e d , t h e n t h i s i n f o r m a t i o n w i l l u l t i m a t e l y b e c o m e p u b l i c l y k n o w n ( o r o b s o l e t e ) a s i n v e s t o r s r e c e i v e t h e f i r m ' s q u a r t e r l y a n d a n n u a l f i n a n c i a l r e p o r t s . I n a d d i t i o n , m a n a g e r s c a n v o l u n t a r i l y r e v e a l t h e i r p r i v a t e i n f o r m a t i o n b y i s s u i n g r e p o r t s , s u c h a s management f o r e c a s t s o f f u t u r e e a r n i n g s . We o b s e r v e t h a t , f r o m t i m e t o t i m e , m a n a g e r s i s s u e s u c h r e p o r t s , b u t t h e c r i t e r i a t h e y u s e i n d e t e r m i n i n g when t o make t h e m i s n o t w e l l u n d e r s t o o d . A k e y c h a r a c t e r i s t i c o f t h e r e p o r t i n g o f p r i v a t e m a n a g e m e n t i n f o r m a t i o n i s t h a t m a n a g e r s d o n o t a l w a y s r e p o r t t h e i r i n f o r m a t i o n a n d t h a t t h e y r e v e a l ( o r w i t h -h o l d ) b o t h " g o o d " a n d " b a d " n e w s . S e v e r a l r e c e n t p a p e r s p r o v i d e m o d e l s o f m a n a g e r s ' v o l u n t a r y d i s c l o s u r e d e c i -s i o n s . T h e m o d e l s a r e t y p i c a l l y c o n s t r u c t e d s o t h a t m a n a g e r s d o n o t a l w a y s d i s c l o s e o r w i t h h o l d t h e i r i n f o r m a -t i o n , d e s p i t e r a t i o n a l b e h a v i o u r b y b o t h t h e p r i v a t e l y i n f o r m e d m a n a g e r s a n d i n t e r e s t e d p a r t i e s e x t e r n a l t o t h e f i r m . I n d i s c l o s u r e m o d e l s , i t i s a s s u m e d t h a t t h e m a n -a g e r s d e c i d e w h e t h e r o r n o t t o d i s c l o s e t h e i r i n f o r m a t i o n , 88 b u t t h e y d o n o t l i e i f t h e y c h o o s e t o d i s c l o s e . T h e m o t i v a t i o n n o t t o l i e i s n o t e x p l i c i t l y m o d e l e d , b u t i s d e r i v e d f r o m e i t h e r t h e a s s u m e d t h r e a t o f s i g n i f i c a n t p e n a l t i e s i f m a n a g e r s a r e " c a u g h t " m i s - r e p r e s e n t i n g t h e i r i n f o r m a t i o n o r t h e a s s u m e d a v a i l a b i l i t y o f a c o s t l e s s v e r i f i c a t i o n m e c h a n i s m . C o n s e q u e n t l y , t h e s e m o d e l s d o n o t g e t i n t o " s i g n a l l i n g " i s s u e s . 1 A d e t a i l e d s u r v e y a n d c l a s s i f i c a t i o n o f t h e e x i s t i n g l i t e r a t u r e i n t h i s r e s e a r c h a r e a i s p r o v i d e d i n t h e p r i o r c h a p t e r . I n t h i s c h a p t e r , we p r o v i d e a m o d e l t o f u r t h e r d e v e l o p t h e r e s u l t s o f p r i o r w o r k s . T h e m a i n f e a t u r e s a n d c o n t r i b u t i o n s o f o u r m o d e l a r e a s f o l l o w i n g . O u r m o d e l e x p l i c i t l y c o n s i d e r s t h r e e p l a y e r s . We f o c u s o n t h e d i s c l o s u r e d e c i s i o n made b y t h e p r i v a t e l y i n f o r m e d m a n a g e r o f a n " i n c u m b e n t " f i r m (I) w h i c h i s u n d e r t a k i n g a n i n v e s t m e n t i n a p r o d u c t m a r k e t f o r w h i c h i t r e q u i r e s f u n d s f r o m t h e c a p i t a l m a r k e t . T h e c o n s e q u e n c e s o f h i s d i s c l o s u r e d e c i s i o n d e p e n d o n t h e a c t i o n o f a n o p p o n e n t , t e r m e d t h e " e n t r a n t " (E), a n d t h e " c a p i t a l m a r k e t ' s " (M) v a l u a t i o n o f t h e s e c u r i t i e s i s s u e d b y t h e i n c u m b e n t . R e l a t i n g o u r m o d e l t o t h e k e y d i m e n s i o n s we u s e d t o c l a s s i f y t h e a n a l y t i c a l d i s c l o s u r e m o d e l s i n t h e 1 T h e r e h a v e b e e n a n u m b e r o f m o d e l s i n w h i c h management a c t i o n s , s u c h a s t h e i r c h o i c e o f d i v i d e n d p o l i c y o r c a p i t a l s t r u c t u r e , a r e v i e w e d a s m e t h o d s o f p r o v i d i n g o u t s i d e r s w i t h a s s u r a n c e s t h a t t h e y a r e n o t l y i n g . 89 l a s t c h a p t e r , we s u m m a r i z e o u r a s s u m p t i o n s a s f o l l o w s : (1) T h e m a n a g e r s e e k s t o m a x i m i z e t h e e x p e c t e d e n d - o f - p e r i o d v a l u e o f t h e i n i t i a l s h a r e -h o l d e r s ' e q u i t y i n I . (2) T h e m a n a g e r m u s t o b t a i n f u n d s f r o m M a n d t h e " c o s t " o f t h o s e f u n d s d e p e n d s o n M ' s b e l i e f s r e g a r d i n g t h e m a n a g e r ' s p r i v a t e i n f o r m a t i o n a n d t h e a c t i o n t h a t E w i l l t a k e . (3) T h e i n f o r m a t i o n i s p r o p r i e t a r y i n t h e s e n s e t h a t i t s d i s c l o s u r e c a n i n f l u e n c e I ' s e n d -o f - p e r i o d c a s h f l o w . (4) T h e i m p a c t o f d i s c l o s u r e o n I ' s e n d - o f -p e r i o d c a s h f l o w i s n o t e x o g e n o u s , b u t i n s t e a d d e p e n d s o n t h e E ' s a c t i o n . (5) E e m p l o y s a s i m p l e d e c i s i o n r u l e : E " e n t e r s " i f , a n d o n l y i f , t h e e x p e c t e d l e v e l o f I ' s p r i v a t e i n f o r m a t i o n ( b a s e d o n t h e i n f o r m a t i o n a v a i l a b l e t o E) e x c e e d s E ' s " b r e a k - e v e n " p o i n t . " E n t r y " b y E r e d u c e s I ' s e n d - o f - p e r i o d c a s h f l o w . T h e r e i s n o o t h e r e x p l i c i t m o d e l l i n g o f t h e p r o d u c t m a r k e t . (6) T h e p r o b a b i l i t y t h a t t h e m a n a g e r h a s n o p r i v a t e i n f o r m a t i o n i s a s s u m e d t o b e z e r o . A l t e r n a t i v e l y , we c a n p e r m i t t h e p r o b a -b i l i t y o f n o p r i v a t e i n f o r m a t i o n t o b e p o s i t i v e , a n d t h e n a s s u m e t h a t t h e m a n a g e r c a n c o s t l e s s l y c o m m u n i c a t e w h e t h e r o r n o t h e h a s r e c e i v e d i n f o r m a t i o n . T h a t i s , n o i n f o r m a t i o n c a n b e d i s t i n g u i s h e d f r o m n o n -d i s c l o s u r e . (7) We c o n s i d e r a c o n t i n u u m o f p o s s i b l e m a n a g e r " t y p e s " , i . e . , a c o n t i n u u m o f p o s s i b l e p r i v a t e i n f o r m a t i o n s i g n a l s . (8) T h e m a n a g e r m a k e s h i s d i s c l o s u r e d e c i s i o n a f t e r h e o b s e r v e s h i s p r i v a t e i n f o r m a t i o n . O u r b a s i c m o d e l i s v e r y s i m i l a r t o W a g e n h o f e r [ 1990 ] e x c e p t t h a t i n h i s m o d e l I r e q u i r e s n o f u n d s f r o m t h e 90 c a p i t a l m a r k e t a n d t h e m a n a g e r s e e k s t o m a x i m i z e t h e c u r r e n t m a r k e t v a l u e o f t h e f i r m . W i t h r e s p e c t t o t w o d i m e n s i o n s , o u r m o d e l i s t h e same a s t h a t o f D a r r o u g h a n d S t o u g h t o n [ 1 9 9 0 ] , b u t we d i f f e r f r o m t h e i r m o d e l i n t h a t t h e y o n l y c o n s i d e r b i n a r y p r i v a t e i n f o r m a t i o n — t h e m a n a g e r g e t s e i t h e r " g o o d " news o r " b a d " n e w s . A k e y f e a t u r e t h a t d i s t i n g u i s h e s o u r a n a l y s i s f r o m b o t h o f t h e s e p a p e r s , a n d m o s t o t h e r d i s c l o s u r e m o d e l s , i s t h a t we i n t r o d u c e p r i v a t e e n t r a n t i n f o r m a t i o n . T h a t i s , we a l l o w f o r t h e p o s s i b i l i t y t h a t I may n o t know E ' s b r e a k - e v e n p o i n t a n d , t h e r e f o r e , d o e s n o t know w h a t b e l i e f s w i l l i n d u c e E t o e n t e r . T h e m a j o r i m p a c t o f t h i s c h a n g e i s t o e l i m i n a t e e q u i l i b r i a i n w h i c h I p a r t i a l l y d i s c l o s e s h i s i n f o r m a t i o n a n d E p l a y s a m i x e d s t r a t e g y . I n t h e m o d e l i n w h i c h E h a s p r i v a t e i n f o r m a t i o n , E p l a y s a p u r e s t r a t e g y , w h e t h e r I f u l l y d i s c l o s e s h i s p r i v a t e i n f o r m a t i o n o r n o t . S e c t i o n 3 . 2 p r e s e n t s t h e b a s i c e l e m e n t s o f o u r d i s -c l o s u r e m o d e l , i n c l u d i n g a s t a t e m e n t o f t h e s e q u e n c e o f e v e n t s . S e c t i o n 3 . 3 i d e n t i f i e s t h e a l t e r n a t i v e d i s c l o s u r e p o l i c i e s t h a t I m i g h t e m p l o y , c h a r a c t e r i z i n g h i s e x p e c t e d w e a l t h a s a f u n c t i o n o f h i s i n f o r m a t i o n f o r b o t h t h e f u l l d i s c l o s u r e a n d p a r t i a l d i s c l o s u r e p o l i c i e s . T h i s c h a r a c -t e r i z a t i o n i s p r o v i d e d f o r t h r e e d i f f e r e n t a s s u m p t i o n s w i t h r e s p e c t t o I ' s k n o w l e d g e a b o u t E ' s b r e a k - e v e n p o i n t . S e c t i o n 3 . 4 i d e n t i f i e s t h e c o n d i t i o n s u n d e r w h i c h f u l l d i s c l o s u r e e q u i l i b r i a e x i s t , p r o v i d i n g e x p l i c i t c h a r a c t e r -i z a t i o n o f t h e s e c o n d i t i o n s i n t e r m s o f t h e a m o u n t o f c a p i t a l r e q u i r e d b y I a n d t h e c o s t s i n c u r r e d i f E e n t e r s I ' s m a r k e t . S e c t i o n 3 . 5 e x t e n d s t h i s c h a r a c t e r i z a t i o n t o t h e i d e n t i f i c a t i o n o f t h e c o n d i t i o n s u n d e r w h i c h p a r t i a l d i s c l o s u r e e q u i l i b r i a e x i s t . S e c t i o n 3 . 6 d i s c u s s e s some o f t h e i s s u e s t h a t a r i s e w h e n t h e r e a r e m u l t i p l e e q u i l i b r i a , a n d p r e s e n t s t h e i m p l i c a t i o n s o f some r e f i n e m e n t s o f t h e b a s i c s e q u e n t i a l e q u i l i b r i u m c o n c e p t . F i n a l l y , s e c t i o n 3 . 7 p r o v i d e s some c o n c l u d i n g r e m a r k s . A n i n t e r e s t i n g a s p e c t o f t h e e q u i l i b r i a i d e n t i f i e d i n t h i s p a p e r i s t h a t t h e r e a r e two t y p e s o f f u l l d i s c l o s u r e e q u i l i b r i a a n d t w o t y p e s o f p a r t i a l d i s c l o s u r e e q u i l i b r i a . T h e f u l l d i s c l o s u r e e q u i l i b r i a d i f f e r o n l y i n t h e way i n w h i c h M a n d E w i l l r e s p o n d t o n o n - d i s c l o s u r e . I n o n e t y p e , n o n - d i s c l o s u r e w i l l i n d u c e M t o p r o v i d e t h e d e s i r e d c a p i t a l a t t h e l e a s t f a v o u r a b l e t e r m s p o s s i b l e . I n t h e o t h e r t y p e , n o n - d i s c l o s u r e w i l l i n d u c e E t o e n t e r I ' s m a r k e t w i t h p r o b a b i l i t y o n e . T h e p a r t i a l d i s c l o s u r e e q u i l i b r i a d i f f e r w i t h r e s p e c t t o t h e r e l a t i o n s h i p b e t w e e n t h e m a r k e t v a l u e o f t h e d i s c l o s i n g a n d n o n - d i s c l o s i n g f i r m s . I n t h e " l o w " c a s e , t h e m a r k e t v a l u e o f t h e n o n -d i s c l o s i n g f i r m s i s l e s s t h a n a l l d i s c l o s i n g f i r m s , w h e r e -a s i n t h e " h i g h " c a s e , t h e r e a r e some d i s c l o s i n g f i r m s t h a t h a v e l o w e r m a r k e t v a l u e s t h a n t h e n o n - d i s c l o s i n g f i r m s . T h e k e y f a c t o r i n t h e e x i s t e n c e o f t h e v a r i o u s e q u i -l i b r i a i s t h e r e l a t i v e i m p o r t a n c e t o I o f u n d e r - v a l u a t i o n b y M v e r s u s e n t r y b y E . T h e i m p o r t a n c e o f u n d e r - v a l u a t i o n i n c r e a s e s a s t h e a m o u n t o f c a p i t a l r e q u i r e d i n c r e a s e s , w h e r e a s t h e i m p o r t a n c e o f e n t r y i n c r e a s e s .as e n t r y c o s t s i n c u r r e d b y t h e i n c u m b e n t 2 i n c r e a s e . T h e o t h e r i n t e r e s t i n g r e s u l t s p e r t a i n t o t h e r e f i n e -m e n t o f p o s s i b l e m u l t i p l e e q u i l i b r i a . U n d e r a s i m p l i f i e d d i s t r i b u t i o n a s s u m p t i o n , we p r o v e d t h a t b o t h f u l l d i s c l o s -u r e a n d p a r t i a l d i s c l o s u r e w i l l n o t f a i l t h e C h o a n d K r e p s ' i n t u i t i v e s t a b i l i t y c r i t e r i o n i f t h e y d o e x i s t . H o w e v e r , a f u l l d i s c l o s u r e e q u i l i b r i u m w i l l f a i l G r o s s m a n a n d P e r r y ' s p e r f e c t e q u i l i b r i u m c r i t e r i o n i f t h e r e a l s o e x i s t s a p a r t i a l d i s c l o s u r e e q u i l i b r i u m . F u r t h e r m o r e , a p a r t i a l d i s c l o s u r e e q u i l i b r i u m w i l l f a i l t h e G r o s s m a n a n d P e r r y c r i t e r i o n when t h e r e e x i s t s a n o t h e r p a r t i a l e q u i l i b -r i u m w h i c h d o m i n a t e s t h e f i r s t . 2 I n m o s t o f t h e e n t r y game l i t e r a t u r e , " e n t r y c o s t " r e f e r s t o t h e c o s t i n c u r r e d b y t h e e n t r a n t i f h e c h o o s e s t o e n t e r a m a r k e t . I n t h i s c h a p t e r , we u s e " e n t r y c o s t " t o r e f e r t o t h e r e d u c t i o n i n p r o f i t i n c u r r e d b y t h e i n c u m b e n t i f t h e e n t r a n t e n t e r s . 93 3.2 The Basic Model We f o c u s on t h e d i s c l o s u r e d e c i s i o n made by t h e manager o f an incumbent f i r m t h a t i s about t o i n v e s t i n a new m a r k e t . The manager a c t s on b e h a l f o f t h e f i r m ' s c u r r e n t e q u i t y - h o l d e r s and I i s used t o denote b o t h t h e manager a c t i n g i n t h a t c a p a c i t y and t h e c u r r e n t e q u i t y -h o l d e r s . I i s assumed t o seek t o maximize t h e e x p e c t e d e n d - o f - p e r i o d c a s h f low o f t h e f i r m . The f o c u s on "expected c a s h f low" i m p l i e s r i s k n e u t r a l i t y , w h i c h can be m o t i v a t e d by an as sumpt ion t h a t the c u r r e n t e q u i t y - h o l d e r s a r e w e l l - d i v e r s i f i e d i n v e s t o r s 3 and t h e r i s k s a s s o c i a t e d w i t h I ' s d e c i s i o n s a r e d i v e r s i f i a b l e . I ' s f o c u s on t h e e n d - o f - p e r i o d v a l u e , as opposed t o c u r r e n t market v a l u e , a l s o r e s u l t s from d i v e r s i f i c a t i o n . As demons tra ted by F e l t h a m and C h r i s t e n s e n [1988] , w e l l - d i v e r s i f i e d i n v e s t o r s i n a l a r g e economy can a c h i e v e an e f f i c i e n t a l l o c a t i o n o f r e s o u r c e s and consumpt ion w i t h o u t knowing each manager 's f i r m - s p e c i f i c i n f o r m a t i o n as l o n g as t h e manager o f each f i r m i n an i n v e s t o r ' s p o r t f o l i o a c t s so as t o maximize t h e " t r u e v a l u e " o f i n v e s t o r ' s e q u i t y . The b a s i c sequence o f event s a r e d e p i c t e d i n T a b l e 3 -3 P a u l F i s c h e r r a i s e s an i n t e r e s t i n g q u e s t i o n w i t h r e g a r d t o t h e o b j e c t i v e s o f w e l l - d i v e r s i f i e d i n v e s t o r s i f t h e y h o l d s h a r e s i n b o t h f i r m s I and E. We e f f e c t i v e l y assume t h e f i r m s a r e owned by two d i f f e r e n t s e t s o f w e l l d i v e r s i f i e d i n v e s t o r s a n d , hence , they have no i n c e n t i v e t o m o t i v a t e t h e managers* o f t h e f i r m s t o c o l l u d e . 94 1 . I n a d d i t i o n t o t h e i n c u m b e n t ( I ) , we c o n s i d e r t h e c a p i t a l m a r k e t (M) a n d a p o t e n t i a l e n t r a n t ( E ) . I n s e r t T a b l e 3 - 1 h e r e T h e p l a n n e d i n v e s t m e n t r e q u i r e s k d o l l a r s o f c a p i t a l , w h i c h m u s t b e o b t a i n e d f r o m t h e c a p i t a l m a r k e t (M) . T h e e n d - o f - p e r i o d c a s h f l o w o f t h e f i r m ( I ' s p a y o f f ) i s a r a n d o m v a r i a b l e x , f r o m w h i c h I w i l l c o m p e n s a t e M f o r t h e f u n d s s u p p l i e d . I ' s p r i v a t e i n f o r m a t i o n a b o u t x i s r e p r e -s e n t e d b y a r a n d o m v a r i a b l e /2; t h e r e a l i z e d v a l u e \i i s I ' s t y p e . We a s s u m e t h a t \X i s d e n o m i n a t e d s o t h a t i t s c u m u -l a t i v e d i s t r i b u t i o n f u n c t i o n , d e n o t e d $(ju) , i s d e f i n e d o n t h e u n i t i n t e r v a l [ 0 , 1 ] . I ' s e x p e c t e d p a y o f f i f t h e i n v e s t m e n t i s n o t u n d e r -t a k e n i s JT° > 0 . I f t h e i n v e s t m e n t i n t h e new m a r k e t i s u n d e r t a k e n , t h e n t h e p a y o f f w i l l b e i n f l u e n c e d b y w h e t h e r E , a p o t e n t i a l c o m p e t i t o r , c h o o s e s t o e n t e r t h e same m a r k e t . I f E d o e s n o t e n t e r ( e = 0 ) , t h e n I w i l l b e a m o n o p o l i s t a n d t h e c u m u l a t i v e d i s t r i b u t i o n f u n c t i o n f o r x g i v e n t h a t I i s t y p e / i i s F ( x | / z , 0 ) , x e [ 0 , « > ) . On t h e o t h e r h a n d , i f E d o e s e n t e r ( e = l ) , t h e n I w i l l b e a d u o p o l i s t a n d t h e c u m u l a t i v e d i s t r i b u t i o n f u n c t i o n f o r x g i v e n t h a t I i s t y p e /x i s F ( x | / ^ , 1 ) , x e [ 0 , o o ) . T h e p o s t e r i o r m e a n s i n 95 both cases are assumed to be l i n e a r functions of u; 4 i n p a r t i c u l a r , 7t(|A,0) - E[^\ifO] - J xdF(xln,0) - a\x + b o eo 11(11,1) = E[.xlu,,l] - j xdF(j>du.,l) - c\i + d 0 We make the following assumptions with respect to the payoff parameters: (A.l) a > 0 and a-c = S e [0,a]. The expected payoff i s an increasing function of u (e.g., a bigger u indicates a more favourable market) and there i s a non-negative v a r i a b l e entry cost, S. (A.2) d-k > i r ° and b-d = A e [0,b-k - r r 0 ] . Entry by I i s desirable even i f u = 0 and E enters, and there i s a non-negative fi x e d entry cost, A. (A.3) S > 0 and/or A > 0. There i s a s t r i c t l y p o s i -t i v e entry cost. Two s p e c i a l cases are of p a r t i c u l a r i n t e r e s t i n subsequent analysis: Variable entry cost: d = b and a-c = 6 e (0,a]. ^Appendix 3.A describes a product market i n which the s e l l i n g p r i c e i s a l i n e a r decreasing function of the t o t a l output supplied by I and E and I has private information about the intercept of that p r i c e function. The expected p r o f i t s are not l i n e a r functions of I ' s pr i c e information, but the appendix demonstrates how the l i n e a r model used i n t h i s paper can be interpreted as a representation of that market. 96 F i x e d e n t r y c o s t : 5 c = a a n d b - d = A e ( 0 , b - k - 7 r 0 ] . T h e s e r e l a t i o n s h i p s a r e d e p i c t e d i n F i g u r e 3 - 1 . W h e r e a s I w i l l e n t e r t h e m a r k e t n o m a t t e r w h a t i n f o r m a t i o n h e h a s , E ' s e n t r y c o s t s a r e a s s u m e d t o b e s u c h t h a t h e w i l l o n l y e n t e r i f h i s e x p e c t a t i o n a b o u t I ' s t y p e /x i s a t l e a s t a s l a r g e a s h i s b r e a k - e v e n p o i n t , d e n o t e d y . We c a n m o t i v a t e t h i s b y a s s u m i n g t h a t E t o o m a x i m i z e s h i s e x p e c t -e d e n d - o f - p e r i o d c a s h f l o w a n d t h a t h i s v a l u e i s a l s o a n i n c r e a s i n g l i n e a r f u n c t i o n o f /x, w h e r e fi r e p r e s e n t s i n f o r -m a t i o n a b o u t d e m a n d i n t h e m a r k e t o f i n t e r e s t . L e t y d e n o t e M a n d E ' s i n f o r m a t i o n a b o u t p a t t h e t i m e t h e y make t h e i r d e c i s i o n s , l e t t h e i r p o s t e r i o r b e l i e f s w i t h r e s p e c t t o p b e r e p r e s e n t e d b y t h e c u m u l a t i v e d i s t r i b u t i o n f u n c t i o n $ ( / x | y ) , a n d l e t t h e i r p o s t e r i o r e x p e c t a t i o n w i t h r e s p e c t t o p h e d e n o t e d v ( y ) . H e n c e , E ' s b r e a k - e v e n p o i n t i s a r a n d o m v a r i a b l e y w i t h a p r i o r c u m u l a t i v e d i s t r i b u t i o n f u n c t i o n G ( y ) d e f i n e d o n t h e u n i t i n t e r v a l . E l e a r n s h i s b r e a k - e v e n p o i n t (y = Y) 5 D a r r o u g h a n d S t o u g h t o n [1990] a n d W a g e n h o f e r [ 1990 ] f o c u s o n t h i s c a s e . I n s e r t F i g u r e 3 - 1 h e r e i (3 .2 .1 ) o 97 p r i o r t o m a k i n g h i s e n t r y d e c i s i o n ; h e e n t e r s w i t h c e r -t a i n t y i f v ( y ) > y a n d d o e s n o t e n t e r i f v ( y ) < y . 6 We a l l o w f o r t h e p o s s i b i l i t y t h a t E may p l a y a m i x e d e n t r y s t r a t e g y i f h e i s i n d i f f e r e n t b e t w e e n e n t e r i n g a n d n o t e n t e r i n g . H e n c e , we r e p r e s e n t h i s s t r a t e g y a s a f u n c t i o n o f t h i s p o s t e r i o r e x p e c t a t i o n v w i t h r e s p e c t t o I ' s t y p e a n d h i s own b r e a k - e v e n p o i n t : e ( v , Y)< - 1 if v > Y 6 [ 0 , 1 ] i f " v - Y ( 3 . 2 . 2 ) - 0 if v < Y I a n d M d o n o t o b s e r v e E ' s b r e a k - e v e n p o i n t p r i o r t o m a k i n g t h e i r d e c i s i o n s . H o w e v e r , t h e y d o o b s e r v e t h e i n f o r m a t i o n y t h a t E r e c e i v e s a b o u t I ' s t y p e a n d , t h e r e -f o r e , know h i s p o s t e r i o r e x p e c t a t i o n v ( y ) . C o n s e q u e n t l y , f r o m I a n d M ' s p e r s p e c t i v e , g i v e n p o s t e r i o r e x p e c t a t i o n v a n d E ' s s t r a t e g y e ( » ) , t h e p r o b a b i l i t y t h a t E w i l l e n t e r i s i p ( v ) - | e ( v , Y > d G ( Y ) ( 3 . 2 . 3 ) o O b s e r v e t h a t t h e r e a r e t w o r e a s o n s why I a n d M may b e ^ e a s s u m e t h a t t h e p l a y e r ' s s t r a t e g i e s i n t h i s t h r e e -p e r s o n game c o n s t i t u t e a s e q u e n t i a l e q u i l i b r i u m . S e q u e n t i a l r a t i o n a l i t y r e q u i r e s t h a t E s e l e c t t h e a c t i o n t h a t m a x i m i z e s h i s e x p e c t e d p a y o f f g i v e n h i s b e l i e f s a t t h e t i m e h e t a k e s h i s a c t i o n . 98 u n c e r t a i n a b o u t w h e t h e r E w i l l e n t e r . F i r s t , t h e y may b e u n c e r t a i n a b o u t h i s b r e a k - e v e n p o i n t . S e c o n d , e v e n i f t h e y know y ( b e c a u s e G ( y ) i s c o n c e n t r a t e d o n a s i n g l e m a s s p o i n t ) , E may b e i n d i f f e r e n t b e t w e e n e n t e r i n g / n o t e n t e r i n g a n d b e p l a y i n g a m i x e d s t r a t e g y . T h e s e t w o p e r s p e c t i v e s p l a y a n i m p o r t a n t r o l e i n o u r s u b s e q u e n t a n a l y s i s . We r e f e r t o c a s e s i n w h i c h G ( y ) i s c o n c e n t r a t e d a t a s i n g l e m a s s p o i n t y a s o n e s i n w h i c h E ' s b r e a k - e v e n p o i n t i s common k n o w l e d g e . 7 a n d t o c a s e s i n w h i c h G * ( y ) > 0 V y e ( 0 , 1 ) a s o n e s i n w h i c h E ' s b r e a k - e v e n p o i n t i s n o t  common k n o w l e d g e . O b s e r v e t h a t i n t h e l a t t e r c a s e , m i x e d s t r a t e g i e s a r e o f n o c o n s e q u e n c e a n d t h e p r o b a b i l i t y t h a t E w i l l e n t e r i s p ( v ) - G ( v ) ( 3 . 2 . 4 ) T h a t i s , t h e p r o b a b i l i t y o f e n t r y i s e q u a l t o t h e p r o b -a b i l i t y t h a t E ' s t y p e i s l e s s t h a n E ' s e x p e c t a t i o n a b o u t [i g i v e n y . ( I f E ' s b r e a k - e v e n p o i n t i s common k n o w l e d g e , t h e n ( 3 . 2 . 4 ) d e f i n e s t h e maximum e n t r y p r o b a b i l i t y g i v e n e x p e c t a t i o n v . ) M a n d E h a v e t h e same i n f o r m a t i o n y a b o u t I ' s t y p e when t h e y make t h e i r d e c i s i o n s . T h i s i n f o r m a t i o n c o n s i s t s o f t w o e l e m e n t s : a r e p o r t ( o r " n o r e p o r t " ) made b y I r e g a r d i n g h i s t y p e a n d t h e c o n t r a c t a o f f e r e d t o M i n 7 T h a t i s , G ( y ) = 0 V y e [ 0 , y ) a n d G ( y ) = 1 V y e [ y , l ] . 99 r e t u r n f o r k u n i t s o f c a p i t a l . L e t m r e p r e s e n t t h e r e p o r t ( m e s s a g e ) s e n t b y I r e g a r d i n g h i s t y p e a n d l e t M ( u ) = {u ,n} r e p r e s e n t t h e s e t o f p o s s i b l e r e p o r t s t h a t c a n b e s e n t b y I i f h e i s t y p e u , w i t h m = u r e p r e s e n t i n g d i s -c l o s u r e o f h i s t y p e a n d m = n r e p r e s e n t i n g " n o r e p o r t " . O b s e r v e t h a t we d o n o t a l l o w I t o l i e a b o u t h i s t y p e . T h i s c a n b e m o t i v a t e d b y a s s u m i n g t h a t e i t h e r t h e r e i s a c o s t l e s s v e r i f i c a t i o n m e c h a n i s m a n d I c h o o s e s w h e t h e r t o u s e t h a t m e c h a n i s m o r t h e r e a r e p e n a l t i e s i m p o s e d b y a n t i -f r a u d l a w s a n d d e t e c t i o n m e c h a n i s m s t h a t a r e s u f f i c i e n t t o d e t e r I f r o m l y i n g . A n i m p l i c a t i o n o f t h i s a s s u m p t i o n i s t h a t v ( u , a ) = u f o r a l l a . A k e y i s s u e i s t h e n a t u r e o f t h e c o n t r a c t o f f e r e d b y I t o M i n r e t u r n f o r c a p i t a l k . F o l l o w i n g D a r r o u g h a n d S t o u g h t o n [ 1 9 9 0 ] , i n m o s t o f o u r a n a l y s i s we a s s u m e t h a t I o b t a i n s i t s c a p i t a l b y o f f e r i n g M e q u i t y i n t h e f i r m . 8 A n o b v i o u s a l t e r n a t i v e w o u l d b e t o i s s u e d e b t , p a r t i c u l a r -l y i f t h e d e b t i s r i s k l e s s ( i . e . , F ( k | u , e ) = 0 , V u e [ 0 , l ] , e e { 0 , l } ) . I f d e b t i s r i s k y , t h e n much t h e same i s s u e s a r i e s a s o c c u r w i t h t h e i s s u a n c e o f e q u i t y . T h e e q u i t y c o n t r a c t i s r e p r e s e n t e d b y a , t h e s h a r e o f 8 T h e a s s u m p t i o n t h a t I o b t a i n s c a p i t a l t h r o u g h o n l y i s s u i n g e q u i t y r e m o v e s t h e p o s s i b i l i t y o f s i g n a l l i n g t h r o u g h t h e c h o i c e o f p a y o f f f u n c t i o n o n t h e s e c u r i t y , a s i s d o n e i n B r e n n a n a n d K r a u s [ 1 9 8 7 ] . O f c o u r s e , s u c h s i g n a l l i n g i s n o t n e c e s s a r y i n o u r a n a l y s i s s i n c e i t i s a s s u m e d t h a t d i r e c t d i s c l o s u r e i s v i a b l e . 100 I ' s p a y o f f t o b e r e c e i v e d b y M. M c a n e i t h e r a c c e p t (r=0) o r r e j e c t ( r = l ) t h e c o n t r a c t , 9 a n d we a s s u m e t h a t M w i l l o n l y r e j e c t a c o n t r a c t i f , b a s e d o n i n f o r m a t i o n y , M b e l i e v e s t h a t t h e c o n t r a c t h a s a n e g a t i v e n e t p r e s e n t v a l u e . 1 0 L e t V ( v , p ) d e n o t e t h e e x p e c t e d e n d - o f - p e r i o d c a s h f l o w o f t h e f i r m g i v e n t h a t M h a s e x p e c t a t i o n v a b o u t I ' s t y p e a n d b e l i e v e s t h a t E w i l l e n t e r w i t h p r o b a b i l i t y p_, i . e . , V ( v , p ) - p - * ( v , l ) + (1 - p ) - i t ( v , 0) ( 3 . 2 . 5 ) T h i s v a l u e d e t e r m i n e s t h e m i n i m u m s h a r e o f I ' s p a y o f f t h a t M w i l l a c c e p t i n r e t u r n f o r c a p i t a l k , g i v e n e x p e c t a t i o n v a n d e n t r y p r o b a b i l i t y p . We r e p r e s e n t t h a t m i n i m u m s h a r e b y a * ( v , p ) - J c / V ( v , p ) ( 3 . 2 . 6 ) 9We m u s t s t r e s s t h a t t h e m a r k e t i s a p l a y e r i n t h e g a m e , b u t i t i s n o t a s t r a t e g i c p l a y e r . I n o t h e r w o r d s , t h e m a r k e t i s n o t a f u l l y a c t i v e p l a y e r i n o u r game i n t h a t i t d o e s n o t p l a y s t r a t e g i c a l l y . I n s t e a d , t h e m a r k e t i s q u i t e p a s s i v e a n d i s o n l y m o d e l l e d t o t h e e x t e n t o f c o n s i d e r i n g how i t f o r m s b e l i e f s a b o u t t h e f i r m ' s c a s h f l o w s . 1 0 We c o u l d a l l o w M t o p l a y a m i x e d s t r a t e g y i f t h e e x p e c t e d n e t r e t u r n i s z e r o . H o w e v e r , I c a n a l w a y s a v o i d t h i s c a s e b y s e t t i n g a s l i g h t l y h i g h e r . I t i s s u f f i c i e n t f o r o u r a n a l y s i s t o a l l o w o n l y E t o p l a y m i x e d s t r a t e g i e s , a n d t h e n o n l y when h i s b r e a k - e v e n p o i n t i s common k n o w l e d g e . 101 3 . 3 I ' s S t r a t e g y C h o i c e I ' s d i s c l o s u r e s t r a t e g y i s r e p r e s e n t e d b y N c [ 0 , 1 ] , t h e s e t o f s i g n a l s u t h a t w i l l n o t b e d i s c l o s e d . T h e s e t o f s i g n a l s u t h a t w i l l b e d i s c l o s e d a r e d e n o t e d D = [ 0 , 1 ] \N. T h e r e a r e t h r e e b a s i c k i n d s o f d i s c l o s u r e s t r a t e g i e s : ( i ) F u l l D i s c l o s u r e ( F D ) : D = [ 0 , 1 ] , N = 0; ( i i ) F u l l N o n - d i s c l o s u r e ( F N ) : D = 0, N = [ 0 , 1 ] ; a n d ( i i i ) P a r t i a l D i s c l o s u r e (PD) : D <= [ 0 , 1 ] , N = [ 0 , 1 ] \D, w h e r e b o t h D a n d N h a v e p o s i t i v e m e a s u r e . I ' s E x p e c t e d E n d - o f - p e r i o d W e a l t h : I ' s e x p e c t e d e n d - o f - p e r i o d w e a l t h , g i v e n s i g n a l u , c o n t r a c t a , m a r k e t r e s p o n s e r , a n d e n t r y p r o b a b i l i t y p_, i s W ( u , a,r.p) - ( 1 - r ) • (1-a) - V ( u , p ) + r - i c ° ( 3 . 3 . 1 ) O b s e r v e t h a t W(» ) i s a n i n c r e a s i n g l i n e a r f u n c t i o n o f u f o r e v e r y a e [ 0 , l ) , r e [ 0 , 1 ) , a n d p _ e [ 0 , l ] . R e c a l l t h a t i f I d i s c l o s e s h i s t y p e u , t h e n M a n d E ' s e x p e c t a t i o n i s v ( y ) = u . I n t h i s c a s e t h e p r o b a b i l i t y t h a t E w i l l e n t e r i s p = G ( u ) a n d s e q u e n t i a l r a t i o n a l i t y i m p l i e s t h a t t h e b e s t c o n t r a c t t h a t M w i l l a c c e p t i s a * ( u , G ( u ) ) . C o n s e q u e n t l y , I ' s maximum e x p e c t e d w e a l t h , g i v e n d i s c l o s u r e o f u a n d a n a c c e p t e d e q u i t y c o n t r a c t , c a n b e r e p r e s e n t e d a s 102 W D (u) = W ( u , a * ( u , G ( u ) ) , 0 , G ( u ) ) - [1 - i c / V ( u , G ( u ) ) ] - V ( n , G ( u ) ) - V ( u , G ( u ) ) - k (3.3.2) T h a t i s , I ' s e x p e c t e d w e a l t h i s e q u a l t o h i s e x p e c t e d p a y o f f m i n u s t h e c o s t o f t h e c a p i t a l i n v e s t e d . A s s u m e t h a t i f I d o e s n o t d i s c l o s e h i s i n f o r m a t i o n , t h e n h e w i l l o f f e r t h e l e a s t c o s t c o n t r a c t t h a t M w o u l d a c c e p t g i v e n M a n d E ' s e x p e c t a t i o n w i t h r e s p e c t t o I ' s t y p e g i v e n n o n - d i s c l o s u r e . I n t h a t c a s e , g i v e n n o n - d i s -c l o s u r e e x p e c t a t i o n v , t h e c o n t r a c t o f f e r e d a n d a c c e p t e d i s a * ( v , p ( v ) ) a n d t y p e u ' s e x p e c t e d w e a l t h c a n b e e x p r e s s e d a s W H ( | i , v , p ( v ) ) - W ( u , a * ( v , p ( v ) ) , 0 , p ( v ) ) - [1 - J c / V ( v , p ( v ) )] - V ( u , p ( v ) ) (3.3.3) F o r a n y g i v e n e x p e c t a t i o n v a n d e n t r y p r o b a b i l i t y p ( v ) , WN i s a n i n c r e a s i n g l i n e a r f u n c t i o n o f u . I s e l e c t s t h e d i s c l o s u r e c h o i c e t h a t w i l l m a x i m i z e h i s e x p e c t e d e n d - o f - p e r i o d w e a l t h . E q u a t i o n s ( 3 . 3 . 2 ) a n d ( 3 . 3 . 3 ) s p e c i f y t y p e / i ' s e x p e c t a t i o n s f o r d i s c l o s u r e a n d n o n - d i s c l o s u r e , r e s p e c t i v e l y , g i v e n h i s b e l i e f s a b o u t how E a n d M w i l l r e s p o n d t o h i s c h o i c e . L a t e r we e x a m i n e t h e i n t e r v a l s o v e r w h i c h I w i l l c h o o s e t o d i s c l o s e (WD > WN) a n d n o t t o d i s c l o s e (WD < WN) h i s t y p e . H o w e v e r , f i r s t we 103 c o n s i d e r t h e n a t u r e o f WD u n d e r s p e c i f i c d i s t r i b u t i o n a l a s s u m p t i o n s w i t h r e s p e c t t o E ' s b r e a k - e v e n p o i n t . I ' s E x p e c t e d w e a l t h f r o m f u l l d i s c l o s u r e ; I n t h i s a n a l y s i s we a s s u m e t h a t t h e p r i o r b e l i e f s a b o u t E ' s b r e a k - e v e n p o i n t a r e c h a r a c t e r i z e d b y a b e t a d i s t r i b u t i o n o n t h e u n i t i n t e r v a l , 1 1 i . e . , Y G(Y> - / P o - t ^ - U - O ^ d t V Y e ( 0 , l ) o w h e r e (3Q i s t h e n o r m a l i z i n g c o n s t a n t a n d /3 t , /?2 > 0 a r e e x o g e n o u s p a r a m e t e r s . T h e mean a n d v a r i a n c e o f t h i s d i s t r i b u t i o n a r e Y - E l y ] - P l Pi + P2 V a r t y ] -P r P 2 ( P i + P 2 ) 2 - ( P i + P 2 + i ) We r e s t r i c t o u r a n a l y s i s t o t h r e e s p e c i a l c a s e s : y Common K n o w l e d g e : /S, = n y , /32 = n ( l - y ) , a n d n -* <of s o t h a t v a r [ y ] -*• 0 a n d Y = y w i t h p r o b a b i l i t y o n e . U n i f o r m D i s t r i b u t i o n : /31 = /?2 = 1 , s o t h a t G ( y ) = y a n d y = 1 /2 U n i m o d e l D i s t r i b u t i o n : (Hy, f32 > 1 ( a n d f i n i t e ) . I n t h e u n i f o r m a n d u n i m o d e l c a s e s , G ' ( y ) > 0 V y e ( 0 , l ) , 1 1 S e e D e g r o o t [ 1 9 7 0 , p . 4 0 ] , 104 and we r e f e r to these as si t u a t i o n s i n which E 1 s break-even point i s not common knowledge. Figure 3-2 depicts WD f o r each of the three cases, and i s represented by the dark l i n e denoted "ABCD". Observe that WD i s bounded below by ?r(u,l) - k and above by 7r(u,0) - k. These are the expected net payoffs given that E enters or does not enter, r e s p e c t i v e l y . 1 2 Insert Figure 3-2 here Observe that when E•s break-even point y i s common knowledge, WD i s a "Z-shaped" broken-line. I t i s equal to 7r(u,0) - k f o r ue[0,y), and then drops to TT(U,1) - k for u e ( y , l ] . The dis c r e t e drop i s caused by the increase i n E's entry p r o b a b i l i t y from zero to one as the signa l u s h i f t s from being l e s s than E's break-even point to ex-ceeding i t . In the two cases i n which E's break-even point i s not common knowledge, W0 i s s t r i c t l y between the two bounds. In the uniform d i s t r i b u t i o n case, W0 i s concave and, i n Figure 3-2(b), "B" = W0(u*) i d e n t i f i e s the i n t e r i o r maxi-mum. In the unimodel d i s t r i b u t i o n case, WD i s i n i t i a l l y concave and then convex, producing an "S-shaped" curve. 1 2In t h i s figure, a = 1 5 , b = 37, c = 6 , d = 31, and k = 28. In the unimodel d i s t r i b u t i o n case, )31 = 5 and 0 2 = 10, implying that /30 = 10,010. 105 In Figure 3-2(c), "B" = w 0(u*) i s the l o c a l i n t e r i o r maxi-mum and " C " = W0(u.) i s the l o c a l i n t e r i o r minimum. (Recall, from (3.2 . 4 ) , that p(u) = G(u).) Lemma 3 . 3 . 1 ; 1 3 I f I and M's b e l i e f about y i s a uniform d i s t r i b u t i o n on (0,1), then WD i s con-cave ( s t r i c t l y concave i f 6 > 0). I f t h e i r b e l i e f i s a beta d i s t r i b u t i o n with /3,, 0 2 > 1, then: (a) There e x i s t s a type u Q e (0,1) such that WD i s s t r i c t l y concave on the i n t e r v a l (0,/x0) and s t r i c t l y convex on the i n t e r v a l ( u 0 , l ) ; and (b) There e x i s t types u* and u. such that u* e(0,u 0) i s a l o c a l i n t e r i o r maximum and u. e(u 0,l) i s a l o c a l i n t e r i o r minimum. C h a r a c t e r i z a t i o n o f D i s c l o s u r e and N o n - d i s c l o s u r e S e t s : The "Z" and "S" shapes of WD i n the common knowledge and unimodel d i s t r i b u t i o n cases (see Figure 3-2), and the l i n e a r i t y of WM, implies that, i n these cases, WN cannot i n t e r s e c t Wp more than three times. Furthermore, the concavity of WQ i n the uniform d i s t r i b u t i o n case and the l i n e a r i t y of WN implies that, i n t h i s case, WN cannot i n t e r s e c t WD more than twice. 1 3See the appendix for a proof of t h i s lemma, as well as the proofs f o r other lemmas and propositions. 106 Lemma 3.3.2:14 I f y = Y i s common knowledge or y has a unimodel beta d i s t r i b u t i o n , then WN i n t e r s e c t s WD at most three times. I f Y N A S A uniform d i s t r i b u t i o n , then WM i n t e r s e c t s W0 at most twice. To i l l u s t r a t e t h i s r e s u l t , Figure 3-3 depicts a case i n which y = y is common knowledge and the entry cost i s va r i a b l e . The dark l i n e "UVWXYZ" represents the maximum of W0 and WN at each /i i f , and only i f , WD(/i) > WN(/z,v ,p(v)) . Insert Figure 3-3 here An important implication of Lemma 3.3.2 i s that, i n the common knowledge and unimodel cases, i f N and D are non-empty sets with p o s i t i v e measure, then N and D consist of i n t e r v a l s and the number of i n t e r v a l s i n each set i s no more than two. Furthermore, i f both N and D consist of two i n t e r v a l s , then there e x i s t three types jx, < /x2 < /x3 at which WH i n t e r s e c t s WQ. These types are such t h a t : 1 5 1 4This lemma can be proven rigorously, but the proof i s tedious and we merely appeal to the reader's i n t u i t i o n given the shapes depicted i n Figure 3-2. 1 5In general, N consists of two i n t e r v a l s , but D can cons i s t of a single i n t e r v a l , with D2 empty. I t i s possible to have Dj empty, but only i n "knife-edge" cases that are not generic. 107 N - Nx U N2, withNx- [ 0 , u j , N2 - [ U 2 , U 3 ] D - Dx U D2, with Dx - u2) , D2 - (u 3 ,1] ( 3 . 3 . 4 ) In the common knowledge case, " 2 = y, whereas i n the unimodel d i s t r i b u t i o n case 0 < u x < ji* < u 2 < u, < u 3 < 1 In the uniform d i s t r i b u t i o n case, N consists of two i n t e r v a l s and such that: 0 < \xx < U * < u 2 < 1 N - N x U N2, withNx- [ C l l J , Nj - [^ 2/l] D - ( u ^ U j j ) ( 3 . 3 . 5 ) Observe that i f a n o n - t r i v i a l non-disclosure region N e x i s t s , then i t always includes types close to zero. However, i t does not necessarily follow that the d i s c l o -sure region D always contains types close to one. 108 3.4 F u l l Disclosure E q u i l i b r i a The basic equilibrium concept used i n t h i s paper i s that of a sequential equilibrium. 1 6 In our disc l o s u r e game, a sequential equilibrium i s represented by r = (N,a,r,e,v). The f i r s t element i s I's disc l o s u r e p o l i c y (characterized by h i s non-disclosure set N). The second (a) i s a function s p e c i f y i n g the contract offered to M by each type n e [0,1]. The t h i r d (r) i s a function s p e c i f y -ing the p r o b a b i l i t y with which M w i l l r e j e c t each possible contract given each possible report. The fourth (e) i s E's entry p r o b a b i l i t y given each possible break-even point t and each possible report and contract from I. The f i f t h (v) i s a function specifying M and E's expectation about I•s type given each possible report and contract from I. Sequential e q u i l i b r i a must have sequentially r a t i o n a l s t r a t e g i e s that are based on consistent b e l i e f s . Consis-tency of b e l i e f s implies that the poster i o r expectation v i s computed by Bayes' theorem i f possible. Sequential r a t i o n a l i t y requires that E enter i f h i s p o s t e r i o r expec-t a t i o n v i s l e s s than h i s break-even point and that M accept a contract i f v and a are such that he expects to earn a p o s i t i v e p r o f i t s . I, on the other hand, must have 1 6See Kreps and Wilson [1982]. We take some l i b e r t y i n applying t h e i r concept since, t e c h n i c a l l y , sequential e q u i l i b r i a are only defined f o r f i n i t e types and actions. 109 no incentive to disclose h i s information i f /xeN and have no incentive to o f f e r a contract other than a(/x) . In t h i s section we focus on f u l l d i sclosure e q u i l i b -r i a , i . e . , N = 0 . The following lemma s p e c i f i e s the basic condition that must be s p e c i f i e d f o r the existence of a f u l l d i s c l o s u r e equilibrium. Lemma 3.4.1; A f u l l disclosure sequential equi-l i b r i u m e x i s t s i f , and only i f , there i s an ex-pectation v such that W D(U) * W N(U.,V,G(V) ) V |i 6 [0,1] (3.4.1) where G(v) i s the maximum entry p r o b a b i l i t y that i s consistent with (3.2.2) and (3.2.3). This lemma establishes that, i f the r e q u i s i t e expec-t a t i o n v e x i s t s , then a f u l l d isclosure equilibrium can be sustained by l e t t i n g M and E hold expectation v i f I does not d i s c l o s e h i s information, no matter what contract he of f e r s . Furthermore, the necessity part of the lemma allows us to i d e n t i f y f u l l d isclosure e q u i l i b r i a by con-s i d e r i n g a s i n g l e non-disclosure expectation f o r a l l contracts. We r e f e r to a f u l l disclosure equilibrium that i s sustained by non-disclosure expectation v, s a t i s f y i n g (3.4.1), as an FD-v equilibrium. I n i t i a l l y we consider two extreme cases i n which f u l l d i s c l o s u r e i s the only sequential equilibrium. Later we 110 consider conditions under which the existence of f u l l d i s closure e q u i l i b r i a depend on the parameter values. Exogenous Entry Choice; E's action i s i r r e l e v a n t to I's disclosure p o l i c y choice i f E's p r o b a b i l i t y of entry i s independent of E's b e l i e f about / i . This occurs, f o r example, i f E's type i s known to be equal to e i t h e r zero or one. In the f i r s t case, E w i l l enter no matter what I disc l o s e s and i n the l a t t e r case E w i l l not enter no matter what I di s c l o s e s . Observe that, i n t h i s s e t t i n g , I would l i k e to have M hold as high an expectation of £ as possible, since t h i s w i l l give I the most favourable contract terms. However, as i s well-known, i n equilibrium i t i s not possible for I to withhold information i n an attempt to increase M's expectations. To see that t h i s i s the case, consider any measurable set N c [0,1]. I f M believes that I i s employ-ing t h i s strategy, then the best contract that I can obtain with non-disclosure i s a*(v,p), where However, fo r every n > v, iteN, V(/x,p) - k > w N(jx,v,p), for any exogenous p r o b a b i l i t y of entry p e [ 0 , l ] . That i s , the better types i n any non-disclosure "pool" always wants to l e t the market know that t h e i r firm i s worth more than the (3.4.2) 111 average member of that "pool". Proposition 3.4.2;17 I f the p r o b a b i l i t y of entry p i s independent of E's b e l i e f s , then the only sequential equilibrium i s a FD-0 e q u i l i -brium, i . e . , a f u l l - d i s c l o s u r e equilibrium i n which M holds b e l i e f v = 0 i f I does not d i s -close. C a p i t a l Obtained By Issuing Riskless Debt; I f I can issue r i s k l e s s debt to obtain the required k u n i t s of c a p i t a l , then the current market value of h i s firm i s immaterial to h i s disclosure decision. In t h i s case, I i s only concerned with E's b e l i e f s . In p a r t i c u -l a r , I would l i k e E to believe that u i s l e s s than y, so as to avoid the negative impact of E•s entry i n t o h i s market. I f E's type i s not common knowledge, then I i s moti-vated to always reveal u i n order to minimize the prob-a b i l i t y that E w i l l enter. To see t h i s , consider a mea-surable non-disclosure set N c [0,1] and l e t v = /2(N). Observe that the poorer types i n the pool, i . e . , a l l u < v, ueN, prefer to disc l o s e t h e i r type because G(u) < G(v). 1 7The preceding discussion sketches the proof of t h i s r e s u l t . 112 Proposition 3 . 4 . 3 1 1 8 I f I can obtain h i s c a p i -t a l by issuing r i s k l e s s debt and E's type i s not common knowledge, then the only sequential equi-l i b r i u m i s an FD-1 equilibrium, i . e . , a f u l l d i s c l o s u r e equilibrium i n which E holds b e l i e f v = 1 i f I does not d i s c l o s e . I f E's type i s common knowledge (y = y) , then I w i l l reveal h i s private information i f u < y a n c * v > y a n c * w i l l not d i s c l o s e i t i f u > y and v < y. Consequently, any equilibrium disclosure p o l i c y must be such that e i t h e r : (i) N c [y, l ] or ( i i ) [y,l] c N and p(N) < y. In (i) , any disclosure strategy such that N c [y,l] i s an equilibrium strategy — non-disclosure induces E to enter and a l l types i n the non-disclosure set are i n d i f f e r e n t between disclosure and non-disclosure. This equilibrium always exi s t s when E's type i s common knowledge and I can issue r i s k l e s s debt. In ( i i ) , i f u e [ y , l ] , then I hides h i s good news through non-disclosure, and non-disclosure does not induce E to enter because I also does not di s c l o s e for s u f f i c i e n t types worse than y. This equilibrium e x i s t s i f , and only i f , y > Ji (the a p r i o r i mean of I's type). A f u l l d i s c l o s u r e equilibrium e x i s t s i n t h i s s e t t i n g pro-vided that v > y. 18n The preceding discussion sketches the proof of t h i s r e s u l t . 113 Proposition 3.4.4; I f I can obtain h i s c a p i t a l by i s s u i n g r i s k l e s s debt and E's type i s common knowledge, with y e (0,1), then, (a) FD-v e q u i l i b r i a , V v e iy,l], always e x i s t . (b) An FN ( f u l l non-disclosure) equilibrium e x i s t s i f , and only i f , Y ^ P» (c) PD ( p a r t i a l disclosure) e q u i l i b r i a i n which N c [Y,1] always e x i s t , and PD e q u i l i b r i a i n which [y,l] c N e x i s t i f , and only i f y > P-Simultaneous Concern f o r Undervaluation and Entry; The preceding analysis establishes that an FD-0 equilibrium e x i s t s i f I i s only concerned with how M values h i s firm (I f u l l y d iscloses h i s information i n order to avoid undervaluation). On the other hand, an FD-1 equilibrium e x i s t s i f I i s only concerned with avoiding entry by E (I f u l l y discloses h i s information i n order to minimize the p r o b a b i l i t y of entry by E). We now consider s i t u a t i o n s i n which I i s concerned with both undervalua-t i o n by M and entry by E. This i s ensured by assuming that I must issue equity to M i n order to obtain the desired c a p i t a l and ei t h e r E's type i s not common know-ledge or i t i s common knowledge with Y 6 ( O f 1 ) * F u l l d i s c l o s u r e e q u i l i b r i a can e x i s t i n these contexts, with the form depending on whether undervaluation by M or entry by E i s I's dominant concern. The following proposition provides a precise charac-114 t e r i z a t i o n of the conditions under which various f u l l d i s c l o s u r e e q u i l i b r i a e x i s t when E's break-even point i s ei t h e r uniformly d i s t r i b u t e d or i s common knowledge. Proposition 3.4.5; I f E's break-even point y i s uniformly d i s t r i b u t e d (or common knowledge at y), then one of the three following p o s s i b i l i -t i e s hold: (a) an FD-0 equilibrium e x i s t s i f < d and k e [K^d]; (b) an FD-1 (or FD-y) equilibrium e x i s t s i f K, > 0 and k e [O^K^n[0,d] ; (c) an FD equilibrium does not e x i s t i f K, < Kg and k e (K 1,K 2)n [ 0,d]. In the uniform d i s t r i b u t i o n case K, - — [c + d] K, - — [6 + A] 1 c a and i n the common knowledge case K± - - L [dy + d] K, - J L [by + A] cy ^ ay To obtain greater i n s i g h t into the above proposition we consider the two sp e c i a l cases introduced i n section 3.2: the v a r i a b l e entry cost case i n which A = b-d = 0 and S = a-c > 0; and the fix e d entry cost case i n which 5 = a-c = 0 and A = b-d > 0. For a given basic value b, we can now consider the impact on disclosure of three elements of the model: maximum undervaluation (a), cost of entry (5 or A), and the amount of c a p i t a l required (k). The following 115 depicts the r e l a t i o n s h i p between these elements and the existence of f u l l disclosure e q u i l i b r i a when y i s uniform-l y d i s t r i b u t e d . Variable Entry Cost (d=b and <Se(0,a)): No FD equilibrium e x i s t s i f k £.(0,1^) An FD-0 equilibrium e x i s t s i f k e [K^d], where 6 K, - —b 2 a Small Fixed Entry Cost (c=a and Ae(0 ,5 ) , where A=ab/(a+b)): An FD-1 equilibrium e x i s t s i f k e (0,1^] An FD-0 equilibrium e x i s t s i f k e [K^d], where Kx - A [b+(a-A) ] Kj - Aip < K l cL 3. Large Fixed Entry Cost (c=a and Ae(A,b)): An FD-1 equilibrium e x i s t s i f k e (0,d] The above relationships f o r a l t e r n a t i v e l e v e l s of k and 6 or A are depicted i n Figure 3-4. In the variable entry cost case, a f u l l disclosure equilibrium e x i s t s , based on the threat of under-valuation (FD-0), i f large amounts of c a p i t a l are required. However, i f small amounts of c a p i t a l are required, then there i s no f u l l d i s c l o s u r e equilibrium — the threat of undervaluation i s 116 not s u f f i c i e n t l y strong and f u l l disclosure cannot be sustained by a threat of entry because low types face very small entry costs. As depicted i n Figure 3-4(a), the minimum c a p i t a l requirement necessary for the existence of an FD-0 equilibrium i s an increasing function of the v a r i a b l e entry cost. Insert Figure 3-4 here In the f i x e d entry cost case, a f u l l d isclosure equilibrium based on the threat of entry (FD-1) always ex i s t s f o r at l e a s t small amounts of c a p i t a l . In fact, i f the entry cost i s large, then an FD-1 equilibrium e x i s t s .) for a l l c a p i t a l requirements. On the other hand, i f the entry cost i s small and the c a p i t a l requirements are large, then we again have a s i t u a t i o n i n which there i s a f u l l d i s c l o s u r e equilibrium based on the threat of under-valuation (FD-0). In any event, as i l l u s t r a t e d i n Figure 3-4(b), at l e a s t one f u l l d isclosure equilibrium always ex i s t s i n the f i x e d entry cost case. The minimum c a p i t a l requirement f o r existence of an FD-0 equilibrium i s again an increasing function of the entry cost (for small A). In the two s p e c i a l cases considered above, the range of c a p i t a l requirements over which an FD-0 equilibrium e x i s t s i s independent of whether E's type i s common knowl-edge or not. More generally, i n the v a r i a b l e entry cost 117 case with common knowledge of E's type, the charac t e r i z -ation of existence of f u l l disclosure e q u i l i - b r i a i s p r e c i s e l y the same as above. In the fix e d entry cost case with common knowledge of E's type, we replace a with ay i n the characterization of the range of c a p i t a l f o r which an FD-y equilibrium (instead of an FD-1 equili-brium) i s v i a b l e . Now consider a beta d i s t r i b u t i o n with 0 1 # pz > 1. From Lemma 3.3.2 we know that, under these conditions, there e x i s t s a type /xQe(0,l) such that WD i s convex on (H0,l) and has a l o c a l i n t e r i o r minimum at n.e(nQ, 1) . We also have the following r e s u l t . Lemma 3 . 4 . 6 ; I f G(y) i s a beta d i s t r i b u t i o n with Py, p2 > 1, then there e x i s t s a unique type v e (/x*,l) such that, at n=v, dWD(u) _ dWN(n,v,G(v)) du, dp Using t h i s r e s u l t we obtain the following c h a r a c t e r i -zation of f u l l d i sclosure e q u i l i b r i a . Proposition 3 . 4 . 7 ; I f G(y) i s a beta d i s t r i b u -t i o n with fiy, P2 > 1, then, for v s a t i s f y i n g the conditions of Lemma 3.4.6, one of the following three p o s s i b i l i t i e s must hold: (a) an FD-0 equilibrium exists i f WM(/i,0,0) < W D(M) V n e (M.,1) ; 118 (b) an FD-v equilibrium e x i s t s i f WN(0,v,G(v)) * WD(0) ;-(c) an FD equilibrium does not e x i s t i f neither (a) nor (b) hold. I t i s d i f f i c u l t to determine the parameter values that produce these r e s u l t s because v i s endogenously determined by those values. However, the characterization i s s i m i l a r to the case i n which E's type i s common know-ledge. In the variable entry cost case we again have the s i t u a t i o n i n which there i s never an FD-v equilibrium and an FD-0 equilibrium can be sustained i f ke[b6/a,d]. 119 3 . 5 P a r t i a l Disclosure E q u i l i b r i a The analysis i n the preceding section i d e n t i f i e s conditions under which f u l l d i sclosure e q u i l i b r i a e x i s t . This section i d e n t i f i e s conditions under which p a r t i a l e q u i l i b r i a e x i s t , and examines t h e i r basic c h a r a c t e r i s -t i c s . A p a r t i a l disclosure equilibrium always e x i s t s i f there i s no f u l l d i sclosure equilibrium and, f o r some parameter values, there can be both f u l l and p a r t i a l d i sclosure equilibrium. The following section discusses some of the issues that a r i s e when there are multiple e q u i l i b r i a . General Characterization of E f f i c i e n t P a r t i a l Dis- closure E q u i l i b r i a ; A sequential equilibrium r = (N,a,r,e,v) i s termed a p a r t i a l d isclosure (PD) equilibrium i f both N and D = I\N are measurable subsets of I. The previous section has established that a p a r t i a l equilibrium can only e x i s t i f I faces simultaneous threats of under-valuation by M and entry by E. Hence, i n t h i s section we assume that I must obtain h i s desired c a p i t a l k by issuing equity to M and that E's break-even point i s e i t h e r not common knowledge or i s common knowledge at ye(0,1). In any sequential equilibrium, type uel w i l l o f f e r 120 the optimal contract ct*(v,p(v)) i f he d i s c l o s e s h i s type. 1 9 In t h i s section, we consider only those p a r t i a l d i s c l o s u r e e q u i l i b r i a i n which I o f f e r s optimal contract °*( v»P(v)) i f "cN, where v = p(N) and p(v) i s consistent with (3.2.2) and (3.2.3). That i s , we consider only those e q u i l i b r i a i n which a l l types who do not d i s c l o s e t h e i r p r i v a t e information, o f f e r (and obtain acceptance) of the optimal contract given M and E's b e l i e f s . Lemma 3.3.2, and the associated discussion and f i g -ures, establishes that any p a r t i a l d i s c l o s u r e equilibrium ./Zan be characterized by the points at which WN i n t e r s e c t s WQ. (See figure 3-3 f o r an i l l u s t r a t i o n of the following r e s u l t . ) Lemma 3.5.1; If r = (N,a,r ,e,v) i s a p a r t i a l d i s c l o s u r equilibrium i n which a(ii) = a 0 = a*(v°, P(v 0 ) ) , V /xeN, where v° = v(n,a°) = £t(N) , then (generically) there e x i s t three points 0 < /x, < /x2 < / i 3 < 1 such t h a t : 2 0 (a) N = N, u N2, where N1 = [0,/i,] and N2 = [/x2, M3] • (b) E i t h e r /x, = v° or /x2 = v°. 1 9 T h i s follows from sub-game perfection, since there i s only one type that can provide report /x and M w i l l accept the contract i f he knows i t i s offered by fi. 2 0There are parameter values f o r which ix, = M2/ b u t a n v perturbation of those values w i l l r e s u l t i n /x, < /!•>• 1 2 1 A key feature of the non-disclosure set N i s that i t always contains a set N1 of "bad" types (n close to zero) plus another set N2 of "better" types. consists of types who choose non-disclosure because so doing decreases t h e i r expected c a p i t a l costs (due to over-valuation) more than i t increases t h e i r expected entry costs. N2, on the other hand, consists of types who choose non-disclosure because so doing decreases t h e i r expected entry costs and thereby also decreases t h e i r expected c a p i t a l costs, even though they are subsequently undervalued. Except i n non-generic cases, the disclosure set D always contains a set of "intermediate" types D, = (ny,n2) and may contain a set of "high" types D2 = (/u3,l], i f nz < 1. This implies that, unlike i n Verrecchia [1983] and Dye [1985], the disclosure p o l i c y i s not characterized by a s i n g l e threshold that divides the non-disclosure and disclosure sets. The char-a c t e r i z a t i o n obtained here i s s i m i l a r to that obtained by Wagenhofer [1990]. A second key feature of the non-disclosure set N i s that the p o s t e r i o r non-disclosure expectation v° can be e i t h e r below or above the types i n disclosure set D,. We r e f e r to p a r t i a l disclosure e q u i l i b r i a i n which v° = / i 1 as PD-L e q u i l i b r i a , and those i n which v° = /x2 as PD-H equi-122 l i b r i a . 1 Observe that i n a PD-L equilibrium, a l l types who d i s c l o s e t h e i r information receive a higher market pr i c e than those who choose non-disclosure. On the other hand, i n a PD-H equilibrium, at l e a s t some types who di s c l o s e t h e i r information receive a lower market p r i c e than those who choose non-disclosure. 2 2 Characterization of the Uniform D i s t r i b u t i o n Case; In our characterization of p a r t i a l disclosure equi-l i b r i a , we i d e n t i f y the range of c a p i t a l l e v e l s over which the two types of p a r t i a l disclosure e q u i l i b r i a e x i s t . These ranges are closed i n t e r v a l s contained i n the set [0,d] and, hence, we can represent them as follows: K-H = [k^k^] = the set of c a p i t a l requirements for which a PD-H equilibrium e x i s t s K-L = [k,,]^] = the set of c a p i t a l requirements for which a PD-L equilibrium e x i s t s . To obtain t h i s characterization we must make an e x p l i c i t assumption about the p r i o r b e l i e f s regarding I's type. For t h i s purpose, we assume that fi i s uniformly d i s t r i b u t -2 1While the Wagenhofer [1990] model i s s i m i l a r to ours, i t i s s u f f i c i e n t l y d i f f e r e n t and s p e c i a l i z e d that, unlike our r e s u l t s , FD e q u i l i b r i a always e x i s t and PD-H e q u i l i b r i a never e x i s t . 2 2Observe that, i n a PD-H equilibrium, not a l l types i n D., have a lower market value than the non-disclosure firms. However, because WN has a s t r i c t l y p o s i t i v e slope, there are always types at the low end of D1 that have a s t r i c t l y lower market value than V(v°,p(v°) ) . 123 ed, i . e . , *(/i)=/x. We f i r s t consider the case i n which E i s also uniformly d i s t r i b u t e d . Proposition 3.5.2; I f both I's type and E's break-even point are uniformly d i s t r i b u t e d , then the bounds on the sets K-L and K-H have the follow-ing c h a r a c t e r i s t i c s (where and Kg are defined i n Proposition 3.4.5): (a) K-H = [k^k,] => [minCK,^} ,max{K,K1} ]n[0,d] ; (b) K-L = [k2,kg] = [min{K,Kg} ,max{K ,Kg) ]n[0,d] ; where K - [-16 + A ] - [ A + bIL/2] 2 2 a-6/2 A key implication of t h i s proposition i s that a p a r t i a l d isclosure equilibrium e x i s t s f o r any value of k fo r which there i s no f u l l d isclosure equilibrium. In p a r t i c u l a r , i f K, < Kg < d, then the proposition implies that [K1,Kg] c K-H u K-L. Another key implication i s that both f u l l and p a r t i a l d i s c l o s u r e e q u i l i b r i a e x i s t for some parameter values, for example, i f Kg < K, < d, then [Kg,^] c K-H u K-L, implying that at l e a s t one p a r t i a l disclosure equilibrium as well as both an FD-0 and an FD-1 equilibrium e x i s t i f k e [ Kg, Kj ] . Appendix 3.B provides add i t i o n a l d e t a i l s on the c h a r a c t e r i z a t i o n of K-L and K-H. We summarize and i l l u s -t r a t e that characterization for the v a r i a b l e and fixed 124 entry cost cases. R e c a l l , from section 3.4, that v a r i a b l e entry costs and uniformly d i s t r i b u t e d break-even points produce a case i n which K, = 0 (there are no FD-1 e q u i l i b -ria) and Kg = 6»b/a. Hence, K, < Kj < d, and we obtain the following characterization: k - o < K i kj k 2 ^ min{ic,K2} £ maxficKj} < k 2 where K - [ A f t ] - [ A + — * ] 2 2 a-6/2 Figure 3-5(a) depicts the r e l a t i o n s h i p between Kg, K , and k 2 as S increases from zero to a. A l l three are increas-ing functions of S and, i n t h i s numerical example, k 2 = m i n l K , ! ^ } . 2 3 PD-H e q u i l i b r i a e x i s t i f the c a p i t a l requirements are small, and the allowable c a p i t a l requirement increases as the entry cost increases. P a r t i a l d isclosure e q u i l i b r i a do not e x i s t i f the c a p i t a l requirements are large and the entry costs are small (see Figure 3-4 f o r the conditions under which f u l l d isclosure e q u i l i b r i a e x i s t ) , but PD-L e q u i l i b r i a e x i s t i f c a p i t a l requirements are not too large r e l a t i v e to the entry Z3We found t h i s condition to hold i n other numerical examples, but the complexity of expressions d i d not allow us to prove that i t would always hold when A = 0. 125 costs. F i n a l l y , both PD-L and PD-H e q u i l i b r i a e x i s t i f both the c a p i t a l requirements and the entry costs are large. Insert Figure 3-5 here R e c a l l from Section 3.4, that f i x e d entry costs and uniformly d i s t r i b u t e d break-even points produce a case i n which K1 > Kg = A»b/a, implying that f u l l d i sclosure equi-l i b r i a always e x i s t s . I f S = 0 and a > A (as i n Figure 3-5), then we obtain the following characterization of the p a r t i a l d i s c l o s u r e e q u i l i b r i a : k 2 - K 2 < k 2 - K - k x < K, - k , where K - A • [— + b ~ ^ 2 ) 2 a Figure 3-5(b) depicts the r e l a t i o n s h i p between K,, Kg, and K f o r a l t e r n a t i v e values of A. Observe that there are no p a r t i a l d i s c l o s u r e e q u i l i b r i a i f the c a p i t a l requirements are e i t h e r large or small. Only a narrow band of c a p i t a l requirements can r e s u l t i n p a r t i a l disclosure, and both the upper and lower bounds on that band increase as A increases. 1 2 6 Characterization of the Common Knowledge Case; We again assume that I's type i s uniformly d i s t r i b u t -ed, but now consider the case i n which E's break-even point i s common knowledge at ye(0,1). In t h i s s e t t i n g , M and E's non-disclosure posterior expectation v° i s such that i n a PD-L equilibrium, = v° = y. Furthermore, E's p r o b a b i l i t y of entry given that he observes nondisclo-sure, denoted e°, i s equal to zero i n a PD-L equilibrium, but i s between zero and one i n a PD-H equilibrium. That i s , PD-H e q u i l i b r i a are always such that E i s i n d i f f e r e n t between entry and no entry i f he observes non-disclosure, and he plays a mixed strategy, i n which he enters with p r o b a b i l i t y e° i f I chooses non-disclosure and o f f e r s contract a 0 = a*(v°,e°) . This mixed strategy i s set at the l e v e l that w i l l induce I to choose non-disclosure i f , and only i f , /xeN. Proposition 3.5.3; I f I's type i s uniformly d i s -t r i b u t e d and E's break-even point i s common knowledge at ye(0,1), then the bounds on K-L and K-H have the following c h a r a c t e r i s t i c s (where K, and K2 are as s p e c i f i e d i n Proposition 3.4.5): (a) I f Y < P = 1/2, then K-H = [k,,^] => [minlKjK,} ^ axfKjK,} ]n[0,d] K-L = [kg,)^] ^ [ K 2 , K ] n [ 0 , d ] , where K - [26y + A] [1 + - L ] > K2 ay 2 127 (b) I f Y > P = 1/2, then 2 4 K-H - [ C k J [O.KjflfO ,d] K-L - [0,k2] ^ t O ^ l f l t C c f ] Observe that t h i s proposition has the same two key implications as Proposition 3.5.2 (which considers the case i n which y i s uniformly distributed) '. F i r s t , a p a r t i a l d i s c l o s u r e equilibrium e x i s t s whenever a f u l l d i s c l o s u r e equilibrium does not e x i s t , i . e . , i f K, < K2, then [ K,, Kg ] c K-L u K-H. Second, both f u l l and p a r t i a l d i s c l o s u r e e q u i l i b r i a e x i s t f o r some parameter values, e.g., i f K, > 1^ , then [Kg,^] c K-L u K-H. Further observe that i f E has a high break-even point (y > pZ) , then both types of p a r t i a l disclosure e q u i l i b r i a e x i s t for small c a p i t a l l e v e l s , but neither may e x i s t f o r small c a p i t a l l e v e l s i f E has a low break-even point (y < M)• To provide additional i n s i g h t into these r e s u l t s we again consider the variable and fix e d entry cost cases. In the v a r i a b l e entry cost s e t t i n g (A=0), K, = 0 < K2 = <S»b/a and we obtain the following characterization of K-L and K-H f o r y < pZ: k1 = 0 < k 2 < K2 < K < k1, k 2 2 4The proof provides a more det a i l e d characterization of K-H and K-L. In p a r t i c u l a r , the proof establishes that kg i s s t r i c t l y greater than Kg and that kn may be greater than K,. We omit the additional d e t a i l from the text so that the proposition focuses on the key aspects of the r e s u l t . 128 where K - JLA.[a-y + b] a Numerical examples indicate that k 2 = Kg and K = ic1 < kg. The values f o r kg = Kg and k, » kg are depicted i n Figure 3-6(a) f o r y = 1/3 and values of 6 ranging from zero to a. Observe that PD-H e q u i l i b r i a always e x i s t unless the c a p i t a l requirement i s large and the entry cost i s small, and that there i s a n o n - t r i v i a l region over which both PD-L and PD-H e q u i l i b r i a e x i s t . (In the l a t t e r region, FD-0 e q u i l i b r i a also exist.) Insert Figure 3-6 here I f Y > ji i n the v a r i a b l e entry cost case, then k1 = k 2 = 0 < k 1 fkg. The values of k, and kg are depicted i n Figure 3-6(b) fo r the y = 2/3. In t h i s s e t t i n g , PD-L e q u i l i b r i a always e x i s t unless the c a p i t a l requirement i s large and the entry cost i s small, and there i s a non-t r i v i a l region over which both PD-L and PD-H e q u i l i b r i a e x i s t . In 3-6(b) the overlap of K-H and K-L occurs f o r small c a p i t a l requirements, whereas i n 3-6(a) the overlap occurs f o r intermediate c a p i t a l l e v e l s . The characterization changes considerably when the entry cost i s fixed. Figure 3-7(a) presents an example i n which y = 1/3, while Figure 3-7(b) presents the same 129 example except that y = 2/3. Figure 3-7(a) i s s i m i l a r to the uniform d i s t r i b u t i o n case i n that there i s only a li m i t e d range of c a p i t a l requirements and entry cost values over which PD e q u i l i b r i a e x i s t . Furthermore, within that range there i s considerable overlap between K L and K-H. In Figure 3-7(b), on the other hand, both PD-and PD-H e q u i l i b r i a e x i s t unless the entry cost i s small and the c a p i t a l requirement i s large. Hence, given fixed entry costs, there i s much more opportunity f o r p a r t i a l d i s c l o s u r e e q u i l i b r i a to e x i s t i f i t i s common knowledge that E has a high break-even point instead of a low break even point. Insert Figure 3-7 here The complexity of the case i n which b e l i e f s about y are s t r i c t l y unimodel makes i t d i f f i c u l t to provide a precise characterization of the conditions under which PD L or PD-H e q u i l i b r i a e x i s t . The unimodel d i s t r i b u t i o n l i e s between the two extremes of the uniform d i s t r i b u t i o n and common knowledge cases, and w i l l be very s i m i l a r to the case of common knowledge at y i f G'(y) i s highly peaked. The key difference between the common knowledge and unimodel d i s t r i b u t i o n cases i s that, i n the l a t t e r case, mixed strategies are not required to sustain PD-H e q u i l i b r i a . I f G'(y) i s highly peaked, then the probabil 130 i t y of entry can be s i g n i f i c a n t l y modified by s l i g h t l y s h i f t i n g the non-disclosure expectation i n the v i c i n i t y of the mean y. This i s e s s e n t i a l l y the same as exogenously s h i f t i n g the entry p r o b a b i l i t y e when y i s common knowl-edge and equal to the non-disclosure mean. These s i m i l a r i t i e s suggest (see Figure 3-6 and 3-7) that, with v a r i a b l e entry costs, there i s a broad range of c a p i t a l requirements and entry cost values for which p a r t i a l disclosure e q u i l i b r i a e x i s t , whereas with f i x e d entry costs, there i s only a narrow range of c a p i t a l requirements and entry cost values for which these equi-l i b r i a e x i s t . Whether i t i s PD-L or PD-H e q u i l i b r i a that e x i s t , p a r t i c u l a r l y i n the variable cost case, depends s i g n i f i c a n t l y on whether the mean of E's break-even point i s greater than or les s than the mean of I's type. F i n a l l y , observe that p a r t i a l disclosure e q u i l i b r i a never e x i s t i f the entry costs are small and the c a p i t a l requirements are large. In that se t t i n g , the only equi-librium that e x i s t s i s a f u l l disclosure equilibrium i n which M assigns the lowest possible value to any firm that does not di s c l o s e i t s type. 131 3 .6 Multiple E q u i l i b r i a and Their Refinements The preceding analysis establishes that i n our d i s -closure model there are parameter values f o r which there i s a s i n g l e disclosure equilibrium (either f u l l or par-t i a l ) and there are other parameter values f o r which there are multiple e q u i l i b r i a . I f the multiple e q u i l i b r i a are a l l f u l l d i sclosure e q u i l i b r i a , then they a l l provide I with the same expected wealth — only the b e l i e f held to sustain the equilibrium d i f f e r s and, i n equilibrium, that the out-of-equilibrium strategy never has to be c a r r i e d out. However, substantive issues a r i s e when there are both f u l l and p a r t i a l disclosure e q u i l i b r i a or multiple p a r t i a l disclosure e q u i l i b r i a . We explore these issues more f u l l y i n t h i s section. F i r s t , observe that a l l /zel weakly prefer a p a r t i a l disclosure equilibrium over a f u l l disclosure equilibrium, and a l l /zeN s t r i c t l y prefer non-disclosure (except fi,, /x2, and nz). On the other hand, E has a s t r i c t ex ante pref-erence f o r a f u l l disclosure equilibrium, while M i s i n d i f f e r e n t (he always receives the expected market return). F u l l disclosure e q u i l i b r i a are sustained by e i t h e r the under-valuation of M or entry by E i f I chooses the out-of-equilibrium action of not d i s c l o s i n g h i s type. In our discussion of f u l l disclosure e q u i l i b r i a we e x p l i c -i t l y i d e n t i f i e d the out-of-equilibrium b e l i e f (expecta-132 tion) held by M and E. The issue here i s whether those b e l i e f s are p l a u s i b l e . Cho and Kreps I n t u i t i v e C r i t e r i o n Cho and Kreps [1987] provide an " i n t u i t i v e c r i t e r i o n " that i s a necessary condition f o r the s t a b i l i t y 2 5 of an equilibrium i n a s i g n a l l i n g game. The general thrust of t h e i r c r i t e r i o n i s to permit threats to sustain an equi-l i b r i u m i f among the types that could weakly benefit from a favourable response to the out-of-equilibrium action, there i s at l e a s t one type to which the proposed threat would be an optimal response. Hence, i n an FD-v e q u i l i b -rium, the strategy for M and E to hold expectation v, given non-disclosure and any contract a, can be j u s t i f i e d provided that n = v i s among the set of types who would at le a s t weakly benefit from a more favourable expectation. We s h a l l prove f i r s t i n t h i s section that f u l l d isclosure and p a r t i a l disclosure e q u i l i b r i a s a t i s f y t h i s c r i t e r i o n . The following notation i s used to adapt the Cho and Kreps [1987] i n t u i t i v e c r i t e r i o n to our s e t t i n g . W*(/i) = equilibrium expected wealth f o r type n. Q(T) = the set of possible expectations that can be obtained by varying p r o b a b i l i t y func-tions defined over the set of types T c i , " S t a b i l i t y i s a refinement of Nash e q u i l i b r i a that has been proposed by Kohlberg and Mertens [1986]. 133 i . e . , the smallest i n t e r v a l i n [0,1] that contains T. G*(v) = the minimum p r o b a b i l i t y of entry i f E holds expectation v. , G*(v)) = the minimum contract M w i l l accept given M and E's b e l i e f and entry p r o b a b i l i t y to be G*(v) . (<*,v,p) = 0 i f a > a*(v,p) { i i f a < a (v,p) v (a) = the cutoff point of M and E's b e l i e f given a, i . e . , v* separates the regions of expec-tations i n which r* = 0 and r* = 1. A (a) = The accept region f o r contract a. R(a) = The r e j e c t region f o r contract a. Wt(/i,a) = max W(/x, a, r* (a, v ,G*(v) ) ,G*(v) ) ve[0,l] expected wealth for /x from contract a given the most favourable possible responses from M and E. T*(a) = {ti | W*(/i) < W+(it,a)} the set of types that weakly prefer a i f i t would induce M and E to respond favourably. D e f i n i t i o n 3.6.1: A sequential equilibrium r = (N,a,r,e,v) f a i l s the CK-criterion i f , f o r any out-of-equilibrium contract a, T (a) * 0 and there i s some type /i'eT*(a) such that w * ( f l / ) < veQtt^a)) W(|j ' ,a ,r '(a ,v ,G(v)),G<v)) 134 Proposition 3.6.It Assume that E's break-even point i s eithe r uniformly d i s t r i b u t e d or common knowledge. I f a f u l l disclosure equilibrium e x i s t s , then i t does not f a i l the CK-criterion. The preceding proposition has established that f u l l d i s c l o s u r e e q u i l i b r i a s a t i s f y the CK-criterion. The next proposition establishes that p a r t i a l disclosure e q u i l i b r i a also s a t i s f y t h i s c r i t e r i o n . Proposition 3.6.2: Assume that I's type i s un i -formly d i s t r i b u t e d and E's break-even point i s eit h e r uniformly d i s t r i b u t e d or common know-ledge. I f a p a r t i a l disclosure equilibrium e x i s t s , then i t does not f a i l C K-criterion. Observe that i f T*(a) i s non-empty, then there i s at l e a s t one type that would weakly prefer to o f f e r a i f M and E would respond favourably to that contract. However, the proof establishes that none of these types would o f f e r t h i s contract i f M and E responded unfavourably, even though t h e i r response must be based on an expectation that recognizes that only the types i h T*(a) could conceivably be taking t h i s out-of-equilibrium action. In p a r t i c u l a r , i n an FD - 0 equilibrium, i f o i s desirable to any type y.el given a favourable response, then a i s also preferred by type j u=0 . Consequently, under the CK-criterion, M and E are " j u s t i f i e d " i n holding expectation v = 0 when they 135 observe any out-of-equilibrium contract, and the existence of an FD-0 equilibrium assures us that a l l /iel w i l l at le a s t weakly prefer to di s c l o s e t h e i r type rather than have M and E respond to a on the basis of expectation v = 0. A s i m i l a r r e s u l t holds i f an FD-1 equilibrium e x i s t and an FD-0 equilibrium does not e x i s t . I f both FD-1 and FD-0 equilibrium e x i s t , then there are some a for which T*(a)# 0 and T 2 = 0 . Hence, the b e l i e f v = 0 i s cred i b l e fo r a l l a, whereas v = 1 i s not. Perfect Sequential E q u i l i b r i a Grossman and Perry [1986] provide an a l t e r n a t i v e equilibrium refinement. They do not allow M and E to use "conservative" b e l i e f s i n determining t h e i r responses to an out-of-equilibrium contract offered by I. Instead, GP require M and E to respond on the basis of t h e i r p r i o r b e l i e f s with respect to a l l types /iel that would benefit from the out-of-equilibrium contract i f they responded on the basis of those b e l i e f s . We adapt Grossman and Perry's refinement, with some modification, to our s e t t i n g . 2 6 Z 6 I t i s an open question as to what entry p r o b a b i l i t y we should use i n the case i n which E's break-even point i s common knowledge and v = y. We have chosen to allow p to vary between zero and one (in a l l other s i t u a t i o n s G*(v) = G(v)). This i s consistent with the perspective that the common knowledge case i s the l i m i t of the unimodel d i s -t r i b u t i o n case, i n which G*(v) = G(v) f o r a l l v e [ 0 , l ] . 136 D e f i n i t i o n 3 . 6 . 2 ; A sequential equilibrium r = (N,a,r,e,v) f a i l s the GP-criterion i f f o r any out-of-equilibrium contract a, T*(a) * 0 and there e x i s t s a measurable set T c T*^a) such that f o r v = /i(T) and some pe[G(v),G (v)]: (a) a > a*(v,p) (b) W*(M) < W(ii,a , 0,p) V /xeT (c) W*(/i) > W(/i,a , 0,p) V neI\T C l e a r l y , i f both FD and PD e q u i l i b r i a e x i s t , then the FD equilibrium f a i l s the GP-criterion since a = a° and T = N constitute the basis for f a i l u r e . On the other hand, the lack of a PD equilibrium implies that an FD e q u i l i -brium does not f a i l the GP-criterion, since f a i l u r e implies the existence of a PD equilibrium. Proposition 3.6.3; An FD equilibrium f a i l s the GP-criterion i f , and only i f , there also e x i s t s a PD equilibrium. The f i n a l issue i s whether a PD-equilibrium s a t i s f i e s the GP-criterion. Note that i f there e x i s t two PD-equili-b r i a A and B simultaneously, then following conclusions are mutually exclusive: (i) A dominates B; ( i i ) A i s domi-nated by B; ( i i i ) A and B are non-comparable. Clearly, i f both PD-L and PD-H e q u i l i b r i a e x i s t and one Pareto domina-tes the other with respect p e l , then the Pareto dominated equilibrium f a i l s the GP-criterion. For a s i n g l e or 137 Pareto dominant PD equilibrium, or when two PD e q u i l i b r i a are Pareto non-comparable. We have Proposition 3.6.4: A PD equilibrium f a i l s the GP-criterion i f , and only i f , there e x i s t s another PD equilibrium which dominates i t . 3.7 Concluding Remarks We have explored the extent to which a firm w i l l d i s c l o s e i t s private information i n a context i n which the firm i s concerned about the response to that information (or i t s non-disclosure) by both the c a p i t a l market and competitors i n the firm's product market. In p a r t i c u l a r , we assume that the firm's information can be ordered such that i t would prefer to reveal good news to the c a p i t a l market and bad news to product market. F u l l d isclosure w i l l d e f i n i t e l y occur i f only one of these markets i s of concern to the firm, or i f the response of one market c l e a r l y dominates the other. However, p a r t i a l disclosure e q u i l i b r i a e x i s t when the firm has a r e l a t i v e l y balanced concern f o r the responses of both markets. - The firm's i n t e r e s t i n the c a p i t a l market i s assumed to a r i s e from the desire to obtain c a p i t a l at the most favourable terms possible. We have assumed that the c a p i t a l investment i s desirable no matter what information the firm has and no matter what response occurs i n the 138 product market. Furthermore, we have assumed that the firm must issue equity to obtain that c a p i t a l . Obvious extensions to the current analysis would be to consider the impact of issuing r i s k y debt instead of equity and to allow the range of information to be such that the project i s undesirable for some lower range of signa l s . Appendix 3.A provides a model of competition i n a product market that can be represented by the l i n e a r functions we have used. To obtain the desired l i n e a r i t y , we assume that the firms face a common pr i c e uncertainty that i s a decreasing function of aggregate production and that the competing firms have i d e n t i c a l expected v a r i a b l e costs. An obvious extension of our analysis would be to explore the impact of a l t e r n a t i v e product market assump-tions, e.g., the firms face d i f f e r e n t expected v a r i a b l e costs or compete on p r i c e ( i . e . , a Bertrand equilibrium instead of a Cournot equilibrium). Perhaps the most i n t e r e s t i n g aspect of our r e s u l t s i s that there are two possible p a r t i a l disclosure e q u i l i b r i a . PD-L e q u i l i b r i a are characterized by a c a p i t a l market i n which the non-disclosure firms have a lower market value than a l l disclosure firms. PD-H e q u i l i b r i a , on the other hand, are characterized by a c a p i t a l market i n which some disclosure firms have lower market values than non-dis-closure firms. Since the e q u i l i b r i a apply on a firm-by-139 firm basis, t h i s r e s u l t implies that, i n equilibrium, we would expect to empirically observe firms that choose to withhold information even though i t s release would increase t h e i r market value, while other firms d i s c l o s e information even though withholding i t would increase t h e i r market value. Neither type of p a r t i a l disclosure e q u i l i b r i a e x i s t i f c a p i t a l requirements are large and entry costs are small. They also do not e x i s t i f c a p i t a l requirements are small, the entry cost i s large and fixed, and E w i l l not enter unless he receives bad news (i.e.,y < Ji) . However, PD-H e q u i l i b r i a e x i s t f or small c a p i t a l requirements i f the entry cost i s va r i a b l e or i f E w i l l not enter unless he receives good news ( i . e . , y > Ji) . Furthermore, PD-L e q u i l i b r i a e x i s t f o r only a narrow band of c a p i t a l r e-quirements and entry cost values, except when the entry cost i s fix e d and E w i l l not enter unless he receives good news. 140 Tables t Q I, M, and E hold homogeneous p r i o r b e l i e f s *, F, and G with respect to I's type (p.), I's end-of-period value (pay-o f f x) , and E's break-even point (y). t 1 I learns h i s type (/2 = /i) , which gives him private information about h i s payoff (x) . t 2 I chooses between p u b l i c l y d i s c l o s i n g (m = JU) or not d i s c l o s i n g (m = n) h i s type (private information). t 3 I o f f e r s M a contract, which s p e c i f i e s the share (a) of I's payoff that i s to be given M i n return f o r k units of c a p i t a l . t 4 M and E form a poste r i o r expectation (v = v(m,a)) with respect to I's type (n) given I • s report (m) and the contract (a) he has offered. t 5 M assesses the value of the firm (V = V(v, P ( v ) ) and accepts the contract i f a»V > k, or r e j e c t s i t i f a»V < k. t 6 E learns h i s break-even point (y = y) and enters with p r o b a b i l i t y one (e=l) i f i t i s less than h i s expectation with respect to I's type (y < v) or enters with p r o b a b i l i t y zero (e=0) i f i t i s greater (y > v) . E can choose to enter with a p r o b a b i l i t y between zero and one i f y = v. t 7 I and M share the r e a l i z e d payoff (x = x) : I receives (l-a)»x and M receives a» x. Table 3-1: Sequence of events 141 Figures Figure 3-1: Expected Outcomes, (a) Variable Entry Cost 0 142 ! > 1 Figure 3-2: Expected End-of-Period Wealth Under Full Disclosure. (a) E's Breakeven Point is Common Knowledge 0 y (b) E's Breakeven Point is Uniformly Distributed 0 /i*=l/2=y (c) E's Breakeven Point has a Unimodel Distribution a+b-k c+d-k a+b-k c+d-k a+b-k c+d-k 143 Figure 3-3: Disclosure Versus Non-disclosure E's Breakeven Point is Common Knowledge Figure 3-4: Capital Requirement/Entry Cost Conditions under which Full Disclosure Equilibria Exist E's Breakeven Point is Uniformly Distributed k (a) Variable Entry Cost FD=0-Equilibria-No FD Equilibria 0 A k FXU) X -Equilibri (b) Fixed Entry Cost Both FD-0 and FD-1 Equilibria = b - A Figure 3-5: Capital Requirement/Entry Cost Conditions under which Partial Disclosure Equilibria Exist E's Breakeven Point is Uniformly Distributed 0 K, = kj a A 146 Figure 3-6: Capital Requirement/Entry Cost Conditions under which Partial Disclosure Equilibria Exist Variable Entry Cost/Breakeven Point Common Knowledge k A b = d (a)y= 1/3 <n = 1/2 zBquiIibri2 ^ - s . ^ , b = d 147 Figure 3-7: Capital Requirement/Entry Cost Conditions under which Partial Disclosure Equilibria Exist Fixed Entry Cost/Breakeven Point Common Knowledge !5i _ .2 148 Figure 3-8: End-of-Period Value Curve and Contract Curve E's Breakeven Point is Uniformly Distributed (a) End-of-Period Value Curve a+b c+d A (b) Contract Curve for FD Equilibrium «*(y,y) k/(c+d) R(a) 1 A(a) R ( « ) V v*(a) v2*(a) 1 (c) Contract Curve for PD-L Equilibrium k/(c+d) 149 Figure 3-9: FD Contract Curves with Different Parameter Values N = k/(c+d) 150 Figure 3-10: Comparison of Equilibria 151 Appendix 3.A: Payoffs i n a Cournot Equilibrium Entry Game with Demand Uncertainty Assume that I i s entering a market i n which the expected s e l l i n g p r i c e i s a l i n e a r function of the t o t a l output to be sold i n that market. In p a r t i c u l a r , assume that the production quantity i s scaled such that the s e l l i n g p r i c e i s equal to £ - Q, where £ i s an uncertain demand parameter and Q i s the t o t a l amount produced i n that market. I has private information with respect to £; l e t m denote h i s posterior expectation given that informa-t i o n and l e t [m,m] denote the set of possible values of m. The production quantities f o r I and E are denoted q and q^ ,, r espectively. Hence, Q = q i f E does not enter and Q = q + q^ , i f E does enter. The expected production costs f o r I and E are C*q+k and {•qe+y<ier respectively, where k and k e are investments that must be made at the s t a r t of the period. Observe that the expected unit v a r i a b l e production cost C i s assumed to be the same for both producers. There i s no private knowledge with respect to the v a r i a b l e production costs, although E may have pr i v a t e knowledge of k e. I f E does not enter, then I i s a monopolist i n the market. His expected end-of-period payoff (excluding the investment k) i s 152 Tt (m, q) - [m - g] *q - {»q The optimal production quantity ( d i f f e r e n t i a t e rr with respect to q and set ir% equal to zero) i s q* = [m~C]/2 and the optimal expected payoff i s u*(m) • n (m, q*) - [m-C]2/4 This can be translated into a l i n e a r model i f we represent 1 1s p r i v a t e information as n * (m) - i t * (in) u • Tt* (/ii) - 7i* (m) and define the payoff function parameters as a - [w* (iii) - Tz*(m)] b - 7c*(ffl) Assume that i f E invests k e and enters the market, then he w i l l learn m before he selects q^. That i s , even i f he does not know m when he makes h i s investment d e c i -sion, he w i l l know i t when he makes h i s production d e c i -sions under duopoly. Therefore, when I and E make t h e i r production decisions under duopoly, t h e i r expected payoffs are known to be Tz(m, q, qe) - [m - (q+qe)]»q - C»q Tt g(m,q,qe) - [m - (q+qe)]»qe - C»qe 153 D i f f e r e n t i a t i n g w with respect to q and we with respect to provides the following f i r s t - o r d e r conditions: Q - -|*(™ - C - ge) Qe - - C - g) Solving these two equations i n two unknowns provides the following equilibrium expected payoffs and production q u a n t i t i e s : TzHm) - 7i(/n,g+,g|) - [m - C] 2 / 9 <?+ - (m - 0 / 3 - ic.(jn,gt,gj) - [m - 0 2 / 9 " - (in - 0 /3 Observe that jr+(m) = (4/9) • jr*(m) . Hence, we can express I's expected payoff, given entry, as a l i n e a r function of n, the previously defined representation of pri v a t e information. In p a r t i c u l a r , the payoff function parameters are c - 7i +(/n) - n + (in) d - uf(m) Now consider E's break-even point. Given information y, he w i l l enter i f E[7re+(m) |y] > k e and we can express E's expected p r o f i t given m as a l i n e a r function of n: i^eim) - nt(in) - c«u, + d 154 where fi, c, and d are as defined above. Consequently, E w i l l enter the market i f c»E [uJy] + d * ke This implies that E's break-even point i s y = [k e-d]/c. The preceding demonstrates that the l i n e a r payoff functions used i n t h i s paper can be viewed as representing a firm competing i n a product market i n which the i n i t i a l entrant (I) has private information about the uncertain intercept of a l i n e a r p r i c e function. The l i n e a r repre-sentation of the expected monopoly p r o f i t i s quite general - we can use that representation i n any s e t t i n g i n which I's expected payoff i s a s t r i c t l y increasing function of some s c a l a r representation of h i s private information (with f i n i t e bounds on the set of possible information). However, i t does not necessarily follow that I's and E's du o p o l i s t i c expected p r o f i t s are l i n e a r functions of that same representation of private information. For example, i t i s c r u c i a l i n the above model that I and E have the same expected variable per u n i t production cost. D i f f e r -ences i n t h e i r expected costs w i l l r e s u l t i n rr+ and ir^ being nonlinear functions of fi. That would complicate the analysis of disclosure e q u i l i b r i a , but whether i t would change the q u a l i t a t i v e r e s u l t s i s an open question. 155 Appendix 3.B: Proofs Proof of Lemma 3.3.1 Since E's break-even point i s not common knowledge, WD(u) - V(u,G(u)) - k - G ( U ) T C ( U , 1 ) + ( l - G ( u ) ) 7C (u,0) -k - au + b - [6u + A ] G ( u ) - k- (3.B.1) WD/(u) - a - 6G(u) - [6u + A]G'(u) (3.B.2) In the uniform d i s t r i b u t i o n case, G(/i) = fi and G ' (fi) = 1. Hence, WD//(u) - -26 ^ 0 which establishes that WD i s concave, and s t r i c t l y concave i f 5>0. Furthermore, i f S > 0 , then s e t t i n g (3.B.2) equal to zero establishes that WD has an i n t e r i o r maximum at fi* = (a-A)/(26) i f ae(A,2S+A). I f a < A, then fi* = 0 , and i f a-A > 26 then fi* = 1. In the unimodel case, G(u) - /Pot 8 1 ' 1 (1-t)**-1 dt o G'(u) - P o U^d-u) 6 2" 1 G"(u) - p 0 [(Pi-l) u P l" 2 (l - n ) " 2 " 1 - (P2-l) n ^ d - u ) ^ " 2 ] - G'(u) KPi- 1) - <Pi+P2-2) 1*3 156 Hence, w /(u) - -28G'(u) - [8u + A]G" (u) - _G/ ( l i) Biu) u ( l - u ) where B(u-) = -6 (P 1 +P 2) u 2 + [5 <P1+1) - A (P 1 +P 2-2)] u, + A (P x-1) Given that Py,P2 > ^' w e h a v e B(0) - A(Pi-1) :> 0 B ( l ) - -8 (p 1 +p 2) + [5 ( P 1 + l ) - A (P 1 +p 2-2)] + A (P x - l ) - -<8+A) ( P 2 - l ) < 0 Therefore, B(/x) has at le a s t one root i n [0,1]. To show that B(/n) has only one root i n [0,1], observe that B ;(|i) - -28 (P!+P2) ji + 8 (Pi+1) - A (p 1 +p 2-2) Let /ft s a t i s f y B' = 0. I f / i + $ [0,1], then B(/i) i s monotone i n [0,1], implying that i t s root i n [0,1] i s unique. I f i i + e [0,1], then from B"(/i) = -2<S« (py+p2) < 0, we know that B(/x) i s non-decreasing i n [0,/i+] and i s decreasing i n [M + , 1 ] , implying that B(/x) has a unique root i n [M + , 1 ] -Let fj.Q denote the unique root of B(/z) i n [0,1]. We then have WD"(/x) < 0 i f n e [0,/i0) and WD"(/i) > 0 i f /x e (tz Q , l ] . These i n e q u a l i t i e s imply the conclusions i n ( a ) . Based on (a), i t i s straightforward to show (b) by noting 157 that WD' (/x) i s p o s i t i v e at both ti = 0 and n = 1. Wp must reach i t s maximum and minimum at some i n t e r i o r /n* and ti*, r e s pectively. Q . E . D . Proof of Lemma 3 . 4.1 A f u l l d i sclosure sequential equilibrium e x i s t s i f M and E's consistent and sequentially r a t i o n a l response to non-disclosure and any contract a are such that I weakly prefers d i s c l o s u r e f o r a l l types /xel. To sustain f u l l d i s c l o s u r e e q u i l i b r i a given non-disclosure expectation v, we l e t p(v) = G(v). This i s always the case i f E's break-even point i s common knowledge. To prove the " i f " part of the lemma, l e t M and E hold the stated expectation v f o r non-disclosure and a l l con-t r a c t s a. E w i l l enter with p r o b a b i l i t y G(v) and M w i l l accept the contract i f , and only i f , a > a*(v,G(v)). Hence, under the stated conditions, I w i l l weakly prefer disclosure f o r a l l /xel. To prove the "only i f " part of the lemma, assume that the condition does not hold, and yet there i s a f u l l d i s c l o s u r e equilibrium. This implies that f o r each con-t r a c t oe[0,l] that there e x i s t s an expectation v such that e i t h e r a < a*(v,G(v)) or W0(/x) > (1-a)• V(v,G(v)) V /xel, i . e . , e i t h e r M w i l l r e j e c t a or I w i l l prefer disclosure to acceptance of a (given p(v) = G(v)). Consider the 158 expectation that produces the largest minimum acceptable ownership equity, i . e . , and l e t a 0 = a*(v°,G(v°)) . By assumption, W0 < WN(/i,v°, G(v 0)) f o r some \i > 0, but the existence of a f u l l d i s -closure equilibrium implies that there e x i s t s some expec-t a t i o n v + * v° such that a 0 > a*(v t,G(v +)) and W„(/i) < (1-a°) • V(/i,G(v +)) V /xel. However, that contradicts the as-sumption because WN(u.,vt,G(vt)) * (l-a°) V(u,G(v t)) :>WD(u) V uei and, hence, v + s a t i s f i e s condition (3.4.1). Q . E . D . Proof of Proposition 3 . 4 . 4 As above, l e t p(v) = G(v), the maximum entry prob-a b i l i t y given expectation v. (a) I f I obtains h i s c a p i t a l by issuing r i s k l e s s debt, then WD(u) - G(u) n(u,l) + (l-G(u) ) *(u , 0 ) -k WN(u,v,G(v)) -G(v)«(|i,l) + (l-G(v)) 11(11,0) - Jc For any v > y, we have G(v) = 1 > G(/x) V neZ, so that we always have wD(u) ;> w N(u,v,G(v)) V uei 159 Therefore, a f u l l disclosure equilibrium always e x i s t s i n which N = 0 and ve[y,l] f o r a l l contracts offered with non-disclosure. (b) I f y > p , under f u l l non-disclosure, v = p < y so that G(v) = 0 < G(/Lt) V / i e l . Hence, w D(u) <. w N(u,v ,G(v)) V aei That i s , a f u l l non-disclosure equilibrium e x i s t s i n which N = I and with v = p for a l l contracts offered with non-disc l o s u r e . On the other hand, i f y < Ji, then under f u l l non-disclosure, v = p > y so that G(v) = 1 > G(/i) V / i e l . However, f o r any / i e ( y , p ) , G(/i) = 0 implies that disclosure i s better than non-disclosure f o r I. This contradicts the d e f i n i t i o n of an FN-equilibrium. (c) I f N c [y,l] and v e [ y , l ] , then G(/i) = G(v) = 1 V /xeN and WD(u) - W N(u,v ,G(v) ) V ueN Therefore, a p a r t i a l disclosure equilibrium r e x i s t s i n which N c [Y,1] and v e [ Y , l ] f o r a l l contracts offered with non-disclosure. The s u f f i c i e n c y part of the l a s t condition can be shown by construction. I f y > Ji, then we can f i n d / i + c [0, /Z] such that i f N = [ / i + , l ] , p < v < y and G(v) =0. A p a r t i a l d isclosure equilibrium r then e x i s t s i n which N = 1 6 0 O #1] and v e [0,Y ) • The necessity part can be shown by contradiction. I f Y < p, l e t N be any p a r t i a l disclosure equilibrium s t r a -tegy of I such that [p,l] c N. Then we have v > pZ > y, so G(v) = 1. However, N i s not an optimal strategy for /zeN \ [Y,l] since G(/n) = 0 V /xe N \ [ Y , 1 ] - This contradicts our assumption, so we must have y > pZ. Proof of Proposition 3 . 4 . 5 (a) An FD-0 equilibrium e x i s t s i f , and only i f , In the uniform d i s t r i b u t i o n case, G ( Y ) = Y A N ( * WD(u) - a\i + b - u (8|i + A) - k The concavity of WD (see Lemma 3.3.1) and W D ( 0 ) = WN(0,0, 0), imply that Q . E . D . V U€I WD(u) * WN(u,0,0) WD(1) * WN(1,0,0) ~ c + d - k z ( 1 - -^) (a + b) b V ue[0,l] k * — [5 + A] = K 2 161 In the case where y = y i s common knowledge, since W0 i s "Z-shaped" and WD(0) = W N ( 0 , 0 , 0 ) , i t follows that w D(u) ;> w N(u , 0 , 0 ) V uei W D(y) :> W N(y , 0 , 0 ) ** cy + d - k > ( 1 - 4 ) <ay + b) b ~ k z -^L [67 + A] - K , ay (b) I f v = 1 , then G(v) = 1 and w N ( u , l , l ) - (1 - (cu + d) In the uniform d i s t r i b u t i o n case, the concavity of W D and WD(1) = W N (1 ,1 ,1) imply that W D(u) * W N ( u , l , l ) V \iei ~ WD(0) * W N (0 ,1 ,1) b - k * (1 - —*—) d c+d ~ k z — [c + d] = K. c 1 In the common knowledge case, G(y) = 1 and r^(u,Y,l) - (1 - - .)«(c»u + d) The "Z-shape" of W D , W D(y) = W N ( y , Y , l ) , and W n ' (M , Y , 1 ) < c = W » (M) imply that 162 wD(u) :> w N ( u , Y / D V uei W D (0) 2: W N ( 0 , Y , D Jb - Jt at ( 1 - - J d cy+d ~ k * -4= [cy + d] - K, cy 1 (c) The existence of an F D equilibrium i f Kg < K, i s obvious. I f K, < Kg and kefK^Kg), then i t i s obvious from the proofs of (a) and (b) that there can be no F D - O , F D - 1 , or F D - Y e q u i l i b r i a . To demonstrate that there i s no other non-disclosure expectation v that can sustain a f u l l d i s c l o s u r e equilibrium, assume that an F D - v equilibrium e x i s t s f o r v e ( 0 , l ) . In the uniform d i s t r i b u t i o n case, WD i s s t r i c t l y concave i f S > 0 . The contradiction then follows immedi-ate l y from the fact that WN must e i t h e r i n t e r s e c t WD at ju = v or, i f they are tangent at /i = v , WN > WD V n e l , n*v. I f WD i s l i n e a r ( i . e . , 6 = 0 ) , we cannot have WD > WN V pel because WD' = a-A * WN« = ( 1 - k/(av+b-Av) )»a V v e ( 0 , l ) given that k < Kg. In the common knowledge case, the contradiction follows from the fact that WD and WN must i n t e r s e c t at /Lt = v. To see t h i s , observe that, i f / L i e ( 0 , Y ) , then WD' = a and WN' = ( 1 - k/V(v , 0))»a < a and, i f v e ( 7 , l ] , then W0' = c and WN' = ( 1 - k/V(v,l))«c < c. Q . E . D . 163 Proof of Lemma 3.4.6 From Lemma 3.3.1 we have that dWD/d/i (s p e c i f i e d by (3.B.2)) i s continuous and increasing at a l l /ie(ju*,l), with - o ™Rl -c du du v-i WN i s defined i n (3.3.3), with p(v) = G(v) i n the unimodel d i s t r i b u t i o n case. Observe that d V ^ - (1 - — - , — * „ ) [a -8G(v)] > 0 du V(v,G(v)) (3.B.3) d2W, — - - ^ d V ( v > G ( v ) ) / d v . [ a _ 5 G ( v ) ] dudv [V(v,G(v))] 2 " w n )QG/(v) (3.B.4) V(v,G(v) ) Since dV(v G(v)) _ dW (v) > Q y v 6 dv du (3.B.4) implies that dWN/d/x i s decreasing f o r ve[/x.,l]. This, plus the fa c t that dW^.1,1) . ( 1 * ) c < c du c+d implies that there must be a unique ve(/i*,l) such that dWD| dWK du v d\i "-v 164 Q . E . D . Proof of Proposition 3.4.7 (a) I t i s obvious that an FD-0 equilibrium e x i s t s i f t h i s condition i s s a t i s f i e d . (b) The d e f i n i t i o n of v and the convexity of W0 on O 0 , l ] implies that WD > W„ V / i e [ i i 0 , l ] . The convexity of WD on [O,ii 0] and the fa c t that WD > WN at /i=/i0 implies that WD > WN on [O , jL i 0 ] i f i t holds at /i=0. (c) For any other expectation v, WN i n t e r s e c t s WQ. This follows from the fa c t that WD i s concave on [0,/xQ] and tangency would imply that WN > W0 V /ze[0,/x0], n*v, and in the proof of Lemma 3.4.6 we demonstrate that the expec-t a t i o n defined there i s the only point at which WN i s tangent to the convex portion of Wp. Q . E . D . Proof of Lemma 3.5.1 (a) Lemma 3.3.2 establishes that WN i n t e r s e c t s WD at most three times. Observe that dWD/d/i = a > dWN/d/x at li=0. Therefore, e i t h e r WN > WD at /i = 0 or WN i n t e r s e c t s WD at most twice with WN > WD f o r /xe (/^  ,/i2) . The l a t t e r would contradict our proposition, but i t i s impossible since i n that case ve(ji.,,|i2) and we know that WD(v) = WN(v,v,G(v)) . (b) From the d e f i n i t i o n of WN and WD, we observe that 165 W N(v,v,p(v)) = WD(v) i f p(v) = G(v). This l a t t e r condi-t i o n always holds i f E's break-even point i s not common knowledge. Hence, v must equal one of the three possible i n t e r s e c t i o n points jut, / i 2 , or / i 3 , and i t cannot be / i 3 since N contains no values above nz. Q . E . D . Proof of Proposition 3.5.2 Lemma 3.3.2 establishes that WN i n t e r s e c t s WD at most twice. R e c a l l that WN(v,v,G(v)) = WD(v) . I f v i s a tangency point, then we have f u l l non-disclosure, which can only occur i n the "knife-edge case" i n which WD achieves i t s maximum at / i * = 1/2. I t i s obvious that v cannot be the only i n t e r s e c t i o n point, since that would imply that a l l jxeN l i e above or below the mean of N, which i s an i m p o s s i b i l i t y . Therefore, i n a p a r t i a l d isclosure equilibrium, WN must in t e r s e c t WD exactly twice and N = [ O f M O ^ i l ] ! with /x, < /x2-Since v i s the expectation over N, we have C i 1 v - [f u d u + f u du]» ^ _ ivZ + i-vZ ( 3 . B . 5 ) 2 Hi + 1 - u 2 166 Recall that v = /n1 i n a PD-L equilibrium and v = n2 i n a PD-H equilibrium. We now combine these two conditions with the f a c t that WN = WD at / x , and n2 to specify the conditions that must be s a t i s f i e d i n the two types of PD e q u i l i b r i a . Since WN always equals WD at n = v, the key conditions are that WN and WD are also equal at /x2 i n a PD-L equilibrium and at / i , i n a PD-H equilibrium. PD-L e q u i l i b r i a : Substitute nA = v into (3.B .5) and solve f o r /x2: - 1 U2 - V + [1 - 2v] 2 V V 6 [ 0 , - | ] (3.B.6) The condition that WD = WN at n2 provides the following necessary condition for the existence of a PD-L e q u i l i -brium with expectation ve [ 0 , 1 / 2 ] : au2+Jb- [6u.2+A] u 2-ic - ( 1 r - rs—rr> <au2+jb-[5u2+A] v) (3.B.7) av+jb-[8v+A] v 2 2 ' Solve (3.B .7) for k: k - [5u2 + A] [v + b ~ A v ] r* a - bv (3.B.8) 167 We now determine the values of ke [0,d] for which there e x i s t s a v e [ 0 , 1 / 2 ] such that condition ( 3.B . 8 ) i s s a t i s f i e d with /x2 defined by condition ( 3 . B . 6 ) . Observe that k i s a continuous function of v and that the follow-ing values of k hold f o r the two extreme values of v: v - o - k - ^-[b + A] - K, a v - 1 / 2 - k . [ i , + 4 , [ i + ^ A ^ , Therefore, condition ( 3.B . 8 ) holds f o r a l l values of k between K and K2, i f we ignore the boundary conditions, and that implies condition (a) of the proposition when we introduce the requirement that ke [ 0,d]. P D - H E q u i l i b r i a : Substitute n2 = v into ( 3.B . 5 ) and solve f o r / i 1 : - i i - v - [ 2 v - 1] 2 V v e [ — , 1 ] (3.B.9) 2 Replace /x2 with ny i n ( 3.B . 7 ) to specify the condition that WN = W0 at / i 1 , and make the same su b s t i t u t i o n i n ( 3.B . 8 ) to specify k as a function of ju1 and v: k - [6u, + A]«[v + b " A v ] (3.B.10) a - ov 168 Evaluating (3.B.10) at v = 1/2 and v = 1 establishes that (3.B.10) can hold f o r a l l values of k between K and K,, i f we ignore the boundary conditions, and that implies condi-t i o n (b) of the proposition when we introduce the require-ment that ke[0,d]. Further characterization of P a r t i a l Disclosure E q u i l i b r i a Given that E's Break-even Point i s Uniformly Dist r i b u t e d PD-L E q u i l i b r i a : D i f f e r e n t i a t e (3.B.8) with respect to v: ^ - [ 8 ( v +(l - 2 v ) " ^ ) + A ] [ i - - ^ 5 - ] dv (a-6v) 2 + [ 8(l-(l-2v) 2 ) ] [v + b-Av a-bv ] The second term i s always negative since ( l - 2 v ) " 1 / 2 > 1 V ve(0,1/2), and the sign of the f i r s t term depends on the sign of (a-6v) 2 - (aA-b6). Furthermore, dk dv < 0 if a 2 < aA - bb > 0 if a 2 > aA - bb dk, _ ( A 5 + A ) ( 1 - aA-frA } +  d v V " ^ 2 < a - - ± 6 ) 2 if b - 0 if b > 0 169 Let [k*,k*] represent the range of k values for which there e x i s t s a ve[0,1/2] such that condition (3.B.8) i s s a t i s f i e d , i f we ignore the upper bound d. I f 5 = 0, then dk/dv = A[a-A]/a, implying that K and are the bounds, with t h e i r r e l a t i v e magnitudes depending on the sign of a - A: (L.l) I f fi = 0 and a > A, then k* = K, < K = k* (L.2) I f fi = 0 and a < A, then k* = K < 1^  = k* I f > 0 and a 2 < aA - bfi, then dk/dv < 0 V ve(0,l/2), which implies: (L.3) I f fi > 0 and a 2 < aA - bfi, then k* = K < = k* On the other hand, i f fi > 0 and a 2 > aA - bfi, then both K2 (v=0) and K (V=1/2) are l o c a l minima. This implies that there e x i s t s a global maximum k* > maxIK^ K } . Determining whether m i n l K ^ K } i s a global minimum i s complex and, hence, we summarize t h i s case as follows: (L.4) I f fi>0, a2>aA-bfi, then k* < minfK^ K } < max{K2, K} <k*. To determine k 2 and k2, recognizing the require-ment that ke[0,d], we l e t k 2 = min{k*,d} and k 2 = min{k*, d}. I f k 2 = k 2 =d, then a PD-L equilibrium does not e x i s t . PD-H E q u i l i b r i a : Using e s s e n t i a l l y the same approach as i n the PD-L case provides the following characterization of the range 170 of k values [k^kt] for which there e x i s t s a v e [ l / 2 , l ] such that condition (3.B.10) i s s a t i s f i e d : (H.l) I f S = 0 and a > A, then k^  = K < K, = k +. (H.2) I f S = 0 and a < A, then k,. = < K = k +. (H.3) I f S > 0 and (a-6/2) 2 < aA - b6, then kj. = < K = kt. (H.4) I f S > 0 and (a-6) 2 > aA - b i , then kf < min{K 1 ,K ) < maxIK^K} < k +. We then obtain the desired bounds by l e t t i n g k, = minlk^, d) and ie, = min{k +,d). Q . E . D . Proof of Proposition 3.5.3 Lemma 3.3.2 establishes that WN i n t e r s e c t s WQ at most three times. I t i s straightforward to prove that, i n a common knowledge p a r t i a l disclosure equilibrium, WN i n t e r -sects WD e i t h e r twice, at 0 < ji, <ii2 = y, or three times, at 0 < / i , < n2 = y < i i 3 < i . The expectation f o r the two-inters e c t i o n - p o i n t case i s : v - [f u du + f u d\i]» -Jn L J* l + I*3- |*2 f a I . A I A J L A (3.B.H) 2 m + u 3 - u 2 171 In examining p a r t i a l disclosure e q u i l i b r i a i n t h i s s e t t i n g i t i s usef u l to separately examine the cases i n which Y<l/2 and y>l/2. PD-L E q u i l i b r i a f o r y < 1/2: In a PD-L equilibrium with y < 1/2, there must be three i n t e r s e c t i o n points (since including [y,l] N would r e s u l t i n an expectation greater than y) . Substitute /Lt1 = v and fi2 = y into (3.B.11) and solve f o r nz: U3 - V + [v 2 + (y - v) 2] 2 (3.B.12) The requirement that WD equals WN at nz s p e c i f i e s that ( r e c a l l that the entry p r o b a b i l i t y i s zero under WN, but i s equal to one at nz under WD) : cu 3 + d - k - (1 - a y f k + b ) (au 3 + b) ( 3 . B . 1 3 ) Solve (3.B.13) f o r k: av + b k - [6u3 + A] 3 a (u.3 - v) (3.B.14) Observe that (3.B.12) and (3.B.14) are continuous func-tions of v and that v - 0 - u 3 - Y/ k - K 2 - i [8y + A] v - y =» u 3 - 2y, k - K • [28y + A] [1 + -^L] > K 2 a Y 172 Therefore, condition (3.B.14) holds for a l l k e [Kg,K ] . PD-H E q u i l i b r i a f or y < V 2 : With v = y = i i 2 , we express ix3 as a function of /x.,: _i u 3 - Y + [2u x (Y " 2 (3.B.15) Given v = Y a n ( * the entry p r o b a b i l i t y e e [ 0 , l ] , the expected wealth under non-disclosure i s WN(n,7,e) - (1 - - . * .—r^p) (au+jb-e [8u+A]) N ay+b-e[oY+A] Set WN equal to WD at /x, < y and /x3 > y: a u x + i» - k - W N(ii 1,v /e) (3.B.16) cu 3 + d - k - W N(ji 3,v,e) (3.B.17) Solve (3.B.16) for k, for a given ju, and e, e (5 + A) [ (a-8 e) y + (jb - A e) ] k (y - ux) (a - fie) (3.B.18) Solve (3.B.17) f o r k, set the r e s u l t equal to (3.B.18), and then solve f o r e, for a given /x., and jx3, (7~Hi) (O H3+A)  6 " (y-Hi) (8u3+A) + (u 3-y) ( 5 u 1 + A ) (3.B.19) 173 A PD-H ecjuilibrium e x i s t s for c a p i t a l l e v e l k i f there e x i s t s an i n t e r s e c t i o n point y] that induces an i n t e r s e c t i o n point n3 based on (3.B.15) and an entry p r o b a b i l i t y e based on (3.B.19) such that (3.B.18) holds. Observe that (3.B.15), (3.B.18) and (3.B.19) are a l l con-tinuous functions of /x1 and that: u x - 0 =* u 3 - y, e - 1, and k - Kx - -A= [cy + d] cy \i1 - 7 =» u 3 - 2y~, e - 0, and k - K - [26y + A] [1 + —=] Therefore, condition (3.B.18) holds for a l l values of k between K and PD-L E q u i l i b r i a f o r y > 1/2: In a PD-L equilibrium with y > 1/2, WN can i n t e r s e c t WD e i t h e r twice (/i3 = 1) or three times (/i3 < 1) . Solve (3.B.11) to obtain v = (i, as a function of y = n2 and / i 3 : j. v - [2u 3 (n3 - y)] 2 - (u 3 - y) (3.B.20) WN = WD at /x3 < 1 i s again characterized by (3.B.13) and solving f o r k provides (3.B.14). Evaluate (3.B.14) and (3 . B. 2 0) at /x3 = y: u 3 - Y v - 0, k - K2 [6y + A] 174 At nz = 1 we only require that WN be greater than or equal to WD (a corner s o l u t i o n ) , i . e . , (3.B.13) i s an inequality f o r nz = 1. Restating (3.B.14) to r e f l e c t t h i s i n e quality provides the following condition f o r / i 3 = 1: * * *2 = 1 6 + A ] aVl-vJ > K z (3.B.21) where j. vx = [2 (1 - Y)] 2 " (1 " Y ) ( K 2 > follows from 6+A > 8y+k, av,+b > b, and a» (1-v.,) < ay)• Therefore, a PD-L equilibrium e x i s t s f o r a l l k e [0 , K 2 ] n [ 0 , d ] . PD-H E q u i l i b r i a f o r y > 1/2: With v = y = H2, we express / i , as a function of fxz: _i Hi - Y - tH 3 (2Y - U3) ] 2 (3.B.22) WN = WD at /x1 < Y i s again characterized by (3.B.16) and (3.B.18) restates condition (3.B.16) i n terms of k. I f ^ 3 < 1, then (3.B.19) states the implication of (3.B.17) and (3.B.18) f o r e. Evaluate (3.B.22), (3.B.19), and (3.B.18) at n z = y: u-3 - v - y =* Hi - 0, e - 1, k - Kx 4= [ C Y + d] 175 At / i 3 = 1, (3.B.22) implies that = y - [2y - l ] 1 / z . Let e 1 and represent the corresponding solutions to (3.B .19) and (3.B.18). Observe that (3.B.17) can be restated as an inequal-i t y i f /Lt3 = 1, since t h i s can be a corner s o l u t i o n with WD < WN: c + d - k z WN(1,y, e) (3.B.23) Combining (3.B.18) with (3.B.23) r e s u l t s i n the re s t a t e -ment of (3.B.19) as an inequality: e < e,. A PD-H equilibrium, with / i 3 = 1, ex i s t s f o r c a p i t a l l e v e l k i f there e x i s t s an entry p r o b a b i l i t y ee[0,e^] that s a t i s f i e s (3.B.18), where / i , i s defined by (3.B.22). Observe that k i s a continuous function of e with k = 0 i f e = 0 and k = i f e = e.,. Consequently, considering both /it3 < 1 and / i 3 = 1, PD-H e q u i l i b r i a e x i s t f o r a l l k e [0, max {K 1,K 1}]n[0,d]. Q.E.D. 176 Proof of Proposition 3.6.1 We provide a d e t a i l e d proof f o r the uniform d i s t r i b u -t i o n case and then make b r i e f comments on a s i m i l a r proof for the common knowledge case. Uniform d i s t r i b u t i o n case: I f y i s uniformly d i s t r i b -uted, then G*(/i) = G(n) = p . The proof f o r t h i s case consists of four lemmata. F i r s t , some knowledge about o*(v,v) and V(v,v) i s us e f u l . Figure 3-8 depicts these curves i n the uniform d i s t r i b u t i o n case. 3-8(a) i s the V curve (similar to Figure 3-2(b) but increased i n height by an amount k). 3-8(b) i s the a* curve, representing the equilibrium con-t r a c t offered by a l l n i n an FD equilibrium. 3-8(c) represents the equilibrium contract l i n e i n a PD-v, equi-librium. Note that i n the l a s t case, f o r a l l \i e N = [0,t 1] u [ t 2 , l ] , I o f f e r s one contract a*(v,) and M accepts i t . Insert Figure 3-8 here Observe that T*(a) i s empty i f a i s too small to be accepted by M, even i f M and E's expectation v maximizes V(v,v). Let a 1 represents the smallest a that would be accepted by M, which equals k/V(v*,v*), where v* i s the value of v which maximizes 177 V ( v , v ) - av + b - v [bv + A] Let a 2 represents the smallest a that would be accepted by a l l M no matter what b e l i e f s M holds. The value of a 1 and a2 depends on the shape of V, which, i n turn, i s determin-ed by the parameter values. We can c l a s s i f y a l l d i f f e r e n t s i t u a t i o n s into four cases which are mutually exclusive. The corresponding o*(v ,v) curves are depicted i n Figure 3 -(a) A < c-6, i . e . , b < c+d and a -A > 26. In t h i s case, the V-curve i s monotone increas-ing and, hence, the a*-curve i s monotone de-creasing. Thus, a 1 = k/c+d and a2 = k/b. (b) c-6 < A < c , i . e . , b < c+d and a -A e [0, 26]. In t h i s case, the V-curve has an i n t e r i o r maximum and a minimum at v = 0. Hence, ffl ( a - A ) 2 ~ (3.B.24) — — — i — + b 46 and a2 = k/b. (c) c < A < a , i . e . , b > c+d and a -A e [0,26]. In t h i s case, the V-curve has an i n t e r i o r maximum and a minimum at v = 1. Hence, the a., i s the same as (B.24) but ot2 = k/(c+d). (d) A > a, i . e . , b > c+d and a -A < 0. The V-curve i s monotone increasing and the a*-curve i s monotone decreasing. Hence, a, = k/b and a2 = k/(c+d). Insert Figure 3-9 here 178 Lemma 3.6.1; In a l l cases (a)-(d), T*(a) = 0 i f a < a,. Given any contract a such that a, < a < a 2, there always e x i s t b e l i e f s that w i l l induce the market to accept the contract, and other b e l i e f s that w i l l induce the market to r e j e c t the contract. That i s , both the sets A(a) and R(a) w i l l be non-empty. Let and v 2 denote the market b e l i e f s which separate A(a) and R(a), which are the solutions to a*(v,v) = a: v x(a) - max(o,-l-{(a-A) 2 w - [ (a-A)2+45 (Jb--£) ] "z}} a (3.B.25) v 2(a) - mind, —^-{(a-A) , _ i + [(a-A)2+48(i>- — ) ] 2 » (3.B.26) a We then have following lemma. Lemma 3.6.2; Given a, < a < a 2, the values of v,, and v 2, depending on the d i f f e r e n t cases, are (a) when A < c-d, v., > 0 and v 2 = 1 f o r a l l a; (b) when A e [c-d,c], > 0 for a l l a, v 2 = 1 i f a e [k/(c+d), a2=k/b], v 2 < 1 i f a e [a,, k/(c+d)]; (c) when A e [c,a], v 2 < 1 for a l l a, v, = 0 i f a e [k/b, a 2=k/(c+d)], and v, > 0 i f a e [«,f V b ] ; (d) when A > a, v 1 = 0, and v 2 < 1 for a l l a. 179 Observe that the sets A(a) = {v | r(a,v,v) = 0} = [v,,v2] R(a) = {v | r(a,v,v) = 1} = [0,v 1]u[v 2,1] and i n the cases where v, = 0 or v 2 = 1, one of these i n t e r v a l s i s empty. For a given contract a, the optimal expectation that M and E can hold (from I's perspective) i s the smallest expectation that w i l l induce M to accept the contract. Using the r e s u l t s from Lemma 6.2, the following lemma s p e c i f i e s the optimal expectation for each of the four cases. Lemma 3.6.3; The optimal expectation that M and E can hold i n response to contract a, f o r each of the four cases, i s (a) v, > 0; (b) v, > 0; (c) v, > 0 i f a 6 [ a 1 f k/b], v 2 < 1 i f a e [k/b, k/(c+d)]; and (d) v 2 < 1. Based on t h i s knowledge, the following lemma can be proved. Lemma 3.6.4; I f T*(a) * 0 , then T*(a) = T,UT2, where (i) T, = [0,t.,] and t, > 0 i f an FD-0 e q u i l i -brium e x i s t s ; ( i i ) T 2 = [ t 2 , l ] and t 2 < 1 i f an FD-1 e q u i l i -brium ex i s t s and an FD-0 equilibrium does not e x i s t . Proof of Lemma 3.6.4: The general characterization of 180 T*(a) follows from the fact that W*(/x) = WD(ii) i s concave and W+(ti,a) i s a l i n e a r function of /x. To demonstrate t h i s l i n e a r i t y , f i r s t observe that W* i s a l i n e a r function of /x i f r and p are f i x e d . Next observe that the smallest expectation v such that r*(a,v,v) = 0 i s the optimal expectation f o r a l l /xel. That i s , the desired expectation i s the smallest value of v s a t i s f y i n g a z a*(v,v) k — — av + b - v» [o v + A] which implies v = v, or v 2 according to lemma 3.6.3. Since T*(a) * 0 , W* and W+ must in t e r s e c t at l e a s t once (W+ cannot exceed W* f o r a l l / L t e l since that would require a<a,) . Given the above expectation, an i n t e r s e c -t i o n between W* and W*" s a t i s f i e s at+2?-t»[6t+A] -k - (l-a)»[at+jb-v(5t+A)] (3.B.27) For the moment ignore any bounds on t and l e t t 1 < t 2 be the two roots to t h i s quadratic equation. I f v > 0, then t, = v, implying that t, > 0. Hence, to prove condition (i) we need only prove that v = 0 i s impossible i f T*(a) * 0 and an FD-0 equilibrium e x i s t s , (a.l) FD-0 *» k > K2 = (<S+A)»b/a *» k/b > (6+A+k)/(a+b) . (a. 2) T*(a) = 0 i f W* > W1", V t e l . Assume v=0, t h i s holds i f at+b-t»[6t+A]-k > (l-a)«[at+b] 181 •» a > max{ k/b, (6+A+k)/(a+b) } Hence, from ( a . l ) , i f an FD-0 equilibrium e x i s t s , T*(a) * 0 implies a < a 2 = k/b. This, i n turn, implies that cases (c) and (d) i n which v 1 = 0 w i l l not occur. Hence v., > 0 implying t 1 > 0. For a proof of ( i i ) , note that when an FD-0 e q u i l i -brium does not e x i s t and T*(a) * 0 , t h i s implies that e i t h e r case (c) or (d), i n which k/b < a < k/(c+d), holds. Note that the optimal expectation i s now v 2 l (Because the acceptance set A(a) = [0, v 2 ] , the biggest v that w i l l accept a appears at v 2 instead of 0) . Hence i t i s easy to show that a < k/(c+d) ** v 2 < 1 *» t 2 < 1 Hence an FD-1 equilibrium e x i s t s . Common Knowledge Case; I f y = y i s common knowledge, then G*(v) = 0 V /xe[0, y] and G*(n) = 1 V /xe(y,l]. The proof of the proposition i s s i m i l a r to the proof for the uniform d i s t r i b u t i o n case and i s not given here. Q.E.D. Proof of Proposition 3.6.2 In a PD equilibrium, W* i s the maximum of WD and WN. Lemma 3.6.4 again applies. In the uniform d i s t r i b u t i o n case i t can be shown that i f , T*(a) * 0 , then e i t h e r v = 0 182 or v = 1 i s a credible threat, i . e . , at l e a s t one of these expectations i s such that i t would r e s u l t i n the r e j e c t i o n of a and belongs to T*(a). S i m i l a r l y , i n the common knowl-edge case i t can be shown that, i f T*(a) * 0 , then e i t h e r v = O o r v = y i s a credible threat. Q.E.D. Proof of Proposition 3.6.3 We provide a proof based on the uniform d i s t r i b u t i o n . The proof f o r other d i s t r i b u t i o n s i s more complicated. The " i f " part i s straightforward as discussed above. The "only i f " part can be shown i n two steps. F i r s t , given an out-of-equilibrium contract a, assume M and E hold b e l i e f v (a) = v., (a). Based on v 1 ( a w i l l be accepted and T*(a) = [0,t . , ]u[t 2,1] . I f there e x i s t s a T<=T*(a) such that v, = ji(T), then T forms a PD equilibrium, a contradiction. Second, consider the case i n which M and E hold b e l i e f s v'(a) < v ^ a ) . Let the equilibrium contract corresponding to v 1 be a'. Since v' < v 1 # we have a' > a*. From Figure 6-8, i t can be seen that A(a') ^  A(a*) , i . e . , we have T*(a*) <z T*(a*) since T*(a) = I/A (a) . I f T c T*(a'), then T <= T*(a*) and T forms a PD equilibrium. This again r e s u l t s i n a contradiction. Q.E.D. 183 Proof of Proposition 3.6.4 The " i f " part i s obvious. For the "only i f " part, l e t us assume there does not e x i s t another dominant PD equilibrium. Let the equilibrium non-disclosure contract be a 0, and l e t M and E's b e l i e f i n the equilibrium be v° = v (a0) . For some out-of-equilibrium contract a, < a 0, i f M and E respond with = v(a,), then i t must be that v1 > v°. Otherwise, the contract a, w i l l be rejected. The Wt(a1) curve cannot l i e above W+(a°) otherwise vft(a^) becomes a dominant PD-equilibrium. This implies that they must cross, and T*(a.,) can be e i t h e r [0^,] or [ v ) ( l ] . (See Figure 3-10.) However, one i n t e r v a l cannot form a PD equilibrium so that a T s a t i s f y i n g the GP-criterion condi-t i o n w i l l not e x i s t . Hence, a s i n g l e PD equilibrium w i l l not f a i l the GP-criterion. Insert Figure 3-10 here For > v(a,), i . e . , a > a*(v,v), the arguments are s i m i l a r . Q.E.D. 184 Appendix I M E x — A M yi k 7T° e — e(v,y) p(v) yr (/i, 0) =a/x+b — 7T (/x, 1) =c/i+d <S=a-c — A=b-d Y Y Y M(M)={M#n) in e M(/i) y *(M|y) M(y) r — a — 3.C: Notation Used i n the Paper Incumbent Capital Market Entrant. I's end-of-period value (random) w.c.d.f. F(x|«) I's type, w.c.d.f. $(M) The p r i o r mean of p The r e a l i z e d value of p., I's private information. The amount of investment needed. I's payoff i f the project i s turn down. Entry p r o b a b i l i t y of E . E's strategy given E's b e l i e f v and type y. I and M's b e l i e f about E's entry prob-a b i l i t y . I•s expected end-of-period value given /i and e=0. I's expected end-of-period value given H and e=l. Variable entry cost. Fixed entry cost. E's type w.c.d.f. G ( y ) . Realized value of y, E's private i n -formation. Expected value of y o r common knowl-edge of E's type. Set of possible reports type (xel can send. Message sent by type / i e l . M and E's information about p. M and E's poster i o r b e l i e f s about p given y. M and E•s poster i o r expectation about p given y. The p r o b a b i l i t y with which M re j e c t s the contract a. Share of I's payoff to be received by M. 185 a (v,p) = k/V(v,p) — Minimum share M w i l l accept given v and p. V(v,p) — Firm's market p r i c e given b e l i e f v and P -N — Non-disclosure region, i . e . , I's s t r a -tegy. D — Disclosure region. W(it,a,r,p) — I's expected end-of-period wealth. WD(/i) — I's expected end-of-period wealth under disclosure. WM(M/V,p(v)) — I's expected end-of-period wealth under non-disclosure. K,,K2 — Boundaries of k for a FD equilibrium. k^i/k,,k 2 ,k2 ,K — Boundaries of k for a PD equilibrium. K-H=[k1,ic1] — The set of k for which a PD-H e q u i l i b -rium e x i s t s . K-L= [k2,kg] — The set of k for which a PD-L e q u i l i b -rium e x i s t s . / i t , , i i 2 , / i 3 — Intersections of W0 and WN. /30,/3.,,/32 — Parameters of the beta d i s t r i b u t i o n . FD-v — F u l l disclosure equilibrium sustained by non-disclosure b e l i e f v. PD-L — P a r t i a l disclosure equilibrium with v = h\ . . . . . PD-H — P a r t i a l disclosure equilibrium with v = M2-186 References Brennan, M. and Kraus, A. [1987] " E f f i c i e n t Financing under Asymmetric Information." Working paper, University of B r i t i s h Columbia. Cho, I-k. and D.Kreps [1987] " S i g n a l l i n g Games and Stable E q u i l i b r i a , " Quarterly Journal of Economics Vol.102 pp.179-222. Darrough,M.N. and N.M.Stoughton [1990] "Financial D i s c l o -sure P o l i c y i n an Entry Game." Journal of Accounting and  Economics 12, pp.219-243 Degroot,M.H. [1970] Optimal S t a t i s t i c a l Decisions. New York: McGraw-Hill. Dye,R.A. [1985a] "Disclosure of Non-proprietary Informa-t i o n . " Journal of Accounting Research. Vol.23 No.l spring pp.123-145. Feltham,G.A. and Christensen,P.O. [1988] "Firm-Specific Information and E f f i c i e n t Resource A l l o c a t i o n . " Contem- porary Accounting Research 5 pp.133-169. Grossman,S.J. and M.Perry [1986] "Perfect Sequential Equilibrium." Journal of Economic Theory 39, pp.97-119. Kohlberg,E. and J-F Mertens [1986] "On the Strategic S t a b i l i t y of E g u i l i b r i a . " Econometrica 54, pp.1003-1037. Kreps,D.M. and R.Wilson [1982] "Sequential E q u i l i b r i a . " Econometrica Vol.50 pp.863-894. Verrecchia,R.E. [1983] "Discretionary Disclosure." Jour- nal of Accounting and Economics. Vol. 5 pp.179-194. Verrecchia,R.E. [1990] "Information Quality and Discre-tionary Disclosure." Journal of Accounting and Economics 12 pp.365-80. Wagenhofer,A. [1990] "Voluntary Disclosure with A Stra-t e g i c Opponent." Journal of Accounting and Economics 12 pp.341-63. 187 PART II INCOMPLETE CONTRACTING 188 Chapter 4 INTRODUCTION TO PART II 189 F i f t y years ago, Coase [1937] began to deal with some key questions that neoclassical economic theory had ignored. What i s a firm? What factors determine a firm's size? What are the costs and benefits of integration? Coase's answers are based on h i s fundamental insights that: (1) some kinds of economic a c t i v i t i e s are too c o s t l y to coordinate by using the market p r i c e system; (2) mar-kets and firms are al t e r n a t i v e ways of organizing economic exchanges; and (3) uncertainty and opportunism increase the cost of using the p r i c e system. In recent years, Coase's work has s i g n i f i c a n t l y influenced the development of research i n the theory of organizations. Following Coase, Williamson [1975] [1985] has developed the concept of "transaction cost" and the theory of "transaction cost economics". Williamson [1975] summaries h i s model as follows: The general approach to economic organiz-ation employed here can be summarized compactly as follows: (1) Markets and firms are alt e r n a -t i v e instruments f o r completing a rel a t e d set of transactions; (2) whether a set of transactions ought to be executed across markets or within a firm depends on the r e l a t i v e e f f i c i e n c y of each mode; (3) the costs of wri t i n g and executing complex contracts across a market vary with the  c h a r a c t e r i s t i c s of the human decision makers who  are involved with the transaction on the one  hand, and the objective properties of the market  on the other; and (4) although the human and environmental factors that impede exchanges between firms (across a market) manifest them-selves somewhat d i f f e r e n t l y within the firm, the same set of factors apply to both. 190 For Williamson [1985], the human c h a r a c t e r i s t i c s that most a f f e c t the governance choice are bounded r a t i o n a l i t y and opportunism. The environmental c h a r a c t e r i s t i c s that determine the choice between market and h i e r a r c h i c a l governance are uncertainty, complexity, and small numbers. The existence of a small number of parties, to an exchange increases the l i k e l i h o o d of opportunistic behaviour, while the existence of uncertainty and complexity makes bounded r a t i o n a l i t y operative, thus making i t impossible f o r p a r t i e s to an exchange to a n t i c i p a t e a l l possible future states i n t h e i r r e l a t i o n s . In such a setting, the costs of w r i t i n g and enforcing a contract assuring a l l p a r t i e s to an exchange of an outcome that a l l would deem as ac-ceptable are high enough to be p r o h i b i t i v e . In t h i s s i t u -ation, a market would be an i n e f f i c i e n t means of carrying forward a transaction, and i t w i l l be replaced by a h i e r -archy . One of the c r i t i c i s m s of Williamson's work, as pointed by Kreps [1984], i s that he i s l e s s convincing i n h i s arguments that transacting through a h i e r a r c h i c a l organization w i l l lessen transaction costs. Although Williamson e x p l i c i t l y recognizes that transacting through a h i e r a r c h i c a l framework w i l l also incur transaction costs, he does not provide enough analysis about how they would d i f f e r from market mediated transaction costs. The 191 arguments as to why empirical observations show that h i e r a r c h i c a l transactions usually incur lower transaction costs needs to be developed further. Alchian and Demsetz [1972] also stress a type of transaction s p e c i f i c investment i n developing t h e i r expla-nation of why firms e x i s t . For Alchian and Demsetz, the reason f o r the existence of firms can ultimately be found i n what they c a l l team production. Team production e x i s t s when the c o l l e c t i v e output of a group of i n d i v i d u a l s i s greater than the sum of the output of each of them separ-ately, and where i t i s simultaneously d i f f i c u l t to d i s -cover each i n d i v i d u a l ' s contribution to the group's out-put. Individuals i n these teams have firm s p e c i f i c s k i l l s — s k i l l s whose value i s greater i n combination with other members of the p a r t i c u l a r team than i n other exchange contexts. However, the existence of productive teams does not, by i t s e l f , r e s u l t i n h i e r a r c h i c a l forms of organizations. Teamwork only requires cooperation; i t does not necessar-i l y require an organizational hierarchy. Alchian and Demsetz argue that the c l a s s i c a l firm emerges because of the eventual need to monitor, or meter, the i n d i v i d u a l s that make up a productive team. Because i t i s d i f f i c u l t i n a team to determine the i n d i v i d u a l contributions of each member, each member has an incentive 192 to shirk. The p o s s i b i l i t y of shirking w i l l deter high-output i n d i v i d u a l s from j o i n i n g the team and may discour-age customers and c a p i t a l investors as well. One way to reduce s h i r k i n g i s to provide f o r monitoring of the per-formance of each team member. However, because the moni-t o r also has incentive to shirk, other mechanisms to provide incentives f o r the monitor are necessary. One key structure f o r such incentives i s so c a l l e d property r i g h t s . The structure of property rig h t s can reduce the l i k e l i h o o d of s h i r k i n g by a monitor by causing him to bear the costs of such behaviour. These property r i g h t s include: (1) the r i g h t to the residual p r o d u c t i v i t y of the team beyond that which i s necessary to keep the team operating, (2) the r i g h t to observe'the productive input of i n d i v i d u a l s on the team, (3) the r i g h t to monitor a l l contracts with sources of input into the team, and (4) the r i g h t to s e l l these r i g h t s . These property r i g h t s define the ownership of the firm. The owner of the firm has strong incentives not to shirk h i s monitoring r e s p o n s i b i l -i t i e s , since by doing so, he would not be maximizing h i s personal wealth. K l e i n , Crawford, and Alchian [1978] explore one p a r t i c u l a r cost f o r using the market system — the p o s s i -b i l i t y of post-contractual opportunistic behaviour. The p a r t i c u l a r circumstance they emphasize i s the presence of 193 appropriable s p e c i a l i z e d quasi-rents. A f t e r a s p e c i f i c investment i s made and such quasi-rents are created, the p o s s i b i l i t y of opportunistic behaviour i s very r e a l . There are two possible ways to solve the problem: v e r t i c a l i n tegration or contracts. As assets become more s p e c i f i c and more appropriable quasi-rents are created (and there-fore the possible gains from opportunistic behaviour increase), the costs of contracting w i l l generally increase more than the costs of v e r t i c a l integration. Hence, c e t e r i s paribus, we are more l i k e l y to observe v e r t i c a l integration. Following the work of Coase [1937], Williamson [1975], Alchian and Demsetz [1972], Kle i n , Crawford, and Alchian [1978], Grossman and Hart [1986] [1987] develop a theory of integration. They emphasize the benefits and the costs of "control" i n response to s i t u a t i o n s i n which there are d i f f i c u l t i e s i n wri t i n g or enforcing complete contracts. Contractual r i g h t s can be of two types: speci-f i c r i g h t s and residual r i g h t s . When i t i s too c o s t l y f or one party to specify a long l i s t of the p a r t i c u l a r r i g h t s i t desires over another party's assets, i t may be optimal fo r that party to purchase a l l the r i g h t s except those s p e c i f i c a l l y mentioned i n the contract. Ownership i s the purchase of these residual r i g h t s . For Grossman and Hart, integration i s defined i n 194 terms of the ownership of assets so that at issue i s when one firm w i l l desire to acquire the assets of another firm. I f one party acquires the r i g h t s of c o n t r o l , then that must reduce the r i g h t s of control of the other party. There are p o t e n t i a l costs associated with removing control from those who manage productive a c t i v i t i e s . Therefore, i t i s desirable for firm 1 to integrate firm 2 only when firm I's control increases the productivity of i t s management more than the loss of control decreases the p r o d u c t i v i t y of firm 2's management. A basic idea i n a l l the papers discussed above i s that transaction costs are incurred i n w r i t i n g contracts. In a world where i t i s costless to write contracts, the p a r t i e s engaging i n a transaction would write a complete contract which s p e c i f i e s p r e c i s e l y each party's o b l i g a -t i o n s i n every conceivable state of the world. Under a complete contract, there i s no need for contract renego-t i a t i o n because everything would be anticipated i n advance. Nor would any disputes ever occur since a t h i r d party could (costlessly) determine whether one of the p a r t i e s had breached the contract, and would impose an appropriate penalty. Ownership i s i r r e l e v a n t under com-plete contracting even i f information asymmetries e x i s t . However, the assumption of no transaction costs i s u n r e a l i s t i c . Instead, i n practice, transaction costs are 195 pervasive and unavoidable. A consequence of these costs i s that contracts are always incomplete. An incomplete contract s p e c i f i e s some obligations of the contracting p a r t i e s i n some states but not i n others. Furthermore, contracts are sometimes incomplete even though they spec-i f y the obligations of the contracting p a r t i e s i n a l l states. The incompeletenss i n that context a r i s e s because the obligations are held constant across some states f o r which i t would be "optimal" to specify d i f f e r e n t o b l i g a -t i o n s f o r d i f f e r e n t states. This i s p a r t i c u l a r l y the case f o r low p r o b a b i l i t y events, such as the October 1987 stock market crash which Saly [1991] i s examining. This r e s u l t s i n the p o s s i b i l i t y that the part i e s w i l l e i t h e r be forced or be motivated to renegotiate the contract. In addition, disputes may occur either because of d i f f e r e n t i n t e r p r e t a -t i o n s of the contract, or due to opportunistic behaviour. The nature of incomplete contracting i s analyzed by Hart and Moore [1988]. They focus on the cost of wri t i n g a contingent clause i n a s u f f i c i e n t l y c l e a r and unambigu-ous way that i t can be enforced. I f the state v a r i a b l e i s complex, t h i s cost may be p r o h i b i t i v e l y high. Thus, the p a r t i e s may end up writing an incomplete i n i t i a l contract, and r e v i s i n g the contract once the state i s r e a l i z e d . Given r a t i o n a l expectations by the pa r t i e s , the p o s s i b i l -i t y of contract renegotiation w i l l a f f e c t the form of the 196 o r i g i n a l contract. In addition, i t may be i n the p a r t i e s ' i n t e r e s t s to constrain, i n the i n i t i a l contract, the f i n a l outcome of the renegotiation process. In other words, the p a r t i e s ' problem i s to design an optimal r e v i s i o n game to be played once the state i s r e a l i z e d . Hart and Moore [1990] contribute further to the theory of property r i g h t s . They extend the idea that ownership i s the control of assets to a multi-asset, m u l t i - i n d i v i d u a l economy and study how changes i n owner-ship a f f e c t the incentives of non-owners of assets (employees) as well as the incentives of owner-managers. One of the key assumptions i n t h e i r analysis i s that each i n d i v i d u a l ' s contribution i s given by h i s Shapley value. The optimal assignment of assets based on t h e i r s e t t i n g i s such that an agent i s more l i k e l y to own an asset i f h i s action i s s e n s i t i v e to whether he has access to the asset and i s important i n the generation of surplus, or i f he i s a c r u c i a l trading partner f o r others whose actions are s e n s i t i v e to whether they have access to the asset and are important i n the generation of surplus. These r e s u l t s help us to understand the boundaries of the firm. These recent advances i n the organization theory should have a great influence on managerial accounting research. Accounting plays an information supporting r o l e i n a firm's economic a c t i v i t i e s . An accounting system can 197 be optimized only i f we understand the firm's strategy i n organizing transactions, e i t h e r i n t r a - f i r m or i n t e r - f i r m . This part of the thesis contributes to incomplete contracting research from the perspective of managerial accounting. The main purpose i s to extend the t r a d i t i o n a l contracting theory analysis of accounting .issues by incor-porating a broader set of contracting strategies. The key issues we focus on are the same as those pursued by Gross-man, Hart, and many others i n the economics f i e l d . What are the benefits of "organizing transactions within the firm?" How can incomplete contracting work within the firm? The d i s t i n c t i v e nature of our analyses, r e l a t i v e to the e x i s t i n g economics l i t e r a t u r e , i s that we examine the problem from an accounting perspective and emphasize the implication of these new theories to managerial accounting research. Each of the following two chapters provides an ana-l y t i c a l model rel a t e d to incomplete contracting. Chapter 5 analyzes contracting strategy by e x p l i c i t l y considering contracting costs. We show how contracting e f f i c i e n c y can be more p r e c i s e l y defined i f we e x p l i c i t l y consider con-t r a c t i n g costs, and how incomplete contracting can improve contracting e f f i c i e n c y through minimizing contracting costs. The r e s u l t s i n t h i s chapter provide new insights f o r the issue of tr a n s f e r p r i c i n g for i n t r a - f i r m transac-198 t i o n s . B a s i c a l l y , we believe that the t r a n s f e r prices should be chosen based on the c r i t e r i o n of minimizing transaction costs. Chapter 6 focuses on the incentive issue within organizations. Agency theory usually assumes complete contracting and, hence, provides so c a l l e d high-powered incentives f o r the agents (see the chapter f o r a d e t a i l e d d e f i n i t i o n ) . This i s consistent with some employee l e v e l s i n a firm, p a r t i c u l a r l y top management. However, most employees' compensation i s not based on e x p l i c i t contin-gent contracts. Instead, they are motivated not to shirk by low-powered incentives. These incentives are provided by the a n t i c i p a t i o n of future contract renewal. In the model, employment contracts are incomplete and short-term. However, the employees' s p e c i f i c human assets provide incentives to maintain long-term employment r e l a t i o n s . I t i s the sharing of the ex post gains from the employment r e l a t i o n that provides incentives f o r the employee and the firm to invest. More accurately, both economic agents are motivated by the anticipated sharing of expected future gains where those expectations w i l l be influenced by the observed, but non-contractible, human asset l e v e l s . 199 References Alchian, A. and H. Demsetz [1972] "Production, Information Costs, and Economic Organization." American Economic  Review. Vol.62, pp.777-795. Coase,R.H. [1937] "The Nature of the Firm." Economica. Vol.4, pp.386-405. Grossman,S.J. and O.D. Hart [1986] "The Costs and Benefits of Ownership: A Theory of V e r t i c a l and Lateral Integra-t i o n . " Journal of P o l i t i c a l Economics. Vol.94, No.4, pp.691-719. Grossman,S.J. and O.D. Hart [1987] " V e r t i c a l Integration and the D i s t r i b u t i o n of Property Rights." i n Economic  Po l i c y i n Theory and Practice eds. Assaf Razin and Efraim Sadka, Sapier conference Volume. New York: MacMillan Press. Hart, O. D. [1987] "Incomplete Contracts and the Theory of the Firm." Working paper No.448, MIT. Hart, O. D. and J . Moore [1988] "Incomplete Contracts and Renegotiation." Econometrica. Vol.56, No.4 pp.755-785. Hart, O. D. and J . Moore [1990] "Property Rights and the Nature of the Firm." Journal of P o l i t i c a l Economy. Vol. 98, No.6, pp.1119-1157. Klein , B., R. G. Crawford, and A. A. Alchian [1978] "Ver-t i c a l Integration, Appropriable Rents, and the Competitive Contracting Process." The Journal of Law and Economics, Vol.21, pp.297-326. Kreps, D. M. [1984] "Corporate Culture and Economic The-ory." Mimeographed. Stanford, C a l i f . : Stanford University. Saly, J . [1991] "The E f f e c t of Major Stock Downturns on Executive Stock Option Contracts." Thesis proposal, Uni-v e r s i t y of B r i t i s h Columbia. Williamson, O. [1975] Markets and Hierarchies The Free Press, N.Y. Williamson, O. [1985] The Economic I n s t i t u t i o n s of Capi- talism. The Free Press, N.Y. 200 Chapter 5 INCOMPLETE CONTRACTING FOR ECONOMIZING CONTRACTING COSTS 201 5.1 Introduction As early as 1937, Coase pointed out that some kinds of economic a c t i v i t i e s are too c o s t l y to coordinate by using the p r i c e system (Coase [1937]). He claimed that markets and firms are al t e r n a t i v e ways of organizing economic exchange. These perceptions l e d him to focus e x p l i c i t l y on contracting processes. Coase's insights were advanced by Williamson [1975] [1985]. Williamson focused on "transaction costs" which are, by Arrow [1974], the costs of running the economic system. Coase and Williamson's work should be extremely important to managerial accounting research. Managerial accounting f a c i l i t a t e s i n t r a - f i r m transactions, which, by Coase's view, are substitutes f o r market transactions. Williamson argues that the main reason f o r a transaction to occur within a firm i s that i t i s more c o s t l y to e f f e c t the transaction as a market exchange between two indepen-dent units than to incorporate both units within a singl e firm. What transaction and organizational c h a r a c t e r i s t i c s allow a firm to provide these advantages? What implica-tions do these organizational c h a r a c t e r i s t i c s have f o r managerial accounting research? These questions have not been explored i n accounting research to any s i g n i f i c a n t extent. Although the existence of transaction costs has been 202 recognized i n accounting research, most of the l i t e r a t u r e to date assumes that these costs are t r i v i a l . Therefore, they are e i t h e r ignored or combined with t r a d i t i o n a l production costs. Sometimes, transaction costs are r e l a -t i v e l y small with respect to transaction gains and, hence, ignoring them w i l l have l i t t l e impact on the analysis. However, there e x i s t situations i n which these costs are n o n - t r i v i a l , and play a c r u c i a l r o l e i n the contracting process. In these cases, ignoring these costs w i l l cause serious bias i n the r e s u l t s . For example, i f contracting costs are ignored, then a bias toward complicated compre-hensive contracting i s present. This i s c e r t a i n l y mis-guided i f complete contracting i s very c o s t l y (perhaps impossible). The above issues motivate us to e x p l i c i t l y consider transaction costs. This i s p a r t i c u l a r l y important when we examine a firm's behaviour i n organizing i n t r a - f i r m trans-actions. A firm's managerial accounting system that r e f l e c t s the firm's strategies and governance structure may be influenced by such considerations. We e x p l i c i t l y consider contracting costs i n a simple i n t r a - f i r m transaction model. The main objective i s to show the influence of contracting costs on contracting s t r a t e g i e s . We show how contracting e f f i c i e n c y can be more p r e c i s e l y defined i f we e x p l i c i t l y consider contract-203 ing costs, and how incomplete contracting can improve contracting e f f i c i e n c y through minimizing contracting costs. Thus we extend t r a d i t i o n a l contracting theory, which emphasizes complete contracting, to a broader con-t r a c t i n g strategy space. In short, taking contracting costs into account, incomplete contracting may be optimal i n many cases. This i s obviously consistent with empiri-c a l observations. We use the concepts "transaction costs" and "con-t r a c t i n g costs" inter-changeably. Observe that, since "transaction cost economics" takes a contract as the main transaction instrument, the transaction r e l a t i o n i s con-t r a c t u a l . The main contributions of t h i s paper are as follows. F i r s t , through a systematic analysis of d i f f e r e n t con-t r a c t i n g processes for an i n t r a - f i r m transaction, we e s t a b l i s h conditions under which complete, n u l l , or incom-plete contracting may be optimal. To reach these r e s u l t s , we provide a formal d e f i n i t i o n f o r contracting costs. Second, i f the incomplete contract i s optimal, we provide a c r i t e r i o n f o r choosing the optimal governance structure and ex ante contract p r i c e s . In p a r t i c u l a r , we i d e n t i f y conditions under which a dual p r i c i n g contract can improve contract e f f i c i e n c y . Third, our r e s u l t s provide a poss-i b l e explanation for observed transfer p r i c i n g p o l i c i e s i n 204 managing repeated transfers of products within an organiz-ation. S p e c i f i c a l l y , we observe that firms e s t a b l i s h " t r a n s f e r p r i c i n g p o l i c i e s " to govern a se r i e s of future transactions. 1 Although the prices s p e c i f i e d by these p o l i c i e s may be renegotiable, most future transactions w i l l be based on these p r i c i n g p o l i c i e s . .In p a r t i c u l a r , r e l a t i v e l y few firms use bargaining between d i v i s i o n s as a means of determining t r a n s f e r p r i c e s f o r repeated transac-t i o n s . 2 Our r e s u l t s show that when the firm faces uncer-t a i n t y and information asymmetry, an incomplete contract i n which a p a i r of prices i s s p e c i f i e d ex ante w i l l mini-mize contracting costs so that the firm's net cash flows w i l l be maximized. Therefore, s e t t i n g a t r a n s f e r p r i c i n g p o l i c y i s an optimal way to govern repeated i n t r a - f i r m transactions. A f t e r t h i s introductory section, the paper i s organ-ized as follows. Section 5.2 discusses contracting cost concepts. A de t a i l e d d e f i n i t i o n of contracting costs i s 'in the following analysis the central management sets a p o l i c y regarding which d i v i s i o n has control of the tr a n s f e r decision and the d i v i s i o n s negotiate ex ante p r i c e s . Although t h i s seems inconsistent with some obser-vations, we believe that the d i v i s i o n s play some r o l e i n the s e t t i n g of these p r i c e s . I t i s u n l i k e l y that the central management can act alone i n deciding the tr a n s f e r p o l i c i e s . We leave t h i s question open for further research. 2Atkinson [1987] found that only 7% of Canadian firms determine tr a n s f e r prices on the basis of negotiation. 205 provided based on Williamson's point of view. Section 5.3 presents basic model elements. Section 5.4 analyzes contracting strategies i n settings with v e r i f i a b l e i n f o r -mation. Section 5.5 analyzes contracting strategies i n settings with u n v e r i f i a b l e information. Section 5.6 extends the r e s u l t s i n Section 5.5 to settings with large ex post bargaining costs, and introduces bargaining under asymmetric information. In section 5.7 we discuss the implications of our r e s u l t s to the transfer p r i c i n g prob-lem. Section 5.8 i s a b r i e f conclusion. 5.2 Contracting Costs As with most other economic a c t i v i t i e s , the contract-ing process incurs costs. In some cases, contracting costs are small r e l a t i v e to the gains r e s u l t i n g from the transactions so that they can be ignored without causing serious bias i n the analysis. In other cases, they are n o n - t r i v i a l so that ignoring them w i l l r e s u l t i n misguided conclusions. Unlike production costs or information costs, which have been extensively studied, there i s l i t t l e l i t e r a t u r e on the t o p i c of contracting costs. Dye [1985] assumes that the cost of writing a contract i s an increasing function of the number of contingencies i n the contract. This i s " a n a l y t i c a l l y convenient", but i s c e r t a i n l y overly 206 s i m p l i f i e d . We follow Williamson [1985], t r e a t i n g contracting costs as the major form of transaction costs. There are both ex ante and ex post transaction costs. The ex ante costs include the costs of dr a f t i n g , negotiating, and safeguarding an agreement. The ex post costs include (i) the maladaption 3 costs incurred when transactions d r i f t out of contract alignment; ( i i ) the haggling costs incur-red i f b i l a t e r a l e f f o r t s are made to correct ex post mis-alignments; ( i i i ) the set up and running costs associated with the governance structure to which disputes are refe r r e d ; and (iv) the bonding costs of e f f e c t i n g secure commitments. A key feature of the above d e f i n i t i o n i s that the contracting process i s viewed as a whole. Writ-ing a contract i s only one step i n t h i s whole process. This point i s p a r t i c u l a r l y important i f the i n t e r a c t i o n of ex ante and ex post contracting costs i s recognized. To make the d e f i n i t i o n more precise, we c l a s s i f y con-t r a c t i n g costs into the following categories: (a) S p e c i f i c a t i o n Costs S p e c i f i c a t i o n costs are the resources spent to c l a r -3Williamson [1985] uses the term adaptation to describe the actions or processes the contracting p a r t i e s take to adjust to environmental conditions. S i m i l a r l y , the term maladaption means poor or inadquate adaptation. 207 i f y the c h a r a c t e r i s t i c s of the uncertain event. This c l a r i f i c a t i o n i s extremely important f o r a contract p r o v i -sion since an equivocal s p e c i f i c a t i o n w i l l not only increase the d i f f i c u l t i e s of v e r i f i c a t i o n i n l a t e r execu-t i o n , but also creates room fo r opportunistic behavior by e i t h e r contracting party so that dispute settlement costs may be incurred with larger p r o b a b i l i t y . Depending on the nature of the uncertain events, t h i s cost can range from t r i v i a l to extremely high. Some events have very simple scale measurements, such as net income, stock p r i c e s , procument quantities, or ages of insurants, which are very easy to specify i n an agreement. In some cases, one math-ematical formula can cover a l l events, even i f the number of events i s i n f i n i t e . In such cases the cost of one event s p e c i f i c a t i o n can be treated as t r i v i a l . In such a case, only the t o t a l s p e c i f i c a t i o n cost has meaning. In the other extreme, some events have very complex charac-t e r i s t i c s . For instance, the q u a l i t y of a product or service, the management e f f o r t required to e s t a b l i s h a well functioning d i v i s i o n , or a manager's non-pecuniary pr i v a t e benefit that does not show up i n a firm's accounts. A l l are very d i f f i c u l t to specify, or the s p e c i f i c a t i o n can be done only with high cost. In i n t r a - f i r m contracting, contract s p e c i f i c a t i o n s are often based on accounting numbers. Hence, the costs 208 to e s t a b l i s h and run an accounting system can be viewed as s p e c i f i c a t i o n costs for i n t r a - f i r m contracting. (b) Ex Post V e r i f i c a t i o n Costs During contract execution, v e r i f i c a t i o n of a p a r t i c u -l a r event r e a l i z a t i o n i s a necessary step i n i d e n t i f y i n g the appropriate provision to be executed. Furthermore, v e r i f i c a t i o n i s necessary f o r a t h i r d party r u l i n g should a dispute between the two contracting p a r t i e s a r i s e . V e r i f i c a t i o n costs are intimately correlated with the s p e c i f i c a t i o n costs. On the one hand, i f an event i s easy to specify, then i t s v e r i f i c a t i o n i s also easy. This implies a p o s i t i v e c o r r e l a t i o n between v e r i f i c a t i o n and s p e c i f i c a t i o n costs. On the other hand, high q u a l i t y s p e c i f i c a t i o n w i l l s i m p l i f y the v e r i f i c a t i o n , which implies a negative c o r r e l a t i o n between v e r i f i c a t i o n and s p e c i f i c a t i o n costs. For s i m p l i c i t y , we pool the above two categories together. However, i n doing so i t must be stressed that the s p e c i f i c a t i o n costs always occur ex ante, while the v e r i f i c a t i o n costs occur ex post. There-fore, when we count these costs, i t i s necessary to spec-i f y the time point at which we account fo r them. We can have an expected cost that i s equal to the t o t a l s p e c i f i -c ation costs plus the expected v e r i f i c a t i o n costs, or a r e a l i z e d cost that i s equal to the t o t a l s p e c i f i c a t i o n 209 costs plus the v e r i f i c a t i o n costs for a p a r t i c u l a r r e a l -ized event. The ex ante expected value and the ex post r e a l i z e d value are i d e n t i c a l only i n the s p e c i a l case where we assume that the v e r i f i c a t i o n costs are constant fo r a l l events. (c) Ex ante negotiation or bargaining costs These costs include the resources spent to f i n d a mutually acceptable agreement. I f the transaction w i l l provide p o s i t i v e gains, then both pa r t i e s have incentives to reach an agreemerit. However, since the d i v i s i o n of those gains i s negotiable, the p a r t i e s must engage i n bargaining to a r r i v e at an agreement. Bargaining costs include not only the resources d i r e c t l y used i n the pro-cess, but also the opportunity costs born by each party due to the delay of the transaction induced by the bar-gaining process. These costs depend c r u c i a l l y on the information structure. Bargaining when the p a r t i e s have asymmetric information incurs p a r t i c u l a r l y high costs. I f contracting i s ex ante complete, or there i s a commitment to non-renegotiation and the s p e c i f i c a t i o n of the provisions i s perfect (so that there w i l l not be any disputes i n contract execution), then the above three categories cover a l l the contracting costs. However, i n general, contracts are incomplete, renegotiation i s 210 allowed, and disputes can a r i s e i n executing the contract. Therefore, the following costs may a r i s e . (d) Ex Post Renegotiation or Bargaining Costs Renegotiation and ex post bargaining i s never d e s i r -able i n c l a s s i c a l comprehensive contracting since a l l relevant future contingencies are f i x e d i n advance through an ex ante complete contract. However, renegotiation i s desirable under incomplete contracting f o r the following reasons. F i r s t , due to the incompleteness of the i n i t i a l contract, there may e x i s t opportunities f o r improvements through renegotiation that would benefit both p a r t i e s . The more incomplete the ex ante contract, the more oppor-t u n i t i e s there e x i s t for such improvements. Second, there may e x i s t maladaption problems since not every appropriate adaptation can be foreseen i n advance; some may not be c l e a r u n t i l the event materializes. Third, the p a r t i e s may i n t e r p r e t an agreement d i f f e r e n t l y due to an equivocal s p e c i f i c a t i o n , a missing provision, or opportunistic s t r a t e g i e s . Hence, ex post bargaining can be viewed as the complement of ex ante bargaining. (e) Dispute Settlement Costs Renegotiation and bargaining i s often the f i r s t step i n r e s o l v i n g disputes raised at the time of contract 211 execution. I f t h i s step i s successful, then the dispute settlement costs include only the renegotiation costs. However, i f t h i s step f a i l s , then a third-party r u l i n g i s necessary. Dispute settlement costs are mainly determined by the governance structure. Williamson [1985] points out that d i f f e r e n t governance structures provide d i f f e r e n t types of t h i r d party r u l i n g s . In a market structure, the court and l e g a l system provide t h i r d party r u l i n g s which are expensive and often i n e f f e c t i v e . The high settlement costs include the resources both p a r t i e s must spend i n the t r i a l process. Neoclassical law emphasizes the r o l e of an a r b i t r a t o r i n a s s i s t i n g the p a r t i e s to resolve disputes. I t has advantage of being more f l e x i b l e . Compared to court r u l i n g s , an a r b i t r a t i o n process lowers settlement costs and r a i s e s settlement effectiveness. F i n a l l y , i n an integrated organization structure, the h i e r a r c h i c a l power i n an organization provides e f f e c t i v e and low cost dispute settlements. Any dispute occurring i n the organization can be s e t t l e d by a higher ranking authority and the top management o f f i c e r holds the r i g h t of f i n a l judgment. This i s the most s i g n i f i c a n t feature of integrated organ-i z a t i o n s . In summary, contracting costs include mainly s p e c i f i -cation and v e r i f i c a t i o n costs, ex ante and ex post bar-gaining costs, and dispute settlement costs. In the model 212 we present i n following sections, the focus i s on i n t r a -firm transactions. Based on the above arguments, the dispute settlement costs i n an organization are low. Hence, f o r s i m p l i c i t y , we ignore dispute settlement costs and focus on the other costs incurred i n the contracting process. 5.3 Basic Model Elements We consider a transaction between a buying d i v i s i o n (B) and a s e l l i n g d i v i s i o n (S). To simplify, we assume that S and B are r i s k - n e u t r a l . and that S supplies B with e i t h e r one u n i t or zero units of a product at t 2 . Let c be the "transfer cost" that S bears i n supplying one unit to B and l e t v be the "transfer value" of the transaction to B i f the product i s supplied by S. Preci s e l y , "trans-f e r cost" i s defined to be the net decrease i n d i v i s i o n S's operating cash flows i f the product i s transferred to d i v i s i o n B, and "transfer value" i s defined to be the net increase i n d i v i s i o n B's operating cash flows i f the product i s received from d i v i s i o n 8. A more d e t a i l e d discussion of the determination of v and c i s provided i n a l a t e r section. I m p l i c i t l y , there i s a central management that i s the f i n a l claimant to a l l income and expenses of the two d i v i -sions, including the compensation paid to S and B. We 213 consider the transaction from the perspective of the cen t r a l management, who want to motivate d i v i s i o n managers to make optimal trading decisions and minimize transaction costs so that the firm's net cash flow can be maximized. From the central management's perspective, at the time of the tran s f e r decision i s made, i t . i s optimal to make the tr a n s f e r i f , and only i f , v > c + TC 2, where TC 2 i s the incremental future transaction costs required to accomplish the transfer. Note that any transaction costs TC1 incurred p r i o r to that point i n time are i r r e l e v a n t (they are sunk costs) r e l a t i v e to the decision made at that point at time. However, transaction costs incurred at e a r l i e r stages i n the process are relevant to determin-ing the operating p o l i c i e s that are implemented. Hence, these e a r l i e r transaction costs TC, may influence those "ex post" costs TC2. This implies that contracting costs, ex ante and ex post, are i n t e r a c t i v e . We assume that the managers of d i v i s i o n s S and B are motivated to maximize t h e i r expected d i v i s i o n a l p r o f i t s . Their objectives may not a l i g n with central management's objective. This implies that when S and B are free to make independent decisions, these decisions may c o n f l i c t with each other, and may deviate from the e f f i c i e n t rules. The incentive contracts f o r motivating S and B's managers are not e x p l i c i t l y modelled i n following a n a l y s i s . We 214 focus on the factors that influence d i v i s i o n a l p r o f i t s . The key issue i s to determine the contracting strategy that the ce n t r a l management should implement to e f f i c i e n t -l y manage the transactions between 8 and B. Note that we are mainly interested i n the transaction between B and 8 i n t h i s paper. Hence, "trading occurs" means that the product i s transferred from 8 to B, and "no trading" means B does not trade i n t e r n a l l y with S. Observe that whether a trade occurs or not, B and 8 must also determine t h e i r optimal actions with respect to other a c t i v i t i e s i n t h e i r d i v i s i o n s . For example, whether a trade occurs may influence the exchanges B and 8 make with the market. Assume at t,, that both c and v are uncertain and randomly d i s t r i b u t e d on the i n t e r v a l s C = [c,c] and V = [y,v], respectively. The j o i n t p r o b a b i l i t y density func-t i o n for v and c i s f ( v , c ) , which i s assumed to be common knowledge at t,,. The values of v and c w i l l be r e a l i z e d at t 2 and the transaction w i l l proceed based on the con-t r a c t ( i f there i s one), and 8 and B's trading decisions. The same model i s analyzed i n a few other papers. For example, Grossman and Hart [1987] use t h i s model to analyze the issue of v e r t i c a l integration under the as-sumptions that: (i) complete contracting i s impossible, due to the u n v e r i f i a b i l i t y of v and c, so that the con-215 t r a c t written at t 1 i s contingent only on the trading quantity; ( i i ) the contract can assign control to e i t h e r one of the p a r t i e s ; and ( i i i ) no ex post renegotiation and bargaining i s allowed. We reconsider t h i s model i n a d i f f e r e n t environment. In our s e t t i n g , renegotiation i s always possible. Spe-c i f i c a l l y , we e x p l i c i t l y consider contracting costs i n d i f f e r e n t regimes. We f i n d that, under the c r i t e r i o n of minimizing contracting costs, not only do we r e p l i c a t e most of Grossman and Hart [1987]'s r e s u l t s , but we also show that incomplete contracting i s optimal i n most cases. This, i n turn, provides a rat i o n a l e f o r the use of ex ante t r a n s f e r p r i c i n g p o l i c i e s f o r repeated i n t r a - f i r m transac-tions within organizations. We s h a l l consider three d i f f e r e n t regimes with respect to the nature of information about v and c. (1) Regime 1. Contracting with v e r i f i a b l e i n -formation: v and c are assumed to be a v e r i f i a b l e components of accounting reports and, hence, complete contracting i s poss-i b l e . (2) Regime 2. Contracting with u n v e r i f i a b l e information: v and c are assumed observ- able but u n v e r i f i a b l e and, hence, they are ex ante non-contractible but ex post con-t r a c t i b l e . (3) Regime 3. Contracting with high ex post bargaining costs: This represents the cases where private information e x i s t s i n the ex post bargaining process. 216 Regime 1 represents the case of complete contracting which i s the focus of c l a s s i c a l contracting theory. Regime 2 i s the case analyzed by most of the e x i s t i n g incomplete contracting l i t e r a t u r e . I t represents the case i n which v and c are not formally reported by any account-ing systems, but perhaps they can be ascertained by man-agers based on informal information that e x i s t s i n the organization. The information that managers use to make these assessments i s assumed to be p u b l i c l y a v a i l a b l e to both S and B, so that consensus about the r e a l i z e d values of v and c are easy to reach. In contrast, i n Regime 3, managers may make t h e i r assessments based on pr i v a t e information. This fact, plus managers' opportunistic behaviour, w i l l very l i k e l y create d i f f i c u l t i e s i n reach-ing an agreement i n the bargaining process. Thus, the contracting costs may be very s i g n i f i c a n t . We analyze these three regimes separately i n the following sections. In a l l cases, the trading quantity q = 1 or 0 i s assumed to be v e r i f i a b l e . 5.4 Contracting with v e r i f i a b l e information Assume v and c are v e r i f i a b l e . Observe that i n t h i s s e t t i n g a l l uncertainty i s exogenous; there are no agency problems. Furthermore, both parties are assumed to be ri s k - n e u t r a l so that r i s k sharing has no value i n improv-217 ing the contracting e f f i c i e n c y . F u l l trading e f f i c i e n c y can be achieved either through ex ante complete contract-ing, or ex post bargaining. The only difference between the two al t e r n a t i v e s i s the influence of transaction costs. D i f f e r e n t contracting procedures to s p l i t the trading gains between par t i e s , given each party's bargain-ing power, may r e s u l t i n d i f f e r e n t net cash flows f o r the ce n t r a l management. (a) A l t e r n a t i v e 1: Ex ante complete contracting B and S can contract at t, and make the contract d i r e c t l y contingent on v and c. A contract can e x p l i c i t l y s p e c ify the e f f i c i e n t trading rule, such as: (i) I f v > c, then S supplies one u n i t to B, i . e . , q = 1, and B pays 8 p 1 ( v / c ) ; ( i i ) I f v < c, then no trade occurs between S and B, i . e . , q = 0, and B pays S p 0. 4 Independent of p, and p 0, 5 the f u l l expected trading gain, gross of the t o t a l expected contracting costs TC P, 4The zero measure events v = c are not important. When t h i s occurs, the trading decision can be set a r b i t r a r i l y . 5p 0 can be thought of as the damages the buyer pays the s e l l e r or v i c e versa. I t i s a kind of penalty f o r a f a i l u r e to complete the transaction. 218 W p - f f (v - c) f (v,c) dvdc ( 5 . 4 . 1 ) J Jv>c can be r e a l i z e d . In Figure 5 - 1 , the possible r e a l i z a t i o n s of a l l combinations of v and c are represented by the rectangle CIKE which i s separated by the l i n e v = c into two regions. The region CIAJE represents a l l p o s i t i v e trading gain events, while the region AKJ represents a l l negative trading gain events. 6 The e f f i c i e n t trading rules require that trading occurs i n the former but does not occur i n the l a t t e r . Insert Figure 5 - 1 here From the central manager's point of view, given the e f f i c i e n t trading rules s p e c i f i e d i n (i) and ( i i ) , i t does not matter what prices p 1 and p 0 are set, because the net cash flows to him are wP - TCP, independent of these t r a n s f e r p r i c e s . Furthermore, i t also does not matter whether B or S bear the contracting costs, since these costs w i l l not influence trading decisions and the central management w i l l be the residual claimant. However, the values of p 1 and p 0 w i l l determine the a l l o c a t i o n of the trading gains between the d i v i s i o n a l managers. I f they 6The shapes of these regions depend on the parameter values of boundaries of V and C. P a r t i c u l a r l y , they can be extended to i n f i n i t y i f eit h e r v and c i s d i s t r i b u t e d on i n f i n i t e i n t e r v a l s . 219 are set properly, the d i v i s i o n s ' incentives to make e f f i -c i e n t trading decisions can be aligned with c e n t r a l man-agement's objectives. The bargaining power of each party i s exogenously given and, hence, these p r i c e s can be determined i n two steps. F i r s t , given p 0, v, and c, p, i s chosen such that v - p x * -p0 * » C i p : - p 0 i V (5 .4 . 2 ) P i - c z p0 These i n e q u a l i t i e s imply that the r e l a t i v e p r i c e P(v,c) = p., - p 0 i s set such that trading i s preferred by both S and B whenever v > c. In addition, P depends on each party's bargaining power. For example, given B's bargain-ing power a, f o r each p a i r of v and c (v > c ) , a Nash bargaining s o l u t i o n can be found by s o l v i n g 7 mpx (v-P)a*(P-c)1-* ( 5 .4 . 3 ) The r e s u l t i n g p r i c e i s P = a«c + (l-a)»v = v - a»(v-c). Using t h i s p r i c e to evaluate the expected gains of B and S, we have, See K a l a i [1985] for a det a i l e d discussion. 220 EG B - ff (v - px) »f ( v , c) » d v d c + ff -p0»f(v,c)»dvdc J Jv>c J Jv<c - ff (v - P - p 0 ) «f"( v, c) » d v d c + ff -pQ"f{ v, c) » d v d c J Jv>c J Jv<c - <x»| j ( v - c) « f (v , c) » d v d c - p 0 J Jv>C - o - W P - p 0 EG s - f f ( p x - c) »f ( v , c) » d v d c + ff p 0 « f " ( v , c) » d v d c J Jv>c J Jv<c - ff (P + p 0 - c) •-£"( v , c) » d v d c + / / p 0 » r " ( v , c) »d v d c - ( l - a ) f | ( v - c ) ' f C v , c) » d v d c + p 0 J Jv>C - ( l - a ) » W p + Po S e c o n d , l e t GQ B a n d GQ S d e n o t e t h e s t a t u s q u o p o s i t i o n s o f B a n d S b e f o r e t h e y come t o c o n t r a c t . W i t h o u t l o s s o f g e n e r a l i t y , we a s s u m e G 0 B + G Q S = 0; t h e n p 0 i s c h o s e n t o s o l v e M * X (EG B - G 0 B ) « . ( E G S - G o 3 ) 1 -- Mp* (a'W* - p 0 - G 0 V « [ ( l - a ) W P + p 0 - Go 3 ] 1 " 0 - Po " G 0 S - - G 0 B T h i s i m p l i e s t h a t e a c h d i v i s i o n ' s n e t g a i n i s d e t e r m i n e d b y i t s b a r g a i n i n g p o w e r . N o t e t h a t t h e r o l e o f p 0 i n c o n -t r a c t i n g i s t o a d j u s t e a c h p a r t y ' s p o s t - c o n t r a c t p o s i t i o n b a s e d o n i t s s t a t u s q u o p o s i t i o n a n d i t s b a r g a i n i n g p o w e r . T h e c o n t r a c t i n g c o s t s o f a c o m p l e t e e x a n t e c o n t r a c t are evaluated as follows. F i r s t , two necessary steps i n an ex ante contract are the s p e c i f i c a t i o n of a l l possible events and the v e r i f i c a t i o n of the r e a l i z e d event. In t h i s example, ex ante s p e c i f i c a t i o n can be implemented by specifying accounting procedures and measurements, while v e r i f i c a t i o n may be accomplished by the firm's accountants or i n t e r n a l auditors. Depending on the nature of v and c, the costs involved i n these procedures may vary consider-ably. We denote these costs as CSV, which consists of the ex ante s p e c i f i c a t i o n costs and the expected value of the ex post v e r i f i c a t i o n costs. Second, contract negotiation w i l l involve costs. For a complete contract, a l l negoti-ations occur ex ante. We denote these negotiation costs by TCN = CN0 + TCN,, where CNQ i s the cost of bargaining with respect to p r i c e p 0, while TCNt i s the t o t a l cost of bargaining with respect to p.,(v,c), f o r a l l possible (v,c) such that v>c. Hence, the t o t a l cost f o r a complete ex ante contract can be expressed as TCP - CSV + TCN (5.4.4) (b) A l t e r n a t i v e 2: "Null contract" and ex post bargaining. B and S can choose a " n u l l contract" i n t h e i r t 1 contract, which merely ensures a basic trading r e l a t i o n at t 2 . This can be done through specifying a "no trade" pay-222 ment p 0, which i s s i m i l a r to p 0 i n the ex ante contracting case, and r e f l e c t s the bargaining power and status quo positions of S and B at t,. 8 Then, they must bargain ex post f o r a pr i c e p,(v, c) a f t e r (v,c) i s r e a l i z e d at t 2 , i f they want trading to occur. In t h i s model, ex post bargaining of p, i s the same as the f i r s t step bargaining of the ex ante complete contract since we assume that between and t 2 nothing happens to influence S and B's bargaining p o s i t i o n s . The same Nash bargaining s o l u t i o n as i n the ex ante contracting case applies to the ex post bargaining process. However, there do e x i s t differences i n both the trading behaviour and contracting cost aspects of these two a l t e r n a t i v e s . For comparison, l e t us assume, f o r each p a i r of v and c, that the ex post bargaining cost f o r p 1(v,c) i s a constant CN,, and i s less than or equal to the ex ante t o t a l bargaining costs TCN..9 Now consider -There i s an i m p l i c i t assumption i n our analysis, that a d i v i s i o n cannot refuse to bargain at t^ — they must bargain and the r e s u l t s depend on t h e i r exogenously s p e c i f i e d bargaining power. p 0 ensures that the expected gains from future negotiations and trades (or no trades) r e s u l t i n expected gains consistent with t h e i r i n i t i a l bargaining power. Hence, i n general, p 0 may not be zero. 9In general, ex post bargaining costs for p. f o r one p a r t i c u l a r r e a l i z a t i o n of (v,c) may be les s than the t o t a l costs of bargaining f o r a l l possible r e a l i z a t i o n s of (v,c). However, i f p., can be expressed as a function of v and c (as well as a), then the costs of bargaining may be independent of the number of r e a l i z a t i o n s . 223 the components of the expected contracting costs f o r the n u l l contract. F i r s t , the costs to specify and v e r i f y the events ( i . e . v and c) , which are incurred for a complete contract, are not incurred f o r a n u l l contract. Second, the negotiation costs CN0 f o r a pr i c e p 0 are the same for both contracts. Third, ex post bargaining, costs w i l l be incurred with the p r o b a b i l i t y that trading occurs. Thus, we can express the expected contracting costs f o r the n u l l contract as ETC 0 - CN0 + CNj/probfex post bargaining occurs) (5.4 .5) Observe that, taking into account the ex post bargaining cost, the e f f i c i e n t trading decision i s d i f f e r e n t than i n the ex ante contracting case. S p e c i f i c a l l y , when the re a l i z a t i o n s of v and c are such that 0 < v - c < CU1 then i n i t i a t i n g the ex post bargaining process to seek a gain smaller then the bargaining costs incurred would not benefit the ce n t r a l management. Hence, the e f f i c i e n t trading region i s characterized by g - 1 if, and only if, v - c - > 0 (5.4 .6) 224 In Figure 5-2, the e f f i c i e n t ex post bargaining region i s represented by CIMNE, which i s obtained by eliminating a p a r a l l e l band from the o r i g i n a l p o s i t i v e trading region. The length of MA i s equal to the ex post bargaining costs CN,. Insert Figure 5-2 here The expected trading gains are w° " ff (v - c)»f(v,c)»dvdc ( 5 . 4 . 7 ) J J v> c+CNL I t i s obvious that W° < Wp and the difference between Wp and W° depends on CN,. P a r t i c u l a r l y , i t i s obvious that Wp - W° i s an increasing function of CN, and i f CN., = 0, wp - w° = 0. On the other hand, the difference between TC P and ETC0 i s ATC - T C P - ETC 0 - CSV + TCNX - Otx»prob{Area CIMNE) ( 5 . 4 . 8 ) which, i n general, i s p o s i t i v e and increasing i n CN, i f we assume CN, = TCN.,.10 Thus, we can prove the following proposition. 1 0This i s to simp l i f y our discussion. In fa c t , as long as TCN, and CN, are p o s i t i v e l y correlated, i . e . , TCN, increases as CN, increases, ATC can be shown to be i n -creasing i n CN.. Proposition 5.1: Assume contracting costs CSV i s n o n - t r i v i a l , and ex post bargaining costs CN, and ex ante t o t a l bargaining costs TCN. are the same, then there e x i s t s a threshold value CN^ such that when CN, < CN,*, W° - ETC 0 > Wp - T C P (5.4.9) Proof: (see appendix) . 1 1 A key assumption i n the above comparison i s that, under ex ante complete contracting, there i s no way to avoid s p e c i f i c a t i o n and v e r i f i c a t i o n costs for those (v,c) i n which trade should not occur (either because v<c or v<c+CSV). Proposition 5.1 says that, when the ex post bargaining costs are r e l a t i v e l y small, the e f f i c i e n c y of a complete contract i s l e s s than a " n u l l " contract. The im-provement mainly r e s u l t s from the savings i n s p e c i f i c a t i o n and v e r i f i c a t i o n costs. However, when the ex post bar-gaining costs are r e l a t i v e l y high, the improvement may disappear due to a serious reduction i n the trading region and the r e s u l t i n g gross trading gain. This r e s u l t i s not obtained by Grossman and Hart [1987] because they ignore contracting costs. The fact that the trading region i s influenced by the ex post bargaining costs shows the d i s t i n c t nature of ex ante contracting and ex post bar-gaining. Ex ante contracting costs are incurred before 11A11 the proofs of propositions are presented i n the appendix i f they do not appear following the propositions. the r e a l i z a t i o n of uncertain events, while ex post bar-gaining occurs a f t e r the r e a l i z a t i o n of the events. The differences i n the e f f i c i e n t trading regions, i . e . , the marginal region MAJN i n the Figure 5-2, w i l l be c a l l e d the marginal adjustment and denoted as M. I f the central management can control the trading decisions made by d i v i s i o n s , then who w i l l bear the ex post bargaining costs again does not matter. However, i f t h i s i s not the case, then there may be incentive issues. For example, i n the next section, we consider the case i n which v and c are unv e r i f i a b l e to the central management. Then, i f d i v i s i o n s do not bear these costs, S and B w i l l have incentive to trade i n M even i f the net benefit i s negative. To a l i g n t h i s divergence, i t i s better f o r the central management to al l o c a t e these costs to d i v i s i o n s . When CN1 i s borne by the d i v i s i o n s , they w i l l make trading decisions consistent with the e f f i c i e n t trading r u l e s . The above analysis demonstrates that even when con-t r a c t i n g information i s v e r i f i a b l e , complete ex ante contracting may not be economically e f f i c i e n t i f the contracting costs are n o n - t r i v i a l . This i s consistent with the observation that incomplete contracts are exten-s i v e l y used i n the r e a l world. 5.5 Contracting with u n v e r i f i a b l e information 227 Assume that v and c are observable by S and B, but un v e r i f i a b l e by the central management. This i s the extreme case of Regime 1 i n which the v e r i f i c a t i o n costs are p r o h i b i t i v e l y high so that CSV i s very large. Hence, ex ante complete contracting i s impossible. However, i f the ex post bargaining costs are small r e l a t i v e to v and c, then the n u l l contract we analyzed i n the l a s t section can be applied to f u l f i l l an e f f i c i e n t trading r e s u l t . In t h i s section, we assume CN, i s small r e l a t i v e to both v and c and other contracting costs such as CSV. We s h a l l show that, i n t h i s setting, the n u l l contract can be improved by an incomplete ex ante contract. An a l t e r n a t i v e to a n u l l contract i s to make the ex ante contract contingent on av a i l a b l e information that i s easy to specify and v e r i f y , e.g., the quantity q to be traded. Such a contract may be i n e f f i c i e n t ex post but the i n e f f i c i e n c y can be corrected through ex post bargain-ing. One commonly used example i s to specify a trading p r i c e p, independent of the uncertain events, i n addition to a n u l l contract: B pays S p, i f q = 1, and p 0 i f q = 0. In addition, the contract should specify some rul e to 228 govern the trading decision. Examples of the l a t t e r 12 are: c (a) Independent trading r e l a t i o n s h i p or non-in-tegration (NI): Each party can decide whether to trade or not. This r e s u l t s i n q = 1 i f , and only i f , both par t i e s are w i l l -ing to trade. (b) Buyer control (BC): B has the power to de-termine whether there i s trading or not. This r e s u l t s i n q = 1 i f , and only i f , B i s w i l l i n g to trade. (c) S e l l e r control (SC): S has the power to de~ termine whether there i s trading or not. This r e s u l t s i n q = 1 i f , and only i f , S i s w i l l i n g to trade. These rules, i n combination with the p a r t i e s ' ex post decisions, determine the quantity traded. As we s h a l l see, t h i s w i l l reduce ex post bargaining costs. We f i r s t use the non- integration r e l a t i o n s h i p to i l l u s t r a t e the nature and cost of such a contract. The r u l e NI and a p a i r of p r i c e s p 0 and p, determine the following trading r u l e : g - 1 if, and only if, c z P z v (5.5.1) where P = p 1 - p Q. Insert Figure 5-3 here 1 2Another case i s one i n which both S and B have no control of the trading decision. This implies that the c e n t r a l management must make the trading decision f o r the two d i v i s i o n s . That i s i n c o n f l i c t with the concept of decentralized firms and, hence, we exclude t h i s case from our a n a l y s i s . Thanks to Rajiv Banker fo r comments on t h i s point. 229 In Figure 5-3, the pr i c e P divides a l l possible events into s i x regions and only the events i n region I s a t i s f y the conditions given by (5.5 . 1 ) . Therefore, without contract renegotiation, trading w i l l only occur i n region I (BCDF) , where B pays S p r i c e p, f o r the t r a n s f e r of the product. Transfer w i l l not occur i n a l l other regions because e i t h e r v < P or P < c or both, so B pays p 0 to S for no t r a n s f e r . Thus the contract covers a l l possible states. The costs of t h i s ex ante contract can be evalu-ated as follows. The costs for specifying and v e r i f y i n g v and c are not incurred. The costs to specify a p a i r of pr i c e s p, and p 0 are n e g l i g i b l e . The costs to bargain over a p a i r of prices i s equivalent to bargaining f o r p 0 i n the n u l l contract case. The prices are chosen such that the ex ante post-contract positions are adjusted to r e f l e c t each d i v i s i o n ' s bargaining p o s i t i o n and power. (A d e t a i l e d discussion appears l a t e r ) . Hence, i t i s reason-able to assume that these costs equal CNQ. That i s , the ex ante cost of t h i s contract i s e s s e n t i a l l y the same as fo r a n u l l contract. However, the trading r e s u l t for t h i s contract i s not e f f i c i e n t because there are states, represented by region II (DFJE) and III (AFBI), i n which the trading gain i s p o s i t i v e and trading should occur, but i t w i l l not occur 230 under t h i s contract. For instance, i n III where c < v < p, - p 0, S i s w i l l i n g to supply because p, - c > p 0, but B i s u n w i l l i n g to buy because v - p, < -p 0. Based on t h i s , Grossman and Hart [1987] conclude that t h i s incomplete contract w i l l r e s u l t i n an e f f i c i e n c y loss i n areas II and I I I . This i s c e r t a i n l y correct i f renegotiation i s not allowed. In our s e t t i n g , however, much of t h i s i n e f f i c -iency can be corrected through renegotiating the p r i c e . Consider, say, a state i n III i s r e a l i z e d , so that trading w i l l not occur because B i s unwilling to buy, as mentioned above. This r e s u l t s i n an opportunity loss f o r S . Since both B and S can observe c and v, they can renegotiate a new p r i c e p, which i s lower than p, such that B i s w i l l i n g to buy under the new p r i c e p,. For example, l e t CNS and CNB, with CNS + CNB = CN,, represent 8 and B's shares of the ex post bargaining costs, respectively. Then, any new p r i c e p, such that C + CN s <; p \ - p 0 <; V - C N B (5.5.2) w i l l induce B to buy because now v - CNB - p, > -p 0 and S i s s t i l l w i l l i n g to supply because p, - c - CNS > p 0. This new contract induces trading and both p a r t i e s are better o f f than not trading under the i n i t i a l contract. Again, the new p r i c e p, depends on the bargaining power B and S have i n the renegotiation. Since the a l l o c a t i o n of the 231 gain i s not an important issue i n the following analysis, we consider any bargaining r e s u l t that s a t i s f i e s (5.5.2). Our only concern i s that B and S have an incentive to reach an agreement on p, through bargaining so that t r a d -ing w i l l occur and e f f i c i e n c y w i l l be regained i n region I I I . In the above discussion, we have taken into account the ex post bargaining cost CN,. For the reason given i n p r i o r discussion, we assume the ex post bargaining costs are born by B and S. Therefore, ex post bargaining w i l l not occur i n the whole region I I I , nor w i l l t r a n s f e r s . For events where v - c < CN1# the benefit net of contract-ing costs i s negative, so that corrective action i s not worthwhile. Therefore, part of the marginal region M must be eliminated from II and I I I . The marginal adjustment of the region III i s the overlapping region of M and I I I . We s h a l l denote i t M,,, and denote the other marginal adjust-ment regions i n the same way. In Figure 5-4, M m i s r e -presented by the p a r a l l e l band inside region I I I . Insert Figure 5-4 here Ex post bargaining incurs cost CN,, and the probabil-i t y of bargaining i s represented by the p r o b a b i l i t y of region II and I I I , subject to marginal adjustments. Hence, where ETC N I represents the expected contracting costs of 232 ETC N I - CN0 + CN^probill + III - MXI - M J J 2 ) (5.5.3) the incomplete contract with the NI governance r u l e . Comparing (5.5.3) with (5.4.5), i t i s obvious that ETC N I < ETC 0 because the n u l l contract requires ex post bargaining i n areas I + II + III - Mj - M n - M m. In words, the Nl-contract i s l e s s expensive than the n u l l contract be-cause of the reduction i n the ex post bargaining costs ( r e s u l t i n g from increased d e t a i l s i n the ex ante con-tract) . Furthermore, the r e s u l t i n g ex ante trading gain i s also a l i t t l e larger than WQ because i n Mj (marginal region i n I, which i s a small t r i a n g u l a r region i n Figure 5-4), trading w i l l occur without ex post bargaining. Therefore, the net benefit of the Nl-contract i s greater than f o r a n u l l contract. Proposition 5.2:13 An optimal ex ante incom-ple t e contract, i n which a p a i r of p r i c e s and an NI governance ru l e are s p e c i f i e d , w i l l r e s u l t i n a higher net gain f o r the central management, i . e . WNI - ETC N I > W° - ETC 0 (5.5.4) Cost evaluation (5.5.3) provides a d i f f e r e n t c r i -t e r i o n f o r choosing p, and p 0. Grossman and Hart [1987] claim that B and S w i l l choose P = p, - p 0 to maximize the 1 3The preceding arguments sketch the proof of t h i s proposition. 233 expected trading gain max w N I _ max (v-c) »f(v, c)'dvdc (5.5.5) C<P We suggest that P be chosen to maximize the no bargain trading region I (BCDF), max P probiti - [Lp f(v,c)«dvdc (5;5.6) C<P or, equivalently, to minimize the bargaining p r o b a b i l i t y of ( I I + I I I ) , excluding the marginal region (MJJ+MJJ, ) i n these areas, m ^ n pzob { 11+ III-MJJ-M^ } (5.5.7) The i n t u i t i o n here i s c l e a r . Since the trading gains can be guaranteed, economizing contracting costs i s a reason-able c r i t e r i o n f o r set t i n g ex ante contracts. Given (5 .5 .7) , the ante bargaining process with respect to p, and p 0 can be s i m p l i f i e d to bargaining with respect to p 0 only. Since, once p 0 i s determined, P can be obtained from (5 .5 .7) , we immediately have p, = P + p 0. Now l e t us evaluate the contracting costs f o r the trading r e l a t i o n s h i p under buyer and s e l l e r c ontrol gov-ernance r u l e s . A buyer control rule, i n combination with a p a i r of pr i c e s p, and p 0, induces a trading r u l e 234 g - 1 if, and only if, v>P (5.5.8) In Figure 5-4, we can see that the trading region {I+II+V} (BCEG) s a t i s f i e s (5.5.8), so that trading w i l l occur i n t h i s region without contract renegotiation. Compared with an Nl-contract, t h i s contract r e s u l t s i n e f f i c i e n t trade i n region I and II but introduces i n e f f i c i e n c y i n region V. Since i n region I I , v > c > P^PQ, S i s unwilling to supply the product since p, - c < p 0, while B i s w i l l i n g to buy since v - p 1 > -p Q. Now B need not ask f o r renego-t i a t i o n , but can simply use h i s control to force S to supply even i f S w i l l incur a l o s s . This r e s u l t i s Pareto e f f i c i e n t and, hence, there i s no renegotiation that can be raised by S that w i l l be accepted by B. The story for an event i n region V i s t o t a l l y d i f f e r -ent. Since c > v > p 1 - p 0, B w i l l decide to trade for a gain of v - P even though S w i l l incur a loss of c - P. However, now S can propose a new p r i c e p 0 such that v - CNiB S px - j50 £ c + CN^ (5.5.9) i . e . , S can reduce the no trade p r i c e p 0 to p 0 inducing B to make a no trading decision. Under (5.5.9) B prefers no trade since v - CNB - p, < -p 0 and S i s better o f f by not trading since p 0 > p 1 - c - CNS. So the new contract makes both p a r t i e s better o f f and w i l l be accepted. As a conse-quence, most of the i n e f f i c i e n c y i n region V i s corrected. Again the correction i s incomplete due to marginal adjust-ment My. The i n e f f i c i e n c y i n III can be corrected i n the same way as i n case NI. This implies that the p r o b a b i l i t y of ex post bargaining under BC i s determined by (III + V -ETC B C - CN0 + CN ^ p r o i ) ( I I I + V - M I X 1 - M V ) (5.5.10) Furthermore, the ex ante prices p, and p 0 under BC should be chosen to minimize prob{III + V - M , n - My} instead of prob{II + III - M n - M , n } i n case NI. S i m i l a r l y , an analysis for the s e l l e r control case w i l l r e s u l t i n E T C s c _ C N q + CN^ p r O j b l j J + I V - MJJ - M I I X } (5.5.11) and the ex ante prices p, and p 0 under SC should be chosen to minimize prob{II + IV - M , , - M , v ) . Similar to Proposi-t i o n 5.3, we have following proposition. Proposition 5.3;14 Both a BC-contract (a p a i r of p r i c e s and a B control governance rule) and SC-contract (a p a i r of p r i c e s and an S control governance rule) r e s u l t i n larger benefits net of contracting costs for the central management than does the n u l l contract, i . e . , w. B C - ETC B C > W° - ETC 0 (5.5.12) w s c _ E T C s c > W ° - ETC 0 (5.5.13) 1 4The preceding arguments sketch the proof of t h i s proposition. From (5.5.3), (5.5.10), and (5.5.11), and the discussion above, we conclude that d i f f e r e n t trading r e l a t i o n s h i p s r e s u l t i n almost the same trading gains but d i f f e r e n t contracting costs. Economizing contracting costs requires: (i) choosing a suitable trading r e l a t i o n s h i p , i . e . , appropriately assigning control between the two trading p a r t i e s ; and ( i i ) choosing suitable ex ante pr i c e s . We summarize the r e s u l t s i n the following prop-o s i t i o n . Proposition 5.4:15 Depending on parameters v, y, c, and c, the advantage of d i f f e r e n t trading r e l a t i o n s h i p s NI, BC and SC can be ordered by t h e i r ex post bargaining p r o b a b i l i t i e s p r o b i l l * 1 + I I I N I - Mg - Mgx) p r o b { l I I B C + - M g - Mg) (5.5.14 prob {IIsc + IVsc - Mg - Mg) where a l l p r o b a b i l i t i e s are minimized by appro-p r i a t e l y choosing ex ante contract p r i c e s p 0 and p.,. The best trading r e l a t i o n s h i p corresponds to the smallest p r o b a b i l i t y . Proposition 5.4 provides the same r e s u l t s through contracting cost analysis as those obtained by Grossman and Hart [1987] through a trading gain comparison. The 5The preceding arguments sketch the proof of t h i s proposition. c a l c u l a t i o n of p r o b a b i l i t i e s i n (5.5.14) i s much simpler than the gains. In addition, our r e s u l t can apply even i f v and c are correlated. The c o r r e l a t i o n may influence the c a l c u l a t i o n of these p r o b a b i l i t i e s , but the proposition i t s e l f w i l l not be affected. Our analysis has i m p l i c i t l y assumed that the prob-a b i l i t i e s of both the v > c region and the v < c region are s t r i c t l y p o s i t i v e . I f t h i s i s not the case, then some of the s i x regions created by the p r i c e P w i l l have zero p r o b a b i l i t i e s . For these corner solutions, we have f o l -lowing proposition. Proposition 5.5; I f prob{v > c> =1, then a l l p r o b a b i l i t i e s i n (5.5.14) are zero. Proof; prob{v > c) = 1 implies y > c. Set y > P > c under any rule, then a l l p r o b a b i l i t i e s i n (5.5.14) are zero. Q . E . D . C l e a r l y , when a l l ex post bargaining p r o b a b i l i t i e s are zero, the governance ru l e can be selected a r b i t r a r i l y . For the r e s t of the paper, we s h a l l r u l e out t h i s t r i v i a l case and assume 0 < prob{v > c ) <1, i . e . , y < c and v > c. I f we impose more r e s t r i c t i v e d i s t r i b u t i o n a l assump-tio n s , we can d i r e c t l y calculate the p r o b a b i l i t i e s i n (5. 5.14). F i r s t , assume that v and c are independent of each other, i . e . , 238 f(v.c) - (j>(v)»T|r(c) (5.5.15) where * and Y are the respective cumulative d i s t r i b u t i o n functions. The following proposition provides the optimal p r i c e s under various governance structure f o r t h i s set-t i n g . Proposition 5.6; Assume 0 < prob{v > c} < 1, v and c are independently d i s t r i b u t e d , and $(v) and 7(c) are d i f f e r e n t i a b l e d i s t r i b u t i o n s with density functions 0(v) and i|r(c). In addition, assume that the optimal P = p, - p 0 which mini-mizes the ex post bargaining p r o b a b i l i t i e s are i n t e r i o r solutions. Then P i s set to s a t i s f y : (i) under BC, p + ijf (P) {[$ (P) -<& (P-CN) ] - [<&(P+CZ\7)-<&(P)]} - 0 (5.5.16) ( i i ) under SC, p + <j>(P) {[T(P)-T(P-CJV)] - [T(P+CW)-T(P)]) - 0 (5.5.17) ( i i i ) under NI, i|;(P)»[l - S>(P)] - Y(P)-<j>(P) (5.5.18) 239 I f P <£ VuC (a corner solution) , P i s set to the boundary of VuC. One can provide a sharper characterization of the r e s u l t s of Proposition 5.6 under the BC and SC governance structures i f more r e s t r i c t i v e assumptions are made. For example, i f CN, i s small r e l a t i v e to P, then we have [$(P) - O(p-cw)] - 1&(P+CN) - $ ( P ) ] -0 (5.5.19) Thus (5.5.16) becomes, assuming <p(v) > 0 V v, p +«• j i|f(c)dc - f i|r(c)dc ~ Y(P) - 1 - Y(P) P which implies that T(P) - \ This means that the solution of (5.5.16), to be denoted as PBC, approximately equals the median of i|r(c). S i m i l a r arguments apply to SC, where P s c i s approximated by the median of 0(v). I f 0(v) i s uniformly d i s t r i b u t e d , then *(v) i s l i n e a r i n v so that (5.5.19) becomes an exact equality. In t h i s s p e c i a l case, under BC, PBC equals to the mean of i|r(c) and, under SC, P s c equals to the mean of 0(v) . With t h i s we have proved parts (i) and ( i i ) of the following c o r o l -l a r y . 240 C o r o l l a r y 5.7; I f v and c are independently and uniformly d i s t r i b u t e d on [y,v] and [c,c], r e -spectively, then the optimal prices which mini-mize the ex post bargaining p r o b a b i l i t i e s are: (i) P B C = c* = (c + c ) / 2 ; ( i i ) P s c = v* = (y + v ) / 2 ; ( i i i ) PNI = (c + v ) / 2 . To provide a d d i t i o n a l i n t u i t i o n about the above analysis, Figure 5-5 depicts the d i f f e r e n t p r i c e settings f o r a given set of parameter values. We see from t h i s figure that d i f f e r e n t p r i c e s r e s u l t i n d i f f e r e n t s i z e s of bargaining regions. In general, the ordering of the price s shown i n t h i s figure, i . e . , P s c > PNI > PBC, holds except when some pri c e s are corner solutions. Insert Figure 5-5 here Proposition 5.6 provides conditions that are sat-i s f i e d by the optimal p r i c e settings. We have shown that i f the d i s t r i b u t i o n functions are d i f f e r e n t i a b l e , the optimal p r i c e s can be approximated by the median of the corresponding density functions under BC and SC. The pr e c i s i o n of the approximation depends on the magnitude of the ex post bargaining cost CN, and the shape of the d i s t r i b u t i o n functions. The smaller i s CN, and the f l a t -t e r i s the d i s t r i b u t i o n density function, the c l o s e r i s 241 the optimal p r i c e P to the median of the d i s t r i b u t i o n function. S p e c i f i c a l l y , when the d i s t r i b u t i o n i s uniform, Corollary 5.7 shows that P exactly equals the median (which equals the mean) of the d i s t r i b u t i o n s . Thus, the optimal p r i c e settings when v and c are independently d i s t r i b u t e d are completely characterized. . Based on Corollary 5.7, i t i s straightforward to prove the following proposition. Proposition 5.8; Assume that v and c are inde-pendently and uniformly d i s t r i b u t e d on [y,v] and [c,c ] , respectively. Suppose also that v > c and y < c, i . e . , 0 < prob{v>c} < 1. Then 1 6 (a) i f v > c > c > y, then BC i s optimal and P = c*; (b) i f c > v > y > c, then SC i s optimal and P = v*; (c) i f v > c > y > c, then BC and SC are better than NI, (i) i f BC i s optimal then P = c*; ( i i ) i f SC i s optimal then P = v*; (d) i f c > v > c > v, then NI i s optimal and P = (c + v)/2. The d i f f e r e n t parameter cases are depicted i n Figure 5-6. 5-6(a) represents the case i n which the v a r i a t i o n of v i s larg e r than the v a r i a t i o n of c and, hence, region III 1 6The following categories exhaust a l l n o n - t r i v i a l s i t u a t i o n s . 242 and V i s r e l a t i v e l y smaller than the other regions. This implies that the ex post bargaining p r o b a b i l i t y w i l l be smaller i n the BC case. In 5-6(b), the reverse i s true, so SC i s optimal. In 5-6(c), IV and V are r e l a t i v e l y smaller than II and I I I , so that both BC and SC w i l l be superior to NI. Which of BC and SC i s optimal depends on the comparision of {II + IV} and {III + V}. For the fig u r e depicted, SC i s better than BC. F i n a l l y , i n 5-6(d), II and III are smaller than IV and V, so NI i s optimal. Note that for s i m p l i c i t y , we do not mark o f f the marginal adjustments i n Figure 5-6. Insert Figure 5-6 here Proposition 5.8 characterizes the optimal governance structure i n terms of the exogenous parameter sets V and C only. The r e s u l t s are s i m i l a r to those reported i n Prop-o s i t i o n 3 of Grossman and Hart [1987]. However, by ex-p l i c i t l y d e fining and minimizing the contracting costs and allowing ex post renegotiation, we expand the trading region to include almost a l l areas with p o s i t i v e trading gains, except a narrow band of marginal adjustment regions. Thus, we conclude that an incomplete contract which s p e c i f i e s a couple of prices and a governance struc-ture can r e s u l t i n almost f u l l production e f f i c i e n c y while at the same time minimizing t o t a l contracting costs. 243 When v and c are correlated with each other, an e x p l i c i t characterization of the ex ante pr i c e s i s d i f f i -c u l t i n general. However, since Proposition 5.4 s t i l l a pplies, numerical procedures can be used to i d e n t i f y the optimal governance structure and corresponding p r i c e s . A general procedure follows. F i r s t , solve the following problems f o r PBC, Psc, and PNI, respectively. max r rc + r r PBC Ij J{c<v<p n rtctCNj J J{p<v<c n ov+cWj) m*£\ff +ff P IJ J{p<c<v n v > c + C N j J JW<c<P n c>v+CNj} ^ f / f :ii r [J J(P<c<v n v>c+CNj J Jk J{c<v<P n v>c+CNj f(v, c) dvdc f ( v , c ) dvdc f ( v , c ) dvdc Second, compare the maximum values of (5.5.20), and sel e c t the governance structure that corresponds to the minimum value. F i n a l l y , an in t e r e s t i n g question i s whether there i s another incomplete contract that i s more e f f i c i e n t than those analyzed above. I t seems quite u n l i k e l y i f we r e s t r i c t our analysis to the two contracting p a r t i e s because a contract with a pa i r of prices has exhausted a l l a v a i l a b l e c o n t r a c t i b l e information, i . e . , the trading quantity. However, i f the central management has a more extensive r o l e i n the contracting process than i s assumed i n the p r i o r analyses, then, even i f v and c are u n v e r i f i -able, a more e f f i c i e n t contract may e x i s t . We delay t h i s issue to the next section. 5.6 Contracting with Large Ex Post Bargaining Costs In the l a s t section, most of our analysis assumes small ex post bargaining costs. In f a c t , larger ex post bargaining costs strengthen the r e s u l t s of Proposition 5.2 and 5.3. In other words, an incomplete contract with a p a i r of p r i c e s and a governance ru l e i s much better than a n u l l contract when CN, i s large. To see t h i s , l e t us go back to Figure 5-4. We can see that i f CN, becomes large, the marginal adjustment Mj becomes s i g n i f i c a n t . This implies that the increased trading gain r e s u l t i n g from the ex ante pr i c e s i s increasing i n CN,. Observe that the other influences of a large CN, to both a n u l l and an incomplete contract are the same. Thus the improvement of an ex ante incomplete contract r e l a t i v e to a n u l l contract i s more s i g n i f i c a n t when the ex post bargaining costs are large. The case of small ex post bargaining costs corre-sponds to symmetric information s i t u a t i o n s . This i s why we assume a symmetric information structure f o r both ex ante and ex post contracting i n the l a s t section. Hence, i n that s e t t i n g , the bargaining games, both ex ante and ex post, are ones of complete information, i . e . , each party knows the other party's p o s i t i o n with c e r t a i n t y . As shown 245 by Rubinstein [1982], while almost any outcome can be supported as a Nash equilibrium, there e x i s t s a unique subgame perfect equilibrium, i n which one party, based on his bargaining p o s i t i o n , makes an o f f e r , which the other party immediately accepts. This implies that the bargain-ing costs involved i n such games should be r e l a t i v e l y low. The case i n which ex post bargaining costs are large corresponds to situ a t i o n s i n which information asymmetry e x i s t s . I f e i t h e r or both r e a l i z a t i o n s of v and c are not p u b l i c l y observable by both B and S, then the two p a r t i e s possess d i f f e r e n t information when they enter into ex post bargaining f o r p r i c e P. Thus, the bargaining games i n these cases are ones with asymmetric information. For such a game, each party must acquire information about the other party's bargaining p o s i t i o n during the bargaining process. The l i t e r a t u r e on bargaining with imperfect informa-t i o n demonstrates that such bargaining may be very c o s t l y . For example, Grossman and Perry [1986a] analyze such a game i n which two part i e s bargain over the p r i c e at which an item i s to be sold. The s e l l e r ' s valuation i s common knowledge but the buyer * s valuation i s known only to the buyer. Each party, i n turn, makes an o f f e r . The other party e i t h e r accepts or responds with a counteroffer. As they bargain, t h e i r payoffs are discounted over time, so 246 that both have an incentive to come to an early agreement. They f i n d that with asymmetric information, the sequential equilibrium concept does not r e s u l t i n a unique outcome fo r the game. Instead the concept puts very l i t t l e res-t r i c t i o n on how the parties divide the surplus from t h e i r trade or how long i t takes to reach an agreement ( i . e . , how many o f f e r s and counteroffers are necessary to reach the equilibrium p r i c e ) . They show that the set of out-comes of the bargaining game can be greatly r e f i n e d by the concept of perfect sequential equilibrium which i s devel-oped i n Grossman and Perry [1986b]. Under some weak assumptions, they f i n d that the game has a unique candi-date perfect equilibrium which consists of an equilibrium p r i c e and a length of the bargaining time. The former i s determined by the positions of both p a r t i e s , i . e . , t h e i r types or true valuations. The l a t t e r depends on the imperfectness of the s e l l e r ' s information about the buy-er's type. The less informative i s the s e l l e r ' s knowledge about the buyer's valuation, the more o f f e r s and counter-o f f e r s are necessary to reach an agreement. This implies that l a r g e r bargaining costs w i l l be incurred and trading gains w i l l be more heavily discounted. Related to our analysis, from a contracting cost point of view, Grossman and Perry have shown that bargain-ing with asymmetric information may involve very high 247 bargaining costs. These costs include not only the resources used to make o f f e r s and counteroffers, but also the opportunity costs due to delaying or forgoing trades with p o s i t i v e gains. The following observation summarizes the above discussion and serves as a connection between the bargaining l i t e r a t u r e and our analysis. Observation 5.9; When e i t h e r or both r e a l i z -ations of v and c are not p u b l i c l y observable by S and B, ex post bargaining costs CN, w i l l be larger than that i n symmetric information cases. Based on Observation 5.9, when ex post information asymmetry e x i s t s , a n u l l contract which requires ex post bargaining f o r every event at which trading occurs must be very i n e f f i c i e n t . On the one hand, when CN, i s large, the marginal adjustment region becomes so substantial that trading occurs only i n a small part of the p o s i t i v e gain region. On the other hand, even i f a trading occurs, the net gains w i l l be much smaller because of the big bargain-ing costs. Hence the expected net t o t a l gains w i l l be very low. Observe that i f ex ante complete contracting i s impossible, the only choice l e f t i s incomplete contract-ing. Since we have assumed that S and B have homogenous p r i o r b e l i e f s , when they come to bargain f o r an ex ante 248 contract, i . e . , a p a i r of prices and a governance struc-ture, there does not e x i s t information asymmetry at that date. Hence, the ex ante contracting costs are the same as i n the public information cases i n the l a s t section. Once an ex ante contract i s agreed upon, ex post trading decisions only involve comparisons between the p r i c e s and each party's valuation of v or c. Whether the valuations are p u b l i c or private, as long as v > P > c, trading w i l l always be the best choice for both p a r t i e s . Trading w i l l occur i n region I without any influence of ex post i n f o r -mation asymmetry. We summarize the above discussion i n the following proposition. Proposition 5.10;17 When ei t h e r or both r e a l -i z a t i o n s of v and c are not p u b l i c l y observable by S and B, an incomplete contract with a p a i r of p r i c e s p, and p 0 and a governance structure w i l l be more e f f i c i e n t than a n u l l contract. The s i g n i f i c a n c e of Proposition 5.10 i s that i t extends the v a l i d i t y of the analysis i n the l a s t section to the asymmetric ex post information case. The c r i t e r i a f o r choosing optimal governance structure and f o r s e t t i n g of ex ante pr i c e s remain e f f e c t i v e even i f there i s ex post p r i v a t e information. This i s because these c r i t e r i a 1 7The preceding discussion sketches the proof of t h i s proposition. are derived by the p r i n c i p l e of minimizing the ex post bargaining p r o b a b i l i t y , which i s v a l i d whether ex post bargaining costs are small or large. Now l e t us consider the question r a i s e d i n the l a s t section: are there any other incomplete contracts which would be more e f f i c i e n t than the one we ha.ve analyzed. The answer i s a conditional YES. I f some other mechanism can be introduced, contracting e f f i c i e n c y may be improved. Note that i n p r i o r analysis, we i m p l i c i t l y assumed that the contract must balance the transaction between B and S, i . e . , what B pays must be equal to what S receives. This " s i n g l e " p r i c i n g p o l i c y i s necessary when no other mechan-ism can be used, and i t also has the feature that i t automatically r e s u l t s i n a maximum trading region without introducing misincentives to trade i n the negative gain region. This can be seen by n o t i c i n g that the l i n e s v = P and c = P i n t e r s e c t on the l i n e v = c, which separates the p o s i t i v e and negative gains regions. Now we relax t h i s r e s t r i c t i o n by assuming that the c e n t r a l management w i l l permit the p r i c e received by S to d i f f e r from that paid by B. This makes i t possible f o r a "dual" p r i c i n g contract i n which three prices (p.,s, p.,8, p 0) can be set, along with a governance structure. We s h a l l show that when ex post bargaining costs are high, a "dual" p r i c i n g contract may be more e f f i c i e n t than a " s i n g l e " p r i c i n g 2 5 0 contract. F i r s t note that i t i s never desirable to set Ps < PB (where Ps = p,s - p 0, PB = p,B - p0) because such a contract i s always dominated by a single p r i c e P = PB. This can be seen i n Figure 5-7 where Ps1 < P8, so the l i n e s c = Ps1 and v = PB i n t e r s e c t at R, inside the p o s i t i v e gains region. The area I governed by t h i s contract can always be expanded by increasing Ps1 to make the i n t e r s e c t i o n reach the l i n e v = c , i . e . , P S = P B . Therefore, a Pareto im-provement can only occur when Ps > P8. Insert Figure 5-7 here We take the NI governance ru l e as an example. In Figure 5-8, PNI i s the optimal p r i c e under NI governance. Let Ps > PNI > PB and define a dual p r i c i n g contract (p,s, p.,8, p0) such that Ps = p,s - p 0, P8 = p,8 - p 0. This means that i f a trade occurs, B pays p,B while S receives p,s. The d i f f e r e n c e p,s - p,B i s covered by the central manage-ment. As depicted i n Figure 5-8, there are two d i f f e r -ences between t h i s contract and the Nl-contract. F i r s t , region I - M, i s expanded to include the areas BB*M*S and DTN*D*, which implies a reduction of the ex post bargain-ing p r o b a b i l i t y and the expected bargaining costs. At the same time, M, i s expanded from STF to include areas M*XFS and TFYN*, which represents an increase i n expected t r a d -251 ing gain without incurring bargaining costs. These bene-f i t s w i l l be p a r t i c u l a r l y s i g n i f i c a n t when CN, i s large. Second, a dual p r i c i n g contract w i l l always introduce misincentives to trade i n the negative gains region. As shown i n the Figure 5-8, S and B w i l l trade i n the t r i -angle XYF* which w i l l r e s u l t i n negative gains. This i n e f f i c i e n c y cannot be corrected by contract renegotia-t i o n , and represents a deadweight cost of the dual p r i c i n g contract. When the benefit of a dual p r i c i n g contract exceeds i t s deadweight cost, a Pareto improvement over a single p r i c i n g contract i s r e a l i z e d . Insert Figure 5-8 here An optimal dual p r i c i n g contract can be found through choosing Ps and P8 to maximize the difference of the bene-f i t s and the costs. The detailed mathematics i s very s i m i l a r to what we have already provided i n the l a s t section and, therefore, w i l l be omitted here. 5.7 Transfer P r i c i n g f o r Economizing Contracting Costs Transfer p r i c i n g i n decentralized organizations i s a very important but d i f f i c u l t and f r u s t r a t i n g t o p i c . Many researchers have examined t h i s topic from d i f f e r e n t d i r e c -t i o n s , yet our understanding of i t i s f a r from complete. Eccles [1985] provides a detailed summary of the e x i s t i n g 252 t h e o r e t i c a l and empirical l i t e r a t u r e . He also presents a cl e a r p i c t u r e of the transfer p r i c i n g problem from a p r a c t i t i o n e r ' s view point. The main contribution of h i s work i s that he points out a d i r e c t i o n f o r further research i n t h i s area. In p a r t i c u l a r , he claims that t r a n s f e r p r i c i n g p o l i c y must depend on corporate strategy and administrative processes. Hence, no single p o l i c y i s a s o l u t i o n f o r every s i t u a t i o n . P r i o r a n a l y t i c a l research i n t h i s area t y p i c a l l y seeks to characterize the nature of an optimal t r a n s f e r p r i c e under some s p e c i f i e d set of conditions. The r e s u l t s are h e l p f u l , but are rather narrow i n t h e i r scope. Eccles' arguments imply that any tra n s f e r p r i c i n g model i n which the organization strategy i s ignored cannot capture the core of the problem. Hence, i t s explanatory power and assistance to p r a c t i t i o n e r s must be l i m i t e d . To view a t r a n s f e r p r i c e as a simple variable i n an organiza-t i o n ' s production decision, as i n most economic theory and mathematical programming transfer p r i c i n g papers, overly s i m p l i f i e s the problem. Transfer p r i c i n g p o l i c y i s a complex function of many variables. The most important one i s corporate strategy. Unfortunately, Eccles does not c l e a r l y state what he means by "corporate strategy". Based on transaction cost economics, corporate strategy can be interpreted as the 253 way by which a firm manages i t s various transactions. For example, a firm must decide whether a p a r t i c u l a r transac-t i o n should be conducted i n the market or within the organization. I f i t i s better to perform a transaction among i t s d i v i s i o n s , what i s the most economical way to conduct i t . From t h i s perspective, transfer p r i c i n g i t s e l f i s a part of the corporate strategy i n dealing with i n t r a - f i r m transactions. Hence, transfer p r i c i n g p o l i c y must be chosen to economize transaction costs. A d e t a i l e d analysis of transfer p r i c i n g i s beyond the objective of t h i s paper. However, i t i s worthwhile to point out that our basic model has provided a new basis fo r examining t h i s complex topic. To support our claim, i n t h i s section we discuss how the basic r e s u l t s of our analysis can be used to model i n t r a - f i r m t r a n s f e r s . We f i n d that the firm's behaviour i n s e t t i n g ex ante prices endogenously derived i n our model i s quite consistent with Eccles' empirical evidence. We s t a r t with an exploration of the possible nature of the t r a n s f e r value and cost. For s i m p l i c i t y , we pro-vide some examples only. Let D, represent the product B wants S to transfer, and assume that B uses D, to produce D2 f o r external sale. Most obviously, a d i v i s i o n ' s v a l u -ation of the t r a n s f e r i s influenced by i t s operating con-d i t i o n s . The following examples describe three possible 254 conditions under which the s e l l i n g d i v i s i o n might be operating. (a) I f d i v i s i o n S has excess capacity, then the t r a n s f e r cost i s equal to the incremental out-of-pocket cost of producing the trans-f e r product . The l a t t e r w i l l often be the variable production costs. (b) I f d i v i s i o n S can s e l l the t r a n s f e r product i n the market (and w i l l forego the sale i f i t i s transferred), then the t r a n s f e r cost i s equal to the market p r i c e of D1 minus any s e l l i n g costs incurred on exter-nal sales but not incurred on i n t e r n a l t r a n s f e r s . (c) I f d i v i s i o n S i s operating at capacity and w i l l forego the production and sale of an-other product D, i f the o r i g i n a l product i s produced for transfer, then the t r a n -s f e r cost i s equal to the incremental out-of-pocket cost of producing plus the revenue l o s t from the sale of D3 minus the incremental out-of-pocket cost of producing and s e l l i n g D3 that i s avoided. The following examples describe three possible condi-t i o n s under which D i v i s i o n B might be operating: (a) I f d i v i s i o n B has excess capacity and lacks an a l t e r n a t i v e source of the t r a n s f e r prod-uct D,, then the transfer value i s equal to the revenue from sale of D2 minus the i n -cremental out-of-pocket cost of processing D, to obtain and then s e l l D2. (b) I f d i v i s i o n B can acquire D, from an exter-nal source i f D. i s not supplied by S, then the t r a n s f e r value i s equal to the external purchase p r i c e of D1 plus any a c q u i s i t i o n costs that would be avoided i f acquired i n t e r n a l l y . (c) I f d i v i s i o n B i s operating at capacity and 255 would forego the production and sale of another product D4 i f i t produced D2, then the transfer value i s equal to the revenue from sale of D2, minus the incremental out-of-pocket costs to process D2, minus the DA revenue l o s t , and plus the incremental out-of-pocket cost of producing and s e l l i n g D4 that i s avoided. From these examples, we can see that .the valuations might have the following c h a r a c t e r i s t i c s . (a) Uncertainty — Both valuations are influenced by the input and output prices and demands that are deter-mined i n the market. A key c h a r a c t e r i s t i c of the market i s i t s uncertainty about demand and p r i c e . Therefore, the valuation of v and c for any future transfers must involve randomness. (b) U n v e r i f i a b i l i t y — The valuations are based on observations of events that are d i f f i c u l t to document but which s i g n i f i c a n t l y influence the managers• expectations about the cost or value of the t r a n s f e r . 1 8 For example, a key element i n determining the t r a n s f e r value and cost i s the d i v i s i o n ' s opportunities to trade i n the market, which i s never reported by any accounting system. There-fore, i t i s very d i f f i c u l t to e s t a b l i s h formal accounting procedures and measurement c r i t e r i o n to report these valu-1 8Keep i n mind that v and c are expectations based on a l l the information available to the managers at the time they make t h e i r transfer decision. 256 ations. (c) Unobservability — The valuations may depend on many events that are p r i v a t e l y observed by the managers. In other words, the r e a l i z a t i o n s of many events may not be p u b l i c l y observable. For example, events influencing market demand, d i v i s i o n a l capacity, out-of-pocket produc-t i o n costs, the demand for other products a d i v i s i o n could produce, are a l l possible events that may be observed by a d i v i s i o n a l manager only. Therefore, the valuations them-selves may be private information. (d) Complexity — The valuations are based on mul-t i p l e factors and many of these factors are multi-dimen-s i o n a l . For example, s e l l i n g costs and a c q u i s i t i o n costs include various expenses, some of which may not be d i r e c t -l y measurable. Hence, the s p e c i f i c a t i o n and v e r i f i c a t i o n of v and c may be d i f f i c u l t . These valuation c h a r a c t e r i s t i c s are consistent with the assumptions we made i n t h i s paper. They imply that ex ante complete contracting i s very expensive or impossible for i n t r a - f i r m transactions i n most cases. Furthermore, ex post bargaining may be c o s t l y due to asymmetric i n f o r -mation. Therefore, our conclusion that incomplete con-t r a c t i n g i s optimal i n managing transactions with the c h a r a c t e r i s t i c s mentioned above, indicates that incomplete contracting can be used to develop useful t r a n s f e r p r i c i n g 257 models. Our r e s u l t s can be d i r e c t l y applied to the sp e c i a l case i n which no ex ante investments are necessary (e.g., S and B are well established d i v i s i o n s and cap a c i t i e s for producing the transfers are available) and transfers are repeated. To see t h i s , assume that each period B w i l l need one un i t of the product . Assume the t r a n s f e r value of i f i t i s supplied to B by S i s v t, and the tra n s f e r cost S bears to supply i t i s c t, as determined at the date t . v t and c t are independent random var i a b l e s with i d e n t i c a l uniform d i s t r i b u t i o n functions on V and C, respe c t i v e l y . Depending on the governance rule that i s used, the one period contracting costs can be represented by (5.5. 3), (5.5.10), or (5.5.11). Let r be the i n t e r e s t rate per period. The expected net present value of the t o t a l con-t r a c t i n g costs for an i n f i n i t e number of periods can be represented as 1 9 ETC B C - C^o+^^-CN^probiIII+V-M^j-My) (5.7.1) E T C s c _ cU0+^-~CN1»prob{lI+IV-MII-MIV} (5.7.2) ETC N I - CNg+l^CN^projbt II+III-M^-Mj.^} ( 5 . 7 . 3 ) 1 9Evaluated at t=0. 258 where CN0 i s the ex ante negotiation cost for the p r i c e p Q and p,, and CN, i s the ex post bargaining cost f o r new pr i c e p, or p Q. As usual, we ignore the t r i v i a l costs to specify the ex ante contract. This implies that, i n ex ante contracting, the optimal governance ru l e and ex ante p r i c e s should be set i n the same way as i n the one period case given by Proposition 5.3, 5.5 and 5.7. Thus, our model predicts that for repeated i n t r a - f i r m transfers, the best ex ante contracting process i s : (i) to choose a gov-ernance r u l e ; ( i i ) to specify a p r i c e p, based on the governance ru l e selected; and ( i i i ) to choose a p r i c e p 0 such that each d i v i s i o n ' s ex ante expected gain i s con-s i s t e n t with i t s status quo p o s i t i o n and i t s bargaining power. A f t e r the tran s f e r p r i c e i s set and the d i v i s i o n s learn v t and c t, they can decide whether to tr a n s f e r the product or not, or propose to renegotiate the prices based on the value of v t and c t r e a l i z e d i n each period. The tr a n s f e r p r i c e should be consistent with the governance r u l e . The l a t t e r i n turn, depends on the r e l a t i v e v a r i -ations of v and c. From Proposition 5.8, we know that (a) When the v a r i a t i o n of v i s bigger than that of c, then control should be assigned to B, and the corresponding t r a n s f e r p r i c e i s p, = c* + p Q. That i s , under BC, the optimal t r a n s f e r p r i c e i s determined by the mean trans f e r cost. (b) When the v a r i a t i o n of c i s bigger than that 259 of v, then control should be assigned to S, and the corresponding transfer p r i c e i s p, = v* + p 0. That i s , under SC, the optimal transfer p r i c e i s determined by the mean trans f e r value. (c) When v* > c*, BC and SC are better than NI. (d) When v* < c*, then i t i s optimal to l e t the two d i v i s i o n s share c o n t r o l . The tr a n s f e r p r i c e should be set equal to p, — (c + v)/2 + p 0, which s a t i s f i e s V* - < < - c* 2 2 2 That i s , the transfer p r i c e depends on both the t r a n s f e r cost and the tran s f e r value. In summary, i t says the tr a n s f e r p r i c e should be set based on ei t h e r the mean of B's tran s f e r value or the mean of S's tran s f e r cost or both. Eccles [1985] shows empiri-c a l l y that most tra n s f e r p r i c e p o l i c i e s belong to one of the following categories: (i) cost based p r i c i n g ; ( i i ) market p r i c e based p r i c i n g ; ( i i i ) negotiated p r i c i n g ; and (iv) dual p r i c i n g . We can show by examples that the optimal t r a n s f e r p r i c i n g p o l i c y predicted by our model i s consistent with h i s empirical observations. To see t h i s , l e t us r e f e r back to the examples about S and B's oper-ating conditions given i n t h i s section. The three examples of S's operating conditions show that the tr a n s f e r cost may be equal to: (a) the out-of-pocket production cost, which i s often the va r i a b l e pro-duction cost; (b) the market p r i c e less an adjustment f o r savings on s e l l i n g costs; or (c) the out-of-pocket costs (or v a r i a b l e production costs) plus an adjustment f o r the opportunity l o s s . (a) and (c) can be viewed as cost based p r i c i n g p o l i c i e s , while (b) can be viewed as a market p r i c e based p o l i c y . Therefore, i f the uncertainty faced by B i s the main concern of the firm, the.trading decision w i l l be delegated to B, and eithe r cost or market p r i c e based p r i c i n g may be observed. The three examples of B's operating conditions show that the tra n s f e r value may equal: (a) the market price of the f i n a l product l e s s an adjustment f o r processing costs; (b) the market p r i c e of the t r a n s f e r product plus an adjustment f o r savings due to not purchasing i n the market; or (c) the market p r i c e l e s s an adjustment f o r processing and opportunity l o s s . A l l three examples show that i f the uncertainty faced by d i v i -sion 8 i s the main concern of the firm, then the optimal governance r u l e i s SC, and we w i l l observe market p r i c e based p o l i c i e s only. In cases i n which NI i s optimal, negotiated p r i c i n g p o l i c i e s are observed. In Section 5.6, we show that when bargaining costs are large, dual p r i c i n g may be desirable. However, t h i s ignores some other problems i n dual p r i c i n g that are i d e n t i f i e d by Eccles [1985], such as the ambi-guity i t creates about the firm's strategy. In summary, the above discussion shows the s i m i l a r -261 i t i e s between the predictions of our model and empirical evidence. This i s an i n d i c a t i o n that our analysis i s on the r i g h t track. 5.8 Conclusion We formally define contracting costs-and incorporate them into our analysis. By e x p l i c i t l y considering con-t r a c t i n g costs, we show that the contract e f f i c i e n c y concept can be made more precise. We f i n d that the ex ante and ex post contracting costs have d i f f e r e n t i n f l u -ences on contracting r e s u l t s . Through contracting cost minimization, we show i n our simple i n t r a - f i r m transaction model, that incomplete contracting may be superior to complete contracting and n u l l contracting. This r e s u l t provides a foundation f o r incomplete contracting. In t h i s way, our analysis extends t r a d i t i o n a l contracting theory to a broader contracting strategy space. P a r t i c u l a r l y , i n our s p e c i a l s e t t i n g , an incomplete contract, which spec-i f i e s a p a i r of prices and a governance ru l e i n advance, i s superior r e l a t i v e to a complete contract ( i f i t i s available) or a n u l l contract. An incomplete contract may optimize the firm's net cash flows i n managing repeated i n t r a - f i r m transactions. The assumptions f o r deriving these r e s u l t s are that: (i) the ex ante s p e c i f i c a t i o n and ex post v e r i f i c a t i o n costs f o r the transfer cost c and 262 t r a n f e r value v are high; and ( i i ) the ex post bargaining costs are high due to possible information asymmetries. These assumptions are consistent with the c h a r a c t e r i s t i c s of t y p i c a l i n t r a - f i r m transactions. Thus, our r e s u l t s provide a r a t i o n a l e f o r observed tr a n s f e r p r i c i n g p o l i c i e s f o r managing repeated i n t r a - f i r m transactions. In addition, we characterize the optimal governance rule and ex ante p r i c e s . Under more r e s t r i c t i v e assump-tions, the p r i c e s are e x p l i c i t l y expressed as functions of the governance structure and the d i s t r i b u t i o n parameters. Thus we extend the r e s u l t s of Grossman and Hart [1987] to the case i n which contract renegotiation i s allowed and contracting costs are e x p l i c i t l y considered. Our r e s u l t s provide new insights into i n t r a - f i r m transactions. Although we do not present a complete tran s f e r p r i c i n g theory i n t h i s paper, hopefully we have provided a useful basis f o r further research into t h i s important t o p i c i n management accounting. 263 Figures Figure 5-1: Positive and Negative Gain Regions v without Contracting Costs. 264 Figure 5-2: TVading Region of a Null Contract with Ex Post Bargaining Costs. V A V>C N. v=c+CN. / v<c C N , K 265 Figure 5-3: Regions Divided by Ex Ante Prices. I: c<P<v II: P<c<v III: c<v<P IV:v<c<P V: P<v<c VI: v<P<c Figure 5-4: Regions with Marginal Adjustments, V A D B I n N // 1 ^// m /// 1 //As' / / / F M I V VI K I: c<P<v II: P<c<v III: c<v<P IV:v<c<P V: P<v<c VI: v<P<c 267 Figure 5-5: Ex Ante Prices Corresponding to y Different Governance Structures. c E c 268 Figure 5-6: Different Parameter Categories. BC v l 269 Figure 5-7: Suboptimal Dual Pricing Contract. A R F V -p s P P : A dual prices contract. 270 Figure 5-8: Optimal Dual Pricing Contract. D D / I / N / / / / / Y B S / F / A / • B 00*0** / V * / / • F I / P / H * M / N / J G K N I „ S P P P: A singal price contract, B P P : A dual prices contract. 271 Appendix 5: P r o o f s P r o o f o f P r o p o s i t i o n 5.1 When c < v < c + CN,, AW - W p - W° - f f (v - c) »f (v, c)dvdc _ ,, J Jc<v<c*cn1 \A:> • J-) i s increasing i n CN,. Assuming that TCN, = CN,, ATC - CSV + TCNX - CN^probi*) - CSV + C N ^ U - piobi*)) (A5.2) Note that when CN, = 0, AW equals zero while ATC equals CSV, so that AW < ATC. I f AW < ATC for a l l CN,, then (5.4.9) holds f o r CN, < CN,+ = oo. Otherwise, there i s a value CN 1 + + such that AW > ATC. Then, since both Aw and ATC are continuous functions of CN,, there must be a value CN,+ i n [OjCN,**] such that AW - CSV + CNi«(l - protA*}) (A5.3) This implies, f o r a l l CN, < CN,+ , that (5.4.9) i s true. Q . E . D . P r o o f o f P r o p o s i t i o n 5.6 For s i m p l i c i t y , assume v and c are random var i a b l e s i n 272 ( - o o , + o o ) , 2 0 and l e t CN, = R. (i) Under BC, P i s set to minimize I I I + V - M,nBC -M y " , Min P P P +~ C-R j [ 14>(v)dv]y(c)dc+f [ | <J>(vOdv]i|i(c)dc> (AS.4) -«° c+K P P J Note that the marginal adjustments have been r e f l e c t e d i n the choices of the in t e g r a l l i m i t s , and they have d i f f e r -ent signs i n regions III and V. By d i r e c t c a l c u l a t i o n , ( A 5 . 4 ) i s equal to P +80 j [<b(P)-${c+R)]ty(c)dc + | [$(c-R)-Q(P)]ty(c)dc P p p - <& (P) y*i|r (c)dc - j"0(c+i ? ) f (c)dc -foo -foo + (c-R)ty (c)dc - <MP) Ji|r(c)dc p p The f i r s t - o r d e r condition with respect to P i s p $'(P) jty(c)dc + $(P)i|r(P) - <& (P+i?) iJr(P) —oo •foo - ®(P-R)ty(P) - $'(P) fy(c)dc + <&(P)q(P) - 0 (A5.5) 2 0For bounded i n t e r v a l s , the r e s u l t s w i l l not be changed, but the calculations are d i f f e r e n t . 273 This i s equivalent to (5.5.16). ( i i ) Under SC, P i s set to minimize II + IV - M,,sc -M s c. [ P P *" V*R I ^ f l | [ j t ( c ) d c ] ( | » ( v r ) d 7 + J [ f ijr(c) dc]$(v)dv [ - » V-R P P (A5.6) The same procedure as (i) r e s u l t s i n (5.5.17). ( i i i ) Under NI, P i s set to minimize II + I I I -M„ N I - M. N I *n III ( P V-R * - V-R in) r r t *P\I[ / * ( c > d c ] * < v > d v + / t / *(c)dc]<|)(v)dv| (A5.7) Mm, p p (A5.7) can be s i m p l i f i e d as |7(v-i?)4>(v)dv - T(P) |<|>(v)dv (A5.8) P The f i r s t - o r d e r condition f o r (A5.8) i s - T^P) f$(v)dv + Y(P)<t>(P) - 0 (A5.9) p This i s the same as (5.5.18). Q . E . D . Proof of Corollary 5.7 Note that due to the assumption that the cumulative d i s -t r i b u t i o n functions are l i n e a r , (i) and ( i i ) are spe c i a l cases of Proposition 5.6 (i) and ( i i ) , with (5.5.19) holding as an equality. For ( i i i ) , note that 274 T(c) - SL-£ C - £ Substituting into (5.5.18), we have C - C. V - Y C - Q V - y Simplify to get ( i i i ) . Q.E.D. Proof of the Proposition 5.8 The proof can be obtained by d i r e c t l y c a l c u l a t i n g a l l p r o b a b i l i t i e s . We show the f i r s t one as an example. A l l other cases are s i m i l a r . From Figure 5 - 6(a), f o r any P, the area f o r each region excluding the marginal adjust-ment , i s Area(JJ - MIX) - 0.5 (c-P-R)2 + (c-P) (v-c) - 0.5R2 Area(JJJ - MIIX) - 0.5 (P-&-R)2 Area(JV- MIV) - 0.5 (P-£-R)2 + (c-y) iP-JC) - 0.5R2 Area. {V - Mv) - 0 . 5 (c-P-R) 2 Note that the marginal adjustment cannot make the l a s t two terms i n areas II and IV become negative, i . e . , we always 275 have 2 1 (c-P) (v-c) - 0.5R2 * 0 (A5.10) (.C-JZ) (P-£) - 0.5R2 * 0 (A5.ll) Under BC, the minimum Area (III + V - M,n - My i s reached at P = c*. Hence ABC - Min Area (III +V- M I I X - MV) - - i (C-Q-2R) 2 ± 2 } ( A 5 *' Under SC, Asc - Area (II + IV - MIX - MIV) - ABC + (C-P) (v-c) + ( £ - J f ) (P-c) - R2 (A5.13) The l a s t three terms i n (A5.13) are p o s i t i v e because of (A5.10) and ( A 5 . l l ) ; therefore the minimum value of (A5. 13) when P = v* must exceed (A5.12). This proves BC i s better than SC. Under NI, AJJJ - Area (II + III - MXI - MIIT) - ABC + (c-P) (v-c) -0.5R2 (A5.14) The l a s t two terms i n (A5.14) are nonnegative from (A5. 10). Hence, BC i s better than NI. Q . E . D . 21We assume R i s x x s m a l l * ' r e l a t i v e to other parameters. For x x b i g ' ' R, the c a l c u l a t i o n may d i f f e r but the con-clusions w i l l not be changed. 276 Reference Arrow, K. [1974] The Limits of Organization. Norton, N.Y. Atkinson, A. A. [1987] Intra-firm Cost and Resource A l l o - cations; Theory and Practice. CAAA Monograph. Coase,R. [1937] "The Nature of the Firm." Econonometrica Vol.4, pp.386-405. Dye.R.A. [1985] "Costly Contract Contingencies." Interna- t i o n a l Economic Review Vol.26, No.l, pp.233-50. Eccles,R.G. [1985] The Transfer P r i c i n g Problem: A Theory  f o r P r a c t i c e D.C.Heath and co. Lexington, Massachusetts. Grossman,S.J., and O.D.Hart [1987] " V e r t i c a l Integration and the D i s t r i b u t i o n of Property Rights" i n Economic  P o l i c y i n Theory and Practics Spaier conference N.Y.Mac-M i l l a n Press., pp.504-48. Grossman,S.J. and Perry,M. [1986] "Sequential Bargaining under Asymmetric Information" Journal of Economic Theory Vol.39, pp.120-154 Kalai,E. [1985] "Solutions to the Bargaining Problem" i n So c i a l Goals and Social Organizations" Hurwicz,L., D.Sch-meidler, and H.Sonnenschein eds. pp.77-105. Rubinstein,A. [1982] "Perfect Equilibrium i n a Bargaining Model" Econometrica Vol.50, No.l, pp.97-109. Williamson,O. [1975] Markets and Hierarchies The Free Press, N.Y. Williamson,O. [1985] The Economic I n s t i t u t i o n s of C a p i t a l - ism The Free Press. 277 Chapter 6 CONTRACT RENEWAL AND LONG-TERM INCENTIVES IN ORGANIZATIONS 278 6.1. Introduction When a p r i n c i p a l hires a r i s k - and work-averse agent, simultaneous achievement of the e f f i c i e n t a l l o c a t i o n of r i s k and the e f f i c i e n t l e v e l of production i s usually pre-vented by the agents' s e l f - i n t e r e s t e d behaviour. I t may be optimal f o r the p r i n c i p a l to impose more than the e f f i c i e n t l e v e l of r i s k on the agent i n order to improve the l a t t e r ' s motivation to produce. This i s the central theme of principal-agent models that seek to provide a coherent and useful framework within which to examine managerial accounting procedures, and pose managerial accounting questions. The primary construct u t i l i z e d i n agency theory has been the i d e n t i f i c a t i o n of complete contingent contracts fo r motivating economic agents. However, the "complete contracting" approach has d i s t i n c t l i m i t a t i o n s i n the insig h t s that i t can provide because i t ignores contract-ing costs. Although the use of contingent contracts to provide high-powered incentives 1 f o r agents has been found extensively i n various f i n a n c i a l and managerial accounting settings, most employee compensation i s not 1 Williamson [1985] introduces the term "high powered incentives" to r e f e r to the incentives created by the market p r i c e system. We use t h i s term i n a s l i g h t l y d i f f e r e n t way. In t h i s paper, the term "high powered incentives" r e f e r s to contracts which specify an e x p l i c i t r e l a t i o n s h i p between compensation and some measure of performance. 279 based on e x p l i c i t contingent contracts. In most organiz-ations, the decisions as to whom to promote and how to al l o c a t e bonuses and perquisites are, i n pr a c t i c e , often l e f t to the d i s c r e t i o n of supervisors rather than com-p l e t e l y s p e c i f i e d i n an employment contract. Even at the management l e v e l , managers are evaluated both by objec-t i v e , quantitative factors and by subjective, q u a l i t a t i v e factors since the l a t t e r are too d i f f i c u l t to be formal-ized i n any accounting system. The effectiveness of contingent contracts i s hindered i f the performance measures f o r a given agent are s i g n i f i -cantly influenced by factors beyond the agent's control or r e s p o n s i b i l i t y , including events co n t r o l l e d by other agents and uncertain events that are beyond any agents• co n t r o l . In some sit u a t i o n s , the accounting system can e a s i l y provide i n d i v i d u a l performance measures that p r i -marily r e f l e c t the actions of an i n d i v i d u a l agent, thereby making contingent contracting e f f e c t i v e . For example, i f a firm i s only concerned about the quantity produced by an agent and quantity data i s reported by the accounting system, then a piece-rate can provide e f f e c t i v e incentives f o r the worker. However, such systems are rare i n large organizations. Managerial accounting systems mainly report data at an aggregate (e.g., d i v i s i o n a l ) l e v e l , but not the i n d i v i d u a l l e v e l . This i s because the complexity 280 of most employees' tasks, p a r t i c u l a r l y t h e i r cooperative nature, make i t impossible to provide e f f e c t i v e perform-ance measures fo r each i n d i v i d u a l . This point has been i l l u s t r a t e d i n Alchian and Demsetz [1972] and Williamson [1985], using the manual f r e i g h t example: Two men j o i n t l y l i f t cargo into trucks. Solely by observing the t o t a l weight loaded per day, i t i s impossible to determine each person's mar-g i n a l p r o d u c t i v i t y ... The output i s yielded by a team, by d e f i n i t i o n , and i t i s not a sum of separable outputs of each of i t s members. Under the condition of technological non-separability, i n d i v i d u a l p roductivity cannot be assessed by measuring output. An assessment of inputs i s needed. Thus, contin-gent contracts are l e s s prevalent within organizations than at the senior management l e v e l . The l i m i t e d power of c l a s s i c a l agency theory i n examining contracting behaviour within organizations creates a demand for extending the theory to deal with a broader range of contracting strategies and managerial accounting system designs. This paper seeks to contribute to that extension. The model provided i n t h i s paper shows that a contingent contract i s not the only means of pro-v i d i n g incentives i n organizations. Incomplete contract-ing with contract renewal can provide incentives f o r almost a l l employees i n a h i e r a r c h i c a l organization, p a r t i c u l a r l y when a "hard" performance measure fo r an 281 employee i s unavailable. Some special features of our model and the main contribution of t h i s paper to the e x i s t i n g l i t e r a t u r e are described below. F i r s t , we assume that most contracts made within an organization are incomplete contracts. The s p e c i a l nature of the hierarchy provides an environment i n which contract renegotiation, renewal, and dispute r e s o l u t i o n are much easier than i n the market environment. P a r t i c u l a r l y , most employment contracts are short term contracts, and e x p l i c -i t l y or i m p l i c i t l y s p e c i f i e d as renewable. We s h a l l show that t h i s i s a r a t i o n a l structure f o r creating low-powered incentives f o r agents who are employees i n an organiz-ation. This i s a s i g n i f i c a n t extension of c l a s s i c a l agency theory i n which managerial accounting procedures are associated with complete contracting. Second, although we observe the use of high-powered incentives at some l e v e l s i n an organization, most employ-ees appear to be motivated to work hard to contribute to the firm's operation for reasons other than short term benefits. This implies that high-powered incentive may not be the main force d r i v i n g an employee's a c t i v i t i e s within an organization. Instead, the dominating concern of employees may be the long term benefits they perceive w i l l follow from such behaviour. Even i f the wages spec-i f i e d i n short-term contracts are constant, employees w i l l 282 have incentive to provide "high" l e v e l e f f o r t provided the expected future benefits o f f s e t the personal costs of that e f f o r t . This incentive i s not viewed as high-powered because i t i s not created by current compensation that i s e x p l i c i t l y contingent upon a pre- s p e c i f i e d measure of the employee's performance. Instead, i t i s based on predicted consequences that depend upon equilibrium behaviour by both the firm's management and i t s employee. Third, i n most organizations, an employee i s a subor-dinate to a (higher level) manager, h i s supervisor. A supervisor has authority over the subordinate, and i s often responsible for providing a subjective evaluation of the subordinate's performance. Unlike much of the i n f o r -mation provided by accounting systems, subjective judg-ments are u n v e r i f i a b l e and subject to the supervisor's d i s c r e t i o n . What i s the r o l e of such " s o f t " performance measure i n organizations? Our model provides one aspect of the answer. Fourth, the re l a t i o n s h i p between a firm and an employee i s influenced by the human asset associated with the employee. Employment can be viewed as a transaction i n which the firm acquires the services of a human asset from i t s owner, the employee. I f human asset services are p e r f e c t l y tradeable, then these services can be purchased i n the spot market so that long-term r e l a t i o n s h i p s have no 283 value. However, long-term re l a t i o n s h i p s are a s i g n i f i c a n t aspect of the employment r e l a t i o n i n most organizations and we examine those human asset c h a r a c t e r i s t i c s that make such observed organization forms valuable. In addition, s i m i l a r to a firm's other assets, human assets can be developed during an employment period. That development frequently requires investments from both the firm and the employee and we examine how those investments are i n f l u -enced by the employment r e l a t i o n . Our model views employment as a long term r e l a t i o n -ship governed by incomplete short term contracts. The reason the contracts are incomplete i s that, f o r most employees, objective performance evaluation i s unavail-able. When negotiating and renewing the contract, the firm's management and the employee bargain over the gains r e s u l t i n g from human asset transactions. As long as the employee's bargaining power i s p o s i t i v e , the transaction gains w i l l be shared between the p a r t i e s . This w i l l create an incentive f o r the employee to work hard to b u i l d up his/her human asset. Since, i n most cases, b u i l d i n g up a human asset i s correlated with the firm's p r o f i t a b i l i t y , t h i s , i n turn, provides incentives f o r the employee to contribute more to the organization. Our model provides some i n t e r e s t i n g predictions. F i r s t , depending on the balance between the human asset 284 a c q u i s i t i o n and decay rates, employee wages may or may not d i s p l a y downward r i g i d behaviour (Harris and Holmstrom [1982]), i . e . an employee's wage may or may not increase over h i s l i f e time. Second, i f the employment r e l a t i o n i s s u f f i c i e n t l y long-lasting, then the employee's incentive to work hard w i l l be r e l a t i v e l y stable. Third, the incen-t i v e to work hard w i l l decline when the employment r e l a -t i o n i s close to termination. F i n a l l y , incentives are influenced by: the employee's bargaining power, the em-ployee's human asset a c q u i s i t i o n and decay rates, controls on the firm's c a p i t a l investment, the firm's production technology, and the managerial accounting system. Changes i n these elements can induce changes i n incentives. This chapter i s organized as follows. A f t e r t h i s introductory section, Section 6.2 discusses two key con-cepts used i n our model. Section 6.3 provides the model and a n a l y s i s . Section 6.4 discusses the main predictions provided by our model. 285 6.2 Performance Measures and Human Assets (HA) 6.2.1 Hard and Soft Performance Measures In h i e r a r c h i c a l organizations, performance evaluation i s very important i n monitoring, c o n t r o l l i n g , and motivat-ing employees. Agency models focus on complete contract-ing that i s based on "hard" performance measures. Using I j i r i ' s [1971] c l a s s i f i c a t i o n , information i s defined to be hard i f i t i s constructed i n such a way that i t i s d i f f i c u l t f o r people to disagree. In general, accounting systems provide r e l a t i v e l y hard information. However, not a l l information available i n an organization i s hard. Some information may not be included i n the accounting system but s t i l l may have value to management. For example, manager's subjective judgments are very important fo r making decisions. They are both imperfect and unveri-f i a b l e and, hence, disputable. Based on t r a d i t i o n a l contracting theory, such s o f t information has no value (see Gjesdal [1981]). This seems inconsistent with empi-r i c a l observations, i . e . , we observe that subjective performance evaluation i s widely used i n monitoring and motivating employees i n organizations. However, the e x i s t i n g l i t e r a t u r e has not provided an economic rat i o n a l e f o r and explanation of the use of t h i s information i n governing contract r e l a t i o n s . Obviously, unlike evaluations that depend on formal 286 reported accounting information, which may be more objec-t i v e and concrete, subjective judgment i s " s o f t e r " i n the sense that i t i s un v e r i f i a b l e . The q u a l i t y of a subjec-t i v e judgment, including i t s accuracy, speed, consistency, bias and ac c e p t a b i l i t y , w i l l be influenced by both the supervisor's a b i l i t y and the information environment, i . e . , the kind and accuracy of the information that i s ava i l a b l e about the subordinate's a c t i v i t i e s . In addi-t i o n , a supervisor's opportunistic behaviour may induce moral hazard problems. To preclude t h i s kind of behaviour from our analysis, which w i l l focus on the employee's incentives, we s h a l l assume that the supervisor i s w e l l -motivated to make the evaluation on behalf of the firm's owners. That i s , we s h a l l not make a d i s t i n c t i o n between the supervisor who evaluates the employee's performance and the firm's owner who buys the service from the employ-ee's human assets. E f f e c t i v e l y , the firm obtains non-co n t r a c t i b l e information from the supervisor which evalu-ates the employee's performance. Hence, we s h a l l not deal with the agency issue with respect to the supervisor. 6.2.2 Transferable and Non-Transferable Human Assets I t has long been recognized that a firm's value depends on both i t s tangible and intangible assets. Human assets are a very important part of a firm's intangible 287 assets. On the one hand, a firm's normal operation may be ser i o u s l y influenced, or even discontinued, i f i t loses a s i g n i f i c a n t component of i t s human assets. On the other hand, a firm's productivity can be s i g n i f i c a n t l y enhanced by e f f e c t i v e development of i t s human assets. Williamson [1985] c l a s s i f i e s the components of human assets as ei t h e r non-specific or s p e c i f i c . The f i r s t type consists of those employee s k i l l s that are valuable to a broad set of possible employers. I f an employee only provides t h i s kind of s k i l l , then neither the firm nor the employee has a productive i n t e r e s t i n maintaining a con-t i n u i n g employment r e l a t i o n . The firm can e a s i l y h i r e a substitute from the market, and the employee can move to al t e r n a t i v e employment without loss of productive value. Furthermore, a firm's management w i l l have no incentive to provide investments that develop these non-specific human assets unless there i s an e x p l i c i t contract or some other mechanism that w i l l protect the firm's return on i t s investment. The second type, which we r e f e r to as firm-s p e c i f i c , includes s k i l l s that have value only to a par-t i c u l a r employer. This value i s intimately associated with the employment r e l a t i o n . Once the employment r e l a -t i o n i s terminated, the value i s l o s t to both the firm and i t s former employee. Thus, continuity of the employment r e l a t i o n can be valuable to both the firm and i t s 288 employee. The key difference between non-specific and firm-s p e c i f i c human assets, i n Williamson's c l a s s i f i c a t i o n , i s the t r a n s f e r a b i l i t y of the assets. As Williamson points out, f i r m - s p e c i f i c human assets, including i d i o s y n c r a t i c technological experience and i d i o s y n c r a t i c organizational experience such as accounting and data processing conven-ti o n s , i n t e r n a l i z a t i o n of other complex rules and pro-cedures, etc., have l i t t l e value to other firms. Hence, a market f o r such assets does not e x i s t . Consequently, f i r m - s p e c i f i c human assets are non-transferable. By d e f i n i t i o n , a non-specific human asset has value to other firms, so a market demand e x i s t s f o r i t . How-ever, the p r i c e at which a non-specific human asset can be transferred w i l l be influenced by the o b s e r v a b i l i t y of the c h a r a c t e r i s t i c s that determine the asset's value. In p a r t i c u l a r , the market p r i c e of an asset i s influenced by the market's a b i l i t y to access the information that i s av a i l a b l e f o r evaluating i t , and the p r i c e the market would pay f o r i t i f that information was common knowledge. I f the market has perfect information about the asset, then l i k e any other tradeable commodity, a t r a n s f e r i s not d i f f i c u l t . However, i f the market has imperfect or no information, then the market p r i c e may not r e f l e c t i t s "true" value. In the extreme, a non-specific asset may 289 become e s s e n t i a l l y non-transferable because of lack of p u b l i c l y observable information about the asset, and i t may be s i g n i f i c a n t l y undervalued by the market. In t h i s chapter, we are mainly concerned with firm-s p e c i f i c human assets (FSHA). FSHA provide benefits f o r long-term employment r e l a t i o n s and, as we .shall show i n following analysis, can r e s u l t i n the use of low-powered incentives f o r employees i n organizations. However, since employees may hold FSHA and NSHA (Non-Specific Human Assets) concurrently, the trading of NSHA must be con-sidered i n the examination the trading of FSHA. The development of human assets i s a cumulative process which requires investments from both the firm and the employee. For example, t r a i n i n g employees i n new s k i l l s frequently involves contributions by the firm i n terms of t u i t i o n fees or the time of s k i l l e d employees, whereas the employees being trained must provide personal time or e f f o r t . Furthermore, the development process often occurs j o i n t l y with d a i l y production a c t i v i t i e s , i . e . , the a c q u i s i t i o n of human assets i s often obtained d i r e c t l y or i n d i r e c t l y through operating experience. Therefore, human asset a c q u i s i t i o n and d a i l y production a c t i v i t i e s are often p o s i t i v e l y correlated, i . e . , higher current p r o d u c t i v i t y implies greater a c q u i s i t i o n of human assets. Of course, the c o r r e l a t i o n between current pro-d u c t i v i t y and human asset a c q u i s i t i o n may depend on the employees basic personal s k i l l l e v e l . F i n a l l y , employees w i l l bargain over t h e i r share of the gains from human c a p i t a l development when they recon-t r a c t with the firm. The employees' bargaining power depends on the market condition and many other factors, such as the r e l a t i v e strength of the employee's union and the firm's management. 6.3 Model and Analysis 6.3.1 Basic Model Elements We consider a s i t u a t i o n i n which a r i s k - n e u t r a l firm h i r e s a r i s k - and effort-averse employee. The analysis covers T ( f i n i t e ) periods, beginning at t=0 and ending at t=T with period t r e f e r r i n g to i n t e r v a l [ t - l , t ] . The employee's and the firm's u t i l i t i e s with respect to t h e i r net return from the employment r e l a t i o n are time-additive with the same time discount c o e f f i c i e n t y, 2 T Employee: UT(wF : 1 *r> " g Y ^ U t W (6.3.1-1) T Firm: V T(v, ?r> " E Y ^ E t v g (6.3.1-2) t-i 2In general, the time discount rates may not be the same for the firm and the employee. We make t h i s assumption for s i m p l i c i t y only. where3 U t ( t f t ) - E[wt] - - f v a r[tf t] (6.3.2) and wt = a random variable representing the employ-ee's compensation f o r period t ; v t = a random variable representing the firm's benefit from the employment r e l a t i o n i n period t ; r = r i s k aversion c o e f f i c i e n t of the employee. We view employment as a transaction between the firm and the employee i n which the firm acquires the services provided by the employee's human asset. The firm con-t r a c t s with an employee at the beginning of each period. A f t e r contracting, the employee provides h i s e f f o r t e t to the firm's operation with personal cost C(e t) , e t e [0, -H») , and C(0) - 0 C(et) > 0 C"(et) > 0 (6.3.3) However, the employee's e f f o r t alone cannot create a productive outcome. The firm must provide investment to complement the employee's e f f o r t . While the nature of the firm's investment can take a v a r i e t y of forms, including the provision of a good working environment and access to s p e c i a l production f a c i l i t i e s , we assume that the firm's 3The employee's d i s u t i l i t y f o r e f f o r t i s introduced l a t e r . 292 investments can be represented by a single aggregate d o l l a r amount. I f the firm invests c a p i t a l kt ( d o l l a r amount) i n a zero human asset employee who provides e f f o r t e t, then the production output created by these inputs i s a random va r i a b l e Xt. The mean of Xt i s represented by the follow-ing Cobb-Douglas production function m t(Jct,et) - (a+et) bk\'b a>0, 0<2><1 ( 6 . 3 . 4 ) where a and b are constant parameters. (6.3.4) implies that as long as kt>0, even i f the employee owns a zero human asset H*"1 and provides zero e f f o r t , 4 Xt w i l l s t i l l have a p o s i t i v e mean mt. The variance of Xt i s assumed constant over time and i s denoted by a 2. This implies that the variances of Xt i s independent of a l l k t and e t. The employee's human asset decays at a rate of 1-6 percent per period, but i s increased by investments made i n that asset each period. Let Ht and H* be the human asset acquired i n period t and the human asset at time t, respe c t i v e l y ; then t H t - Y, S ^ ' H j 0 < 6 <; 1 ( 6 . 3 . 5 ) j-o 4 Zero e f f o r t does not mean no e f f o r t , but rather a normalized lowest e f f o r t l e v e l . 293 In addition, l e t At and Bt denote f i r m - s p e c i f i c and non-s p e c i f i c human assets i n Ht (FSHA and NSHA), respectively, Ht - A t + B t (6.3.6) and assume the same decay rate f o r At and Bt. Hence, we have A f c B t Hfc A p o s i t i v e human asset H*"1 at the beginning of a period w i l l a d d i t i v e l y enhance the production output, i . e . , the t o t a l output w i l l be Xt + H*"1. In other words, i n our model, human assets d i r e c t l y t r a n s f e r into future produc-t i v i t y without influencing the productive return from the employee's e f f o r t e t or the firm's c a p i t a l investment kt. This assumption i s for t r a c t a b i l i t y only. In general, the pr o d u c t i v i t y of both e t and k t may be influenced by H*"1. We assume that human asset a c q u i s i t i o n i s p o s i t i v e l y c o r r e l a t e d with current operation output. This implies that a higher e f f o r t contribution w i l l r e s u l t i n both higher current period productivity and higher human asset a c q u i s i t i o n . P a r t i c u l a r l y , assume perfect l i n e a r r e l a -j-0 j-o - A fc + B fc (6.3.7-1) (6.3.7-2) (6.3.7-3) 294 tionships between At (Bt) and Xt, A t - <J)tXt ( 6 . 3 . 8 - 1 ) B t - * t X t ( 6 . 3 . 8 - 2 ) Ht - (4>T + i|rt)Xt - h tX t ( 6 . 3 . 8 - 3 ) where <pt and i|rt are constant c o e f f i c i e n t s . 6 Therefore, i n our model, inputs e t and k t contribute to both current and future productivity, as long as the employment r e l a t i o n between the firm and the employee continues. From (6.3.5) through (6.3.8), we have 7 Hfc - Y, a'^hjXj ( 6 .3 .9 ) Throughout the following analysis, except f o r the benchmark case, we assume that the employee's e f f o r t cannot be p e r f e c t l y observed by the firm through any monitoring device. For example, a supervisor who monitors the employee on behalf of the firm cannot observe the 5Imperfect rel a t i o n s h i p s would create a d d i t i o n a l r i s k . Given the employee's s p e c i a l u t i l i t y function, t h i s w i l l not influence the incentives to i n s e r t e f f o r t , provided the r i s k created by the imperfect measurement i s independent of h i s e f f o r t l e v e l . For the case i n which t h i s r i s k depends on employee's e f f o r t , the analysis may be more complicated. 6This implies that At, Bt, and Ht are random variables, since Xt i s a random varia b l e . 7To s i m p l i f y our analysis, we ignore the negative values of Ht, i . e . , we assume the p r o b a b i l i t y d i s t r i b u t i o n s are such that there i s e s s e n t i a l l y . zero p r o b a b i l i t y of negative Ht despite the use of a normal d i s t r i b u t i o n . 295 employee's actions. This i s consistent with the s i t u a t i o n i n which the employee's e f f o r t i s complicated and m u l t i -dimensional, so that i t s s p e c i f i c a t i o n and v e r i f i c a t i o n are very d i f f i c u l t . Also, e f f o r t may not be a one-shot action, but a s e r i e s of actions continuously provided during a long period. These c h a r a c t e r i s t i c s of the em-ployee's e f f o r t make a f i r s t - b e s t e f f i c i e n t contract unattainable. We consider two regimes f o r Xt (the r e a l i z a t i o n of Xt) . In the f i r s t regime, we assume Xt i s a v e r i f i a b l e event and, hence, ex ante c o n t r a c t i b l e . This represents the case where Xt i s reported by an accounting system, ahd i s auditable. In the second regime, Xt i s an observable but u n v e r i f i a b l e event and, hence, i t i s ex ante non-c o n t r a c t i b l e but ex post c o n t r a c t i b l e . This represents the more common case — the i n d i v i d u a l ' s performance evaluation i s not reported by the accounting system. Instead, the employee's performance i s evaluated on the basis of h i s supervisor's subjective judgment, which i s both u n v e r i f i a b l e and imperfect. For s i m p l i c i t y , we also use Xt to denote the subjective evaluation of the employ-ee's performance. Given the assumption of l i n e a r r e l a t i o n s h i p s between Xt and Ht (At, Bt) , the r e a l i z a t i o n of these v a r i a b l e s have the same c h a r a c t e r i s t i c s as Xt. That i s , they are observ-296 able, and they are v e r i f i a b l e only i f Xt i s v e r i f i a b l e . We choose t h i s s e t t i n g to avoid the "learning problem" analyzed by Harris and Holmstrom [1982], so that we can concentrate on incentive issues. The key feature of FSHA i s i t s n o n - t r a n s f e r a b i l i t y . A* has a p o s i t i v e value i f , and only i f , the employment r e l a t i o n continues. Since A* has no value to other firms, there i s no market i n which to trade i t . This implies that any trading of A* can only occur between the o r i g i n a l employer and the employee. In contrast, NSHA i s tr a n s f e r -able. I t has value to other firms, so there w i l l be a market i n which to trade B*. Therefore, trading a human asset must include two parts that are governed by two d i f f e r e n t trading mechanisms. The trading of NSHA i s governed by the market mechanism, while the trading of FSHA i s governed by the bargaining processes within the firm. 6.3.2 Trading NSHA and FSHA Trading NSHA i n the market Consider a case i n which an employee, who owns B units of a NSHA, chooses not to continue h i s employment with a firm but to go to the market. There are other em-ployees seeking to s e l l t h e i r NSHAs, which are substitutable for the employee's asset. There are also 297 firms i n the market t r y i n g to buy the services that can be provided by h i s NSHA. We s h a l l not deal with the problem of how a firm chooses from among the a l t e r n a t i v e p o t e n t i a l employees, but consider only the transaction of B owned by t h i s p a r t i c u l a r employee. A central question i s how to p r i c e the asset to be traded. This w i l l determine who captures the gain from the transaction. F i r s t , we consider the case i n which the value of B i s observable to a l l firms. In t h i s case, the trading p r i c e of B, l i k e any ordinary commodity, i s determined by market demand and supply. A market equilibrium can be summarized by the i m p l i c i t bargaining power of the employee, denoted p m(B) e [0,1], which represents the percentage of NSHA value that can be obtained by the employee when contracting with a firm. In general, p m depends on the nature of the market f o r B. A stronger market demand r e l a t i v e to supply w i l l r e s u l t i n a higher value of p m. In the extreme, p m = 1 implies that the employee dominates the bargaining and captures a l l the gain from the transaction and leaves the firm with zero p r o f i t , while p m = 0 represents the other extreme. Given p m, the p r i c e for B simply equals P = PmB. In the case i n which the employing firm and the employee have private information about B (which the remainder of the market does not have), the analysis would be more complex. This 298 information asymmetry would appear to weaken the employ-ee's bargaining p o s i t i o n , but without a more formal analy-s i s i t i s impossible to assess i t s impact. For simplic-i t y , we assume that a l l firms who are interested i n h i r i n g the employee have the same information about the NSHA as the o r i g i n a l firm. Thus the market p r i c e for B w i l l be Trading FSHA between a firm and an employee While trading NSHA i s determined by a market mechan-ism, trading FSHA can only occur between a p a r t i c u l a r firm and i t s employee. The p r i c e the firm w i l l pay f o r an FSHA with value A i s determined by the bargaining power the employee holds i n contracting with the firm. Let p(A) denote the bargaining power of the employee. We assume that p(A) i s independent of P m(B) and v i c e versa. The bargaining r e s u l t i s affected by: (i) the status quo p o s i -t i o n of each party when bargaining; ( i i ) the bargaining power each party holds; and ( i i i ) the bargaining process. We focus on (i) and ( i i ) , and assume that ( i i i ) i s a Nash bargaining process. Different bargaining processes may a l t e r the p a r t i c u l a r bargaining r e s u l t , but we believe that the general conclusions would not be a l t e r e d . In general, an employee holds both FSHA and NSHA when he comes to contract. Then the status quo p o s i t i o n of the employee i s equal to the market pr i c e f o r h i s NSHA. Thus, we have following conclusion. Proposition 6.1: Let A and B be an employee's FSHA and NSHA at the time of contracting. Assume the employee's bargaining power i s p m(B) i n the market, and p(A) i n the firm. I f p(A) and P_(B) are independent with each other, then a Nash bargaining solution of the p r i c e that the firm w i l l pay for A and B i s P = p m(B)B + p(A)A. 6.3.3 One-Period Model We now examine a one-period model under the s e t t i n g described above. Let t=0 denote the s t a r t i n g point and t=l the ending point of the period. The event sequence i s depicted i n Figure 6-1. t=0 1 + + Contract Investment Output W 1 e T k i H°+X1 A°>0 B°>0 Figure 6-1: Event Sequence f o r One-Period Model The employee begins the period with previously acquired human assets A 0 and B° (the source of that a c q u i s i t i o n i s not modelled i n the one-period model). Observe that i n a one-period model, human asset a c q u i s i t i o n during the 300 period has no value to ei t h e r the firm or the employee since the termination of a l l economic a c t i v i t y at t=l i s common knowledge. Hence, A, and B, are i r r e l e v a n t to the analysis. We assume that A 0 and B° are observed by the firm before contracting. This implies that i t i s common knowledge that an employment r e l a t i o n w i l l bring the firm an expected gain of A0 + B° i n addition to the expected output r e s u l t i n g from the employee's current production e f f o r t . Our main concern i s the case i n which both e, and X, are non-contractible events, so that a contingent contract i s i n f e a s i b l e . However, fo r comparison purposes, we f i r s t derive the usual f i r s t - b e s t and second-best contracts i n a Nash bargaining s e t t i n g . We r e s t r i c t our analysis to wage contracts that are l i n e a r functions of the r e a l i z e d output X,.8 To si m p l i f y notation, i n t h i s section we drop the time subscripts from a l l v a r i a b l e s . Also, since the trading prices f o r A 0 and B°, which equal pmB°+pA°, have already been given i n the above discussion, and are not influenced by incentives with respect to inputs e and k, we exclude them from most formulas. For a complete expression, they should be added back where i t i s 8In the following analyses there i s no loss of gener-a l i t y i n considering only l i n e a r contracts except when we consider the second-best contract. Since l i n e a r contracts may not be optimal i n the second-best cases, there i s a pot e n t i a l l o s s of generality i n our r e s u l t s . necessary. X ~ N(m, a2) m - (a + e) bk1~b ( 6 . 3 . 1 0 ) w(X) - aX + (3 ( 6 . 3 . 1 1 ) Given t h i s contract w(X) (compensation from current inputs k and e) , the u t i l i t i e s of the employee arid the firm (excluding the human asset price) are, respectively, The F i r s t - b e s t Contract Contrary to our assumption, l e t e and k be observable and v e r i f i a b l e by both par t i e s so that they are contract-i b l e events. Since e and k do not influence the uncer-t a i n t y about X, e* and k* should be chosen to maximize The f i r s t - o r d e r conditions f o r t h i s maximization are U(w) - am + p - C(e) - -=-V(X - w) - m - (am + 0) - k ( 6 . 3 . 1 2 - 1 ) ( 6 . 3 . 1 2 - 2 ) m(k,e) - C(e) - Jc - (a+e) bk1-b - C(e) - k ( 6 . 3 . 1 3 ) b (a + e ^ i e 1 - * - C^e) (l-jb) (a + e) bk~b - l ( 6 . 3 . 1 4 - 1 ) ( 6 . 3 . 1 4 - 2 ) 302 This implies that e* i s the unique solution of the equa-t i o n C'(e*) - b (1-b) b (6.3.15-1) and k* i s uniquely determined by JL k* - (1-b) b (a+e*) (6.3.15-2) Contract c o e f f i c i e n t s a and B must r e f l e c t the bar-gaining power of the two p a r t i e s as well as t h e i r aversion to r i s k . Since the firm i s assumed r i s k - n e u t r a l and the employee i s r i s k averse, i t i s optimal to have the firm bear a l l the r i s k and pay the employee a f l a t wage. In other words, the f i r s t - b e s t contract should set a =0. A l t e r n a t i v e l y , a and B can be found by solving the follow-ing problem. 9 'whether the bargaining power used i n (6.3.16) should be p m or p depends on the information the market holds about the production function and the employee's productivity. I f the market has no such information so that p r i c i n g of the expected production i s d i f f i c u l t , then the market influences on the bargaining of the expected production gain disappear. In such cases, bargaining power p should be used here. 303 M a X y P ^ y l - P n a ' P (6.3.16) s. fc. e - e* k - k* The s o l u t i o n to t h i s problem i s summarized i n the follow-ing lemma. Lemma 6.2: The solution of (6.3.16) s a t i s f i e s (i) a = 0 ( i i ) p i s chosen such that U = pa(U+V) and V = (1-p.) (U+V).10 Note that i n Lemma 6.2 XJ + V- m- k- C(e) (6.3.17) which i s the t o t a l gain from the transaction. Lemma 6.2 shows that the f i r s t - b e s t s o l u t i o n provides e f f i c i e n t r i s k sharing, and the pa r t i e s share the gain based on t h e i r bargaining power. Note that when a = 0, then )8 = U, and the wage of the employee i s w - p _ B ° + p A ° + p _ (m - k - C ( e ) ) + C ( e ) 1 0The d i r e c t a d d i t i v i t y of these u t i l i t y expressions follows from the fa c t that mean/variance u t i l i t y functions have been used and the u t i l i t y functions have been scaled such that an increase i n the employee's compensation by $1 increases U by 1 unit and decreases V by 1 un i t . In general, i t i s meaningless to add u t i l i t y functions since intercomparison of u t i l i t i e s across i n d i v i d u a l s i s not acceptable with von Newmann/Morgenstern u t i l i t y functions. 304 Second-best contract when both e and k are non-con- t r a c t i b l e events Now return to our assumption that e i s unobservable by the firm, but l e t X be con t r a c t i b l e . This may occur when the employee's contribution to the firm's income i s formally reported by an accounting system. In that case, X i s v e r i f i a b l e to a t h i r d party who has authority to enforce the contract i f there i s a dispute when the con-t r a c t i s executed. This i s a c l a s s i c a l agency problem, but with a more general bargaining process. Note that the c l a s s i c a l agency l i t e r a t u r e focuses on the e f f i c i e n c y aspects of contracting so that i t can simply assume one contracting party holds a l l bargaining power without reducing the generality of i t s r e s u l t s . Hence, a l l gains from the transaction go to one party and the other party gets only i t s reservation u t i l i t y , which i s exogenoUsly given. In t h i s paper, we are dealing with an agency with a bargaining process; therefore, e f f i c i e n c y i s not the only aspect we consider. Another important issue i n our analysis i s how the trading gains are allocated. In the current case, we assume that both e and k are non-contractible events. The reason e may be non-con-t r a c t i b l e i s the same as i n the t r a d i t i o n a l agency theory. The reason k may be non-contractible i s that the firm's investment i n a p a r t i c u l a r employee may be d i f f i c u l t to 305 separate from i t s other investments. The optimal wage contract w(X) i s the so l u t i o n to the following problem: 1 1 {a.Tk.e) u P " v l ~ P - (6.3.18-1) s.t. e € arg max U (6.3.18-2) Jc e arg max V (6.3.18-3) where U and V are defined by (6.3.12). The sol u t i o n to t h i s problem i s characterized i n the following lemma. Lemma 6.3: The second-best s o l u t i o n of problem (6. 3.18) when both e and k are non-contractible events has the following c h a r a c t e r i s t i c s : (1) Both e and k are n o n - t r i v i a l functions of a, (6.3.19-1) _l _ l k11 - (1-a) b (1-b) b (a + e11) C6.3.1P-?) A - i _ l - i C'(eIX) - a (1-a) b b (1-b) b (2) U = p1B(U + V), V = (1 -pJ (U + V); and (3) a i s determined by d<U+V> -0 (6.3.20) da and a > 0, which deviates from the 1 1As pointed i n a p r i o r footnote, the optimal second-best contract i s not l i n e a r i n general. Our r e s t r i c t i o n on a l i n e a r contract may have a po t e n t i a l loss of generality i n t h i s subsection. 306 e f f i c i e n t risk-sharing solution a = Lemma 6.3 shows that when both e and k are non-con-t r a c t i b l e events, the second-best contract deviates from the e f f i c i e n t arrangement both i n the investment l e v e l s and r i s k sharing. The former claim i s based on the com-parison of (6.3.19) with (6.3.15). Since a ( l - a ) 1 / b " 1 < 1, e" < e* i s obvious, and t h i s , i n turn, implies k 1 1 < k*. The l a t t e r i s based on the values of a derived i n Lemmas 6.2 and 6.3. An e f f i c i e n t arrangement should have the firm to bear a l l the r i s k , i . e . , a = 0, while i n order to induce an e 1 1 > 0, i t must set a > 0. This r e s u l t i s established by c l a s s i c a l agency theory, we merely provide a d i f f e r e n t s e t t i n g . Second-best contract when k i s co n t r a c t i b l e Now we consider the case i n which input k i s con-t r a c t i b l e . This i s possible, f o r example, i f k consists of separable investments that can be v e r i f i e d . The prob-lem i s the same as (6.3.18) except that constraint (6.3. 18-3) i s eliminated. Now k can be chosen to maximize U+V rather than V. The solution of (6.3.18-1) subject to 1 20bserve that U+V i s independent of p m and p, and so i s a. This implies that the bargaining process has no i n f l u -ence on equilibrium r i s k sharing. 307 (6.3.18-2) i s characterized i n the following lemma. Lemma 6 . 4 : The second-best sol u t i o n of problem (6.3.18-1), when k i s a c o n t r a c t i b l e event, has the following c h a r a c t e r i s t i c s : (1) Both e and k are n o n - t r i v i a l functions of a, J c 1 1 - (1-b) (a + e X I) (6.3.21-1) C'(e J I) - ab {1-b) b (6.3.21-2) (2) p i s chosen such that u = p B(U + V), V = (1-P.) (U + V) ; (3) a i s determined by (6.3.20), and a > 0 deviates from the e f f i c i e n t r i s k - s h a r -ing solution a = 0. Lemma 6.4 shows that when one party's input i s a co n t r a c t i b l e event and the other i s not, then the second-best contract s t i l l deviates from the e f f i c i e n t contract. This i s obvious because of a < 1 so that e 1 1 < e* and k n < k*. However, the d i s t o r t i o n of the investment l e v e l and r i s k sharing are d i f f e r e n t than when both e and k are non-co n t r a c t i b l e events. This can be seen from a comparison of (6.3.21) with (6.3.19). However, since the bargaining power assignments i n these two cases are given exogenously (in general, they could be d i f f e r e n t ) , we cannot conclude whether each party or both w i l l be better o f f . The only thing of which we are sure i s that the t o t a l trading gain 308 U+V i s s t r i c t l y larger when k i s co n t r a c t i b l e than when k i s a non-contractible event. X and e are Non-contractible Events Now we examine the case i n which e i s unobservable and X i s non-contractible. In t h i s case, the wage f o r inducing an employment r e l a t i o n can only be a constant equal to the employee's asset p r i c e plus h i s share of the expected gain from production. w - pmB° + pA° + pa [m - C(e) - k] + C(e) (6.3.22) where e and k are the equilibrium input l e v e l s . Given a constant wage, the employee has no incentive to provide an e f f o r t l e v e l higher than the minimum l e v e l e=0. Recogniz-ing t h i s , the firm chooses k to maximize i t s expected u t i l i t y given the employee's lowest e f f o r t input. Again, there i s a differ e n c e between the case i n which k i s con-t r a c t i b l e and the case i n which k i s a non-contractible event. We summarize the r e s u l t s i n Lemma 3.5. Lemma 6 . 5 : When e and X are non-contractible events, then the employee's wage can only be a constant and the expected e f f o r t l e v e l the employee w i l l provide i s zero. The c a p i t a l investment l e v e l , independent of the contract-i b i l i t y of k, i s given by k° - a (6.3.23) 309 The i n t u i t i o n behind Lemma 6.5 follows. When k i s a co n t r a c t i b l e event, then the expected gain i s (m(k,0) -k). The employee and the firm share t h i s gain based on the bargaining power p m and hence, k can be chosen to maximize t h i s gain. This r e s u l t s i n (6.3.23). When k i s a non-contractible event, l e t k be the employee's ex ante b e l i e f about k (in equilibrium, k = k), then the perceived gain i s (m(k,0) - ic) . Since the firm i s the re s i d u a l claimant, f o r any actual investment k, i t s actual gain i s (m(k,0) - k) - pm(m(k,0) - ic). For any k set i n the contract, a s e l f - e n f o r c i n g constraint f o r the firm i s k 6 argmax m(k, 0) - k (6.3.24) which r e s u l t s i n (6.3.23) again. Summary of the One-Period model We derive the following conclusions from the above ana l y s i s . F i r s t , i n a one-period model, a contingent contract (high-powered incentives) i s e s s e n t i a l i f the agent i s to be induced to provide more than the minimal e f f o r t l e v e l . This i s the core of c l a s s i c a l agency the-ory. The cost of t h i s incentive i s i n e f f i c i e n t r i s k sharing — the r i s k averse employee must bear r i s k that should be transferred to the firm when there i s no incen-310 t i v e problem. Second, high-powered incentives require v e r i f i a b l e performance measures. I f such measures are ava i l a b l e from the accounting system, then contingent compensation may be observed. For instance, we observe that a firm's top executives, including the top managers of i t s key r e s p o n s i b i l i t y centres (e.g., d i v i s i o n s ) , are frequently compensated on the basis of contracts that are contingent on firm or d i v i s i o n a l f i n a n c i a l performance measures reported by the accounting system. We also observe that employees operating at the lowest l e v e l of an organization may be paid on a piece-rate or sales commis-sion basis i f the accounting system monitors and reports i n d i v i d u a l production or sales information. In contrast, the accounting system does not report i n d i v i d u a l perform-ance measures fo r many of the firm's employees and the firm t y p i c a l l y compensates them with a wage that i s set at the s t a r t of the period. This r a i s e s the question of whether these employees provide only a minimal l e v e l of e f f o r t and, i f they do not, where do t h e i r incentives come from. A one-period model says YES to the f i r s t question and that i s inconsistent with the r e a l world observations. Therefore, we now consider multi-period models. 311 6 . 3 . 4 Two-Period Model Model Elements We now extend the basic model to two periods. We assume that at t=l the firm and the employee have an opportunity to sign a second period contract. I f contract renewal i s successful, then the employment r e l a t i o n con-tinues. Otherwise, both the employee and the firm go to the market to f i n d new partners. The event sequence i s depicted i n Figure 6-2. 0 1 2 + + + Contract Invest ... Outcome W1 e i k i X 1 . Contract Invest Outcome w2 e 2 1^ x 2 A 0 A ^ X , A1=A"A°+Aj B° B i = * i x i B1=6"B°+B1 Figure 6-2: Event Sequence fo r Two-Period Model The key difference between a two-period model and a one-period model, i n our se t t i n g , i s that, along with the r e a l i z a t i o n of X,, human assets A1 and B1 are acquired before t = l . A1 has value, i f , and only i f , the employment r e l a t i o n continues i n the second period. On the other hand, B1 has value i n both the firm and the competitive market. Based on the discussion of subsection 6.3.2, we assume that the firm and the market have the same informa-312 t i o n about B1 so that the pr i c e for i t w i l l be p mB 1. F i r s t - b e s t benchmark contract f o r the two-period model We f i r s t derive the e f f i c i e n t contract i f a l l e and k are c o n t r a c t i b l e events. This i s done by considering the second period contract f i r s t . Since the economic a c t i v -i t i e s w i l l end at t=2, any human assets acquired i n the second period are i r r e l e v a n t . The f i r s t - b e s t wage con-t r a c t i n the second period depends on whether the p a r t i e s are able to commit to a multi-period contract ( i . e . , long-term contract) . I f they can, then w2 w i l l be independent of the r e a l i z e d value of A1 and B1 — the firm w i l l bear a l l r i s k . However, i f multi-period commitments (by ei t h e r the firm and the employee) are not possible, then w2 w i l l be a random va r i a b l e when viewed from the perspective of t=0. Since the variance of X i s due to an additive noise term, the r i s k i n e s s of w2 w i l l be independent of the f i r s t - p e r i o d input decisions. 1 3 We s h a l l assume i n our analysis that long-term commitment i s impossible (the j u s t i f i c a t i o n w i l l appear l a t e r ) . Hence, contracting i n the second period i s exactly the same as i n the one-period model: e 2 = e* and kg = k* given by (6.3.15). Given A1 and 1 3This r i s k i n e s s of w2 w i l l influence the employee's ex ante expected u t i l i t y . 313 B1 r e a l i z e d at t=l, the employee's second period wage i s equal to w2(A1,B1) - p^B 1 + pA 1 + pm[m2* - C(e*) - ic*] + C(e*) (6.3.25) which can be obtained through Lemma 6.2 with the following u t i l i t i e s U2* - a2m2 + p 2 - ±a\o2 - C(e 2) ( 6.3 . 2 6 - 1 ) V 2 - m2 - (a2m2 + P2) - k2 (6.3.26-2) with a 2 = 0 and /?2 = pm[m2* - C(e*) - k*]. Note that U 2 + and V 2 + are not the t o t a l second period u t i l i t i e s but only the u t i l i t i e s derived from the second period inputs. The t o t a l u t i l i t i e s f o r the employee and the firm, evaluated at t = l , are p mB 1 + pA1 + U 2 + and (1-pJB 1 + (l-p)A 1 + V 2 +, re-spectively. The differences come from the human asset enhancement. Let the u t i l i t i e s r e s u l t i n g from the f i r s t period inputs (evaluted at t=0) be Ui - + Pi - -f a*o2 - C(ex) (6.3.27-1) Vt - - ( a ^ + PJ - kx (6.3.27-2) where e, and k, are the equilibrium inputs. Then the two period expected u t i l i t i e s , evaluated at t=0, are 314 U 2 - P j D B° + pA° + Ul + y (E [pJB-^+pA1 I e^JcJ + U2+) - - ^ V a r t p ^ + p A 1 ] (6.3.28-1) V 2 - ( 1 - p j B 0 + (l-p)A° + Vi + + y (E [ (l-pJiB1* (1-p) A 1 I eltkx] + V2+) (6.3.28-2) These expected u t i l i t i e s h i g h l i g h t the fac t that the employee faces wage r i s k at t=0 and he cannot avoid t h i s r i s k when contracts only hold f o r a single period. The r i s k comes from the negotiation at t=l, when the firm and the employee contract f o r w2 based on the information they have at that point. Since A1 and B1 are random variables, w2 i s also a random v a r i a b l e . However, t h i s r i s k does not a f f e c t the bargaining that takes place at t=0 because the second period wage r i s k i s independent of the choice of e, and k, (due to the additive structure of the production and u t i l i t y functions). Based on above discussion, the f i r s t period contract and inputs can be determined by maximizing the sum of the f i r s t period production and human asset a c q u i s i t i o n . Assume the employee and the firm believe that the employ-ment r e l a t i o n w i l l continue i n the second period. Conse-quently, e, and k, are chosen by solving following prob-lem, 315 ex. kx m i + YE[HJ - ic, - C(e x) ~ ei< * i ( 1 + Y / 2 i ) 7 7 ? i " * i " C ( e i ) (6.3.29) where h, = 0, + t[r 1 i s the human asset a c q u i s i t i o n rate i n the f i r s t period. The term yE[E^] i s the discounted expected value of the incremental production i n the second period r e s u l t i n g from the f i r s t period's inputs. The so l u t i o n to t h i s problem i s characterized by _i _i kl - (1 + yhj b (1 - Jb) b (a + el) (6.3.30-1) C(el) - (1 + yhx)^b(l - b)^'1 (6.3.30-2) I t i s obvious that k,* > k*, and e,* > e*. The f i r s t period wage contract i s the same as i n a one-period model given i n Lemma 6.2 except k* and e* should be replaced by k,* and e,* given by (6.3.30). That i s , w, = pmB° + pA° + P m(U 1 + + V,+) + C(e,*). Note that from (6.3.13) - (6.3.15), k* and e* maximize U + V . Thus, from a single period point of view, k,* and e,* are over-invested and U,+ + v,* < U + V. In addition, i t i s possible that the f i r s t period wage i n a two-period model i s les s than i n a one-period model, even i f the employee's e f f o r t l e v e l i s higher i n the former case. The i n t u i t i o n f o r these differences i s that i n a two-period model, part of the f i r s t period investment i s made because of the return that w i l l be received i n the 316 second period. That i s , the payoffs from these invest-ments, to both the firm and the employee, are deferred to the future period. Second-best Contracts when k i s a non-contractible event (i=l,2) i s contractible, then, c l a s s i c a l agency contracts apply. As i n the f i r s t - b e s t case, we assume that only short-term (one-period) contracts are possible. Conse-quently, the second period contract i s the same as i n the one-period model and the f i r s t period contract must take int o account the e f f e c t s of human asset a c q u i s i t i o n . Lemma 6.6: When both e, and k t are non-con-t r a c t i b l e events, the second-best f i r s t period contract i n a two-period model i s characterized I f a l l e and k are non-contractible events, but X{ by (1) both e 1 and k 1 are n o n - t r i v i a l func-tions of a, i i * x - [ l - a 1 + Y ( V e i > ] *(l-i>> *• (a+ex) (6.3.31-1) C'(ex) Jb(l-ib) b (6.3.31-2) 317 where 81 = 0,p 4- 1\pm represents the employee's t o t a l bargaining power over his acquired human assets; (2) U* = p.CU/ + V>' M d V = ( i - p J <V + V/) ; (3) a i s determined by (6.3.20), and o > 0 deviates from the e f f i c i e n t r i s k - s h a r -ing s o l u t i o n a = 0. Here, Ui+Vi* - (l+YA 1)m 1-ic 1-C(e 1)-f o 2(o+y8 1 ) 2 (6.3.32) i s the t o t a l gain from contracting. A comparison of the re s u l t s of Lemma 6.6 with Lemma 6.3 shows that the bargaining power i n the second period influences the input l e v e l i n the f i r s t period of a two-period model. However, an a n a l y t i c a l comparison of the l e v e l s of k and e i n the two periods i s complex because both k and e are n o n - t r i v i a l functions of a, but the value of a i s d i f f e r e n t i n the two periods. The only s o l i d con-c l u s i o n we obtain here i s that the second-best contract i s d i f f e r e n t i f the expected future benefits of human assets are taken i n t o account. The second-best contract when k, i s a co n t r a c t i b l e event I f k i s v e r i f i a b l e , then as i n a one-period model, the contract w i l l be d i f f e r e n t from the contract given i n Lemma 6.6. The only difference i s that (6.3.31) i s re-318 (1+Y^i) * b (a+e/r) (6.3.33-1) (a+Y0i) (l+YAJ * b (1-b) b (6.3.33-2) where k,11 i s chosen to maximize the t o t a l gain rather than the firm's f i r s t period u t i l i t y . In other words, when we solve (6.3.18), the constraint (6.3.18-3) should be taken o f f as i n the one-period model. The differences between (6.3.33) and (6.3.31) are obvious although we cannot simply determine each party's preference over these two contracts f o r the reason given before. However, i t i s c l e a r that contracting on k does provide an opportunity to improve contracting e f f i c i e n c y . X| and e { are Non-contractible Events I f Xj and e- are non-contractible events, then any ex ante contract can only be a constant. In t h i s subsection, we examine the contracting behaviour i n these cases. Second Period Contracting In the above analysis, we assumed that the employment r e l a t i o n w i l l be continued i n the second period. Now we determine the conditions under which the firm and the placed by ki1 C'^el1) -319 employee have an incentive to continue the employment r e l a t i o n given the opportunity to renew t h e i r contract at t=l . Observe that, given common knowledge that the em-ployment r e l a t i o n w i l l be terminated at t=2 and that the second period performance evaluation X2 cannot enter into the revised wage contract w2, the employee, as i n a one-period model, has no incentive to provide e f f o r t e 2 greater than zero. Thus the firm correspondingly invests k 2 = k° which i s s p e c i f i e d by (6.3.23). The employee's current p r o d u c t i v i t y ( i . e . , h i s incremental p r o d u c t i v i t y from current e f f o r t ) i s i d e n t i c a l to that of any other employee the firm can h i r e i n the market (such employment w i l l l a s t f o r one period only). However, continuing the employment r e l a t i o n i s s t r i c t l y Pareto superior to termin-ating i t as long as the f i r m - s p e c i f i c human asset A1 i s p o s i t i v e . This asset w i l l increase the second period's p r o d u c t i v i t y from B1 + m° to A1 + B1 + m0,14 where m°=m(k0,. 0) i s the current mean productivity created by the employ-ee's lowest e f f o r t . Observe that even i f the firm can contract with a new employee with the same B1, i t w i l l lose i t s share of a valuable asset A1 and repeat a l l the r e s u l t s of the one-period model i n the second period. S i m i l a r l y the employee w i l l be better o f f i f the employ-1 4This assumes that the firm would h i r e another employee from the market with same NSHA. 320 ment r e l a t i o n continues because he can at most get P m(B + m° - k°) i n the market, while bargaining with h i s current employer permits him to obtain a share of the benefits from A1 (as long as p i s positive) . The above discussion implies that i t i s Pareto superior f o r the two p a r t i e s to continue the employment r e l a t i o n rather than to terminate i t . Now consider what happens when the firm and the em-ployee come to the bargaining table at t=l, with A1,B1 > 0. Observe that a f t e r A1 and B1 have been r e a l i z e d , the status quo p o s i t i o n of the employee at t=l i s p m(B 1 + m° -k°), the sum of the p r i c e i f he goes to the market with h i s NSHA B1 and h i s share of expected production outcome. On the other hand, the status quo p o s i t i o n of the firm i s (l-p m) (B1 + m° - k°) , the net return from h i r i n g a new employee with B1 from the market. Let p represent the bargaining power the employee holds at the bargaining table. The following proposition summarizes the above discussion and the Nash bargaining equilibrium f o r the second period wage contract. Proposition 6 . 7 : 1 5 Assume that a f t e r the f i r s t - p e r i o d , the firm and the employee have an opportunity to sign a second period employment 1 5The e x p l i c i t recognition of the contracting costs could change t h i s l i m i t i n g r e s u l t . That i s , things change as the l i m i t s are approached i f there are contracting costs. 321 contract. Contracting i s Pareto superior to not continuing the r e l a t i o n i f , and only i f , the firm s p e c i f i c human asset A1 r e a l i z e d at the end of the f i r s t period i s s t r i c t l y p o s i t i v e and neither party has a l l of the bargaining power, i . e . , 0 < p < 1 . Assume A1 > 0 and B1 > 0 , and the market p r i c e f o r B1 i s p^B1. Then, a Nash bargaining solution w2 i s given by w2 - pm (B1 + m° - k2) + pA1 (6.3.34) where k 2 = k° i s given by Lemma 6.5. Proposition 6.7 assures that continuing employment i s an equilibrium strategy for both p a r t i e s , and the e q u i l i b -rium second period wage contract i s simply a sharing of the expected gain based on the two p a r t i e s ' bargaining power. Thus, a long-term r e l a t i o n s h i p need not be guaranteed by a long-term contract even i f a long-term contract i s ava i l a b l e . This i s p a r t i c u l a r l y s i g n i f i c a n t when the contracting i s incomplete. As Williamson [1985] points out, f o r long term contracts executed under condi-t i o n s of uncertainty, a complete s p e c i f i c a t i o n of the contract i s apt to be p r o h i b i t i v e l y c o s t l y , i f not imposs-i b l e . In addition, Macneil [1978] states: Two common c h a r a c t e r i s t i c s of long-term con-t r a c t s are the existence of gaps i n t h e i r planning and the presence of a range of pro-cesses and techniques used by contract planners to create f l e x i b i l i t y i n l i e u of e i t h e r leaving gaps or t r y i n g to plan r i g i d l y . Our r e s u l t s are also consistent with Alchian and Demsetz's 322 [1972] claim that ... neither the employee nor the employer i s bound by any contractual obligations to continue t h e i r r e l a t i o n s h i p . Long term contracts between employer and employee are not the essence of the organization we c a l l e d a firm. Therefore, although long term contracts o f f e r the apparent advantage of reduced bargaining costs and long-term com-mitment, they may be too expensive due to other contract-ing costs. Based on Proposition 6.7, i n our model, a short-term contract can provide incentives to maintain a long-term r e l a t i o n s h i p and to provide more than minimal e f f o r t . Hence, when v e r i f i a b l e performance measures are unavailable, short-term employment contracts with contract renewal processes are an important incentive mechanism within organizations. F i r s t Period Investment Decisions Under the Nash bargaining s o l u t i o n stated i n (6.3 .34), the employee and the firm share the second period gain r e s u l t i n g from the f i r s t - p e r i o d a c q u i s i t i o n of human assets. The sharing of the gain from the NSHA and the expected output depends on market forces, whereas the sharing of the gain from the FSHA depends on the employ-ee's bargaining power with the firm. The employee re-ceives h i s market value plus p percent of the gain from 323 FSHA. This share of the gain i s a reward fo r continuing the employment r e l a t i o n . I t also provides incentives f o r the employee to choose a f i r s t period e f f o r t l e v e l greater than the minimum e f f o r t . This i s shown i n the following proposition. Proposition 6.8: Assume both e and k are non-c o n t r a c t i b l e events. I f at t=0 the firm and the employee an t i c i p a t e the second period's bargain-ing r e s u l t , then the employee w i l l have incen-t i v e to provide e f f o r t e~ > 0 which i s deter-mined by c'(er) - yB1[i*y(h1-e1)]^'1b(l-b)^'1 1 } <6-3-35" correspondingly, the firm w i l l invest kt** such that _i _i k" - [l + Y ^ - A ) ] b (l-Jb) b (a+eD (6 . 3 . 3 5 - 2 ) Proposition 6.8 has the following implications. F i r s t , a n t i c i p a t i o n of second period contract renewal provides incentives f o r the employee to provide more than minimal e f f o r t i n the f i r s t period. This incentive i s not obtained with short-term risk-bearing, but i s stimulated by the a n t i c i p a t i o n of the benefits that w i l l r e s u l t from an ongoing employment r e l a t i o n . Since these benefits are not provided by an e x p l i c i t contract, the incentives created are low-powered. Second, t h i s incentive depends on: (i) y — the discount rate; ( i i ) <p. and ijr. — the 324 impact of period 1 productivity on the increase i n FSHA and NSHA; ( i i i ) p m and p — the employee's bargaining power i n the market f o r h i s NSHA and the expected produc-t i o n output, and i n the firm f o r h i s FSHA ; and (iv) b — a measure of the r e l a t i v e labour i n t e n s i t y of the produc-t i o n function. For the case i n which k i s a c o n t r a c t i b l e event we have following p a r a l l e l r e s u l t s . Proposition 6.9: Assume k i s a c o n t r a c t i b l e event. I f at t=0 the firm and the employee an-t i c i p a t e the second period's bargaining r e s u l t , then the employee w i l l have incentive to provide e f f o r t e,** > 0 which i s determined by - i - i - i - i C'(e") - yB1(l+yh1) h b(l-b)b (6.3.36-1) Correspondingly, the firm w i l l invest k,** such that _i _i * i * - (l+Y^i) b (l-JM b (a+eD (6.3.36-2) I t i s i n t e r e s t i n g to notice that the c o n t r a c t i b i l i t y of k has no impact i n the f i n a l period ( i . e . , i n the one-period model), but i t does have an impact i n the mult i -period model. This i s because i n the f i n a l period, with the agent receiving a fixed wage, the firm w i l l make the "optimal" choice of k since i t receives a l l incremental benefits from that investment as well as bearing a l l 325 incremental costs. On the other hand, i f k i s not con-t r a c t i b l e i n a multi-period s e t t i n g , while the firm w i l l bear the e n t i r e incremental cost of increasing k and w i l l receive the e n t i r e current incremental benefits from that increase, i t must share the future benefits (through the bargaining process). Thus the r e s u l t s of Proposition 6.5 are fundamentally d i f f e r e n t than f o r Proposition 6.8 and 6.9. The f i r s t period wage contracts, corresponding to (6.3.36), are wx - pmB°+pA°+pm(mr-kr-C(e1**))+C(er) (6.3.37) where m,** = m, (k,**, e,**) , and (k,**^,**) are given by either Propositions 6.8 or 6.9. The pattern of employees* wages over time i s often an issue i n the labour contract l i t e r a t u r e . For example, Harris and Holmstrom [1982] provide a long-term labour contract model i n which worker's a b i l i t y i s assumed unknown. The firm learns about each worker's productivity by observing the worker's output over time. I t i s shown that, i n equilibrium, a worker's wage never declines with age and increases only when the worker's market value increases above h i s current wage. In our two-period model, a comparison of (6.3.37) with (6.3.34) r e s u l t s i n the following c o r o l l a r y . 326 C o r o l l a r y 6 . 1 0 : In a two-period model, the con-d i t i o n f o r the expected second p e r i o d wage t o exceed the f i r s t p e r i o d wage i s Pm (1-8) B ° ] +p [«J>X*- (1-8) A°] > -Pa[(m°-k0)-(mx"-kr)] + (l-p*)C(er) ( « - 3 . 3 8 ) I n e q u a l i t y (6.3.38) has a s t r a i g h t - f o r w a r d i n t e r p r e -t a t i o n . The l e f t - h a n d - s i d e o f the i n e q u a l i t y i s t h e change i n t h e employee's share o f the b e n e f i t s o f h i s human a s s e t s , w h i l e the r i g h t - h a n d - s i d e i s h i s share o f the r e d u c t i o n o f t h e second p e r i o d p r o d u c t i o n g a i n due t o the l o s s o f i n c e n t i v e s . Our c o n c l u s i o n s d i f f e r from H a r r i s and Holmstrom [1982] i n t h a t : ( i ) the second p e r i o d wage w i l l i n c r e a s e i f , and o n l y i f , the i n c r e a s e i n the human a s s e t s i s g r e a t e r than the r e d u c t i o n i n p r o d u c t i o n g a i n ; ( i i ) t h e wage i n c r e a s e w i l l not o n l y be i n f l u e n c e d by t h e worker's market v a l u e , which i s o n l y determined by h i s NSHA, but a l s o by h i s FSHA, which has no market v a l u e ; and ( i i i ) t h e wage may decrease i f the i n e q u a l i t y i s r e v e r s e d . A wage i n c r e a s e can occur i f human a s s e t a c q u i -s i t i o n i n t h e p e r i o d i s h i g h , o r the decay r a t e i s low, o r the p r o d u c t i o n r e d u c t i o n i n t h e second p e r i o d i s low. Any r e v e r s e o f t h e s e c o n d i t i o n s may cause a wage r e d u c t i o n . For example, a s p o r t s p l a y e r ' s wage i s l i k e l y t o decrease s h a r p l y a f t e r h i s peak performance p e r i o d because o f a v e r y h i g h decay r a t e o f h i s human a s s e t s . On the o t h e r hand, we observe examples of senior employees 1 wages increasing not because t h e i r market values increase but because the s p e c i f i c human assets, such as the knowledge of the p a r t i c u l a r firm, i s increasing. F i n a l l y , from (6.3.35-1), i t i s straightforward to determine the following comparative s t a t i s t i c s . Proposition 6.11: In a two-period model with non-contractible k, the incentives created by the a c q u i s i t i o n of human assets and second period contract renewal have the following prop-e r t i e s . The employee's f i r s t - p e r i o d e f f o r t i s : (1) increasing i n the discount rate y; (2) increasing i n and (3) increasing (decreasing) i n p and p B when Y 0 1 <(>) b (6.3.39) 1 + YAL and reach t h e i r maximum when (6.3.39) holds as an equality; (4) increasing (decreasing) i n b i f b >(<) 1 - — where R - X+y (hx-Qx) (6.3.40) and reaches i t s minimum when (6.3.40) holds as an equality. The r e s u l t s of Proposition 6.11 can be interpreted as follows. F i r s t , the discount e f f e c t s are obvious because the employee's investment has future b e n e f i t s . A higher discount rate means higher returns on that investment, 328 which induces a larger incentive to invest. Second, the e f f e c t s of the human asset a c q u i s i t i o n rate are s i m i l a r to the discount rate, higher a c q u i s i t i o n rates r e s u l t i n higher returns on the e f f o r t invested. Third, the e f f e c t s of the bargaining power on the employee's incentive are more subtle as shown by (3). When the employee's bargaining power p or p m are r e l a t i v e -l y small, the employee's incentive to provide e f f o r t i n -creases as h i s bargaining power, e i t h e r i n the market or i n the firm, increases. However, that incentive reaches i t s maximum at some threshold l e v e l . Above that l e v e l , when the employee has r e l a t i v e l y strong bargaining power, the employee's incentive to provide e f f o r t decreases as h i s bargaining power increases. This i s because there are two sides to the influence of an increase of the employ-ee's bargaining power on the employee's ex post gain. On the one hand, the employee's share increases as h i s bar-gaining power increases. On the other hand, an increase on the employee's bargaining power implies a decrease on the firm's bargaining power. This, i n turn, may reduce the firm's incentive to invest c a p i t a l . The r e s u l t i s a reduction i n the production output. The t o t a l influence i s the sum of these two e f f e c t s . When the former exceeds the l a t t e r , an increase i n the employee's bargaining power w i l l increase h i s e f f o r t l e v e l . In the reverse case, a decrease i n e f f o r t l e v e l occurs. In addition, the threshold l e v e l determined by (6.3.39) has an economic in t e r p r e t a t i o n . On the right-hand-side of (6.3.39), b represents the s e n s i t i v i t y of production to the employee's e f f o r t input. On the left-hand-side, the numerator can be viewed as the employee's bargaining power over the output r e s u l t i n g from the inputs, while the denominator 1+yh, can be viewed as the return on h i s e f f o r t input. Hence, the left-hand-side of (6.3.39) i s the "percentage" that the employee can capture from the output of h i s e f f o r t . When t h i s "percentage" i s le s s than the s e n s i t i v -i t y b, the employee's incentives can be improved by i n -creasing h i s bargaining power e i t h e r i n the market or i n the firm. Some further implications of t h i s r e s u l t are discussed l a t e r . F i n a l l y , the r e l a t i v e s e n s i t i v i t y of the outcome to labour and c a p i t a l investments has an i n t e r e s t i n g e f f e c t . I f the production technology i s such that the outcome i s r e l a t i v e l y i n s e n s i t i v e to the employee's e f f o r t l e v e l ( i . e . , b i s close to zero), then increasing that s e n s i t i v -i t y w i l l reduce hi s incentive to work hard. On the other hand, i f the outcome i s r e l a t i v e l y s e n s i t i v e to the em-ployee's e f f o r t l e v e l ( i . e . , b i s close to one), then increasing that s e n s i t i v i t y w i l l increase h i s incentive to work hard. The i n t u i t i o n behind t h i s f a c t i s again the 330 combination of two opposing e f f e c t s . On the one hand, i f the firm's c a p i t a l i s held constant, then the e f f o r t l e v e l always increases as b increases. This can be seen by n o t i c i n g that the factor b ( l - b ) 1 / b " 1 i s a increasing func-t i o n of b f o r a l l b<l. On the other hand, increasing b reduces the firm's incentive to invest c a p i t a l (because 1/b - 1 decreases i n b). This, i n turn, w i l l reduce the employee's ex post gain and h i s incentives. When k i s a contractible event, from (6.3.36-1), we can show that the r e s u l t s of Proposition 6.11(1) and (2) again hold. Condition (6.3.40) i s s t i l l true but with R = 1 + yh,. However the influences of p and p m are d i f f e r -ent. I t i s obvious that e, i s increasing i n both p and p m. That means (6.3.39) i s not true anymore. From (6.3.35-2) and (6.3.36-2), we can see that the firm's c a p i t a l investment choice i s influenced by the same factors as those influencing the employee's e f f o r t choice, but i n a more complicated way. Since the optimal c a p i t a l investment i s a l i n e a r function of the e f f o r t l e v e l , the e f f e c t s of a p a r t i c u l a r parameter can be separated into two parts: a d i r e c t e f f e c t and an i n d i r e c t e f f e c t through the change i n the e f f o r t l e v e l . When the two e f f e c t s go i n the same d i r e c t i o n , such as the influence of the d i s -count rate or human asset a c q u i s i t i o n rate, the conclusion i s simple. However, i f they go i n opposite d i r e c t i o n s , the conclusion depends on the value of the parameters. B a s i c a l l y , the incentive for the firm to invest c a p i t a l has quite d i f f e r e n t c h a r a c t e r i s t i c s than the employee's incentive to provide e f f o r t . To see t h i s , observe that the employee's e f f o r t i s an increasing function of both p m and p when they are small. In p a r t i c u l a r , i f p m = p = 0 , then 6 , = 0 so that e, = 0 , i . e . , the low-powered incen-t i v e s disappear i f the employee loses a l l the bargaining power both i n the market for NSHA and i n the firm f o r FSHA. In contrast, when p m = p = 1 and 6 , = h 1 # then from (6.3.35-2), k, = (1-b) 1 / b(a+e 1**), i . e . , the firm's incen-t i v e to invest s t i l l e xists although i t i s lower than the f i r s t - b e s t l e v e l . The i n t u i t i o n for t h i s d i f f e r e n c e i s that the firm i s the residual claimant. Although i t loses i t s share of the human assets i n the second period bar-gaining, i t s t i l l receives the current production output. This i s p a r t i c u l a r l y c l e a r when k i s c o n t r a c t i b l e . In that case the firm's incentive i s influenced only i n d i -r e c t l y by the bargaining power through the employee's e f f o r t . Summary of the Two-Period Model In our two-period model, human asset a c q u i s i t i o n and anti c i p a t e d second-period contract renewal create an incentive f o r the employee to work hard i n the f i r s t 332 period. This incentive i s not the c l a s s i c a l high-powered type i n that i t i s not created by contingent contracts that r e s u l t i n short term r i s k bearing. The low-powered incentives we have modelled are consistent with the incen-t i v e s that appear to be i n e f f e c t f o r many employees within most organizations. Furthermore, i t provides a s e t t i n g within which to examine the r o l e of u n v e r i f i a b l e performance evaluation i n management accounting systems. I t i s i n t e r e s t i n g to compare the r e s u l t s of d i f f e r e n t incentive mechanisms. We summarize the main r e s u l t s of the f i r s t period contracts i n a two-period model i n Table 6-1. Insert Table 6-1 here A glance at Table 6-1 reveals the following con-clusions. F i r s t , a l l incentive contracts, e i t h e r high-powered or low powered, r e s u l t i n lower e f f i c i e n c y than that of the f i r s t - b e s t bench-mark contract. This can be shown by observing that a < 1 and 6, < h,, so that a l l the c o e f f i c i e n t s i n these c e l l s are l e s s than the f i r s t - b e s t c o e f f i c i e n t . Second, for low-powered contracts, contract-ing on k always creates stronger incentive than not con-t r a c t i n g on k. The economic i n t u i t i o n f o r t h i s r e s u l t i s that when k i s c o n t r a c t i b l e , input d i s t o r t i o n comes from the employee's e f f o r t only. A n t i c i p a t i n g higher invest-333 ment from the firm, the employee w i l l expect a higher ex post gain and correspondingly provide higher e f f o r t . F i n a l l y , a comparison between the high- and the low-pow-ered incentives shows that the high-powered contracts are characterized mainly by the risk-sharing c o e f f i c i e n t a, while low-powered contracts are determined only by the bargaining power p and p m (p and p m influence high-powered incentives too). A more d e t a i l e d comparison between the two mechanisms i s l e f t f o r future research. 6.3.5 Multi-Period Model The r e s u l t s presented i n the l a s t subsection can be immediately extended to a multi-period model. Assume that there are T periods with separating points (0, 1, 2, -,T-1, T). At each point t = 1, 2, T-1, the firm and the employee can e i t h e r terminate t h e i r r e l a t i o n s h i p , or contract to extend the employment r e l a t i o n f o r one more period. The analysis can be started from the l a s t period and traced back. The l a s t period i s exactly the same as i n the two-period model: the employee negotiates a con-stant wage contract at t = T-1 that r e f l e c t s h i s previous-l y acquired human assets (and h i s bargaining power) and the f a c t that he w i l l only provide the minimal l e v e l of e f f o r t , i . e . , eT=0. The firm r a t i o n a l l y invests k T = k°. The second to the l a s t period i s the same as the f i r s t 334 period of a two-period model: the employee w i l l invest eT.1>0 because he predicts that he can capture a p m share of NSHA and the expected output and a p share of FSHA i n the l a s t period contract bargaining. He w i l l choose eT.1 to maximize the difference between t h i s bonus and h i s personal e f f o r t cost, taking the discount.rate into account. For any t (0<t<T), we have following proposi-t i o n . Proposition 6.12: Assume at>0. There e x i s t incentives f o r the firm and the employee to continue t h e i r employment r e l a t i o n . The employee has incentive to i n s e r t more than the minimal e f f o r t l e v e l i n a l l periods except the l a s t period. I f the bargaining power i s con-stant over time and k i s non-contractible, then {kt,et} are characterized by C'(et) - yM(yb,T-t)Qt» [ l + Y M ( Y 8 , r - t ) (ht-Bt)] b • b(l-b)^'1 (6.3.41-1) _1 kt - [l+ yM(y b,T-t) (h t -8 t ) ] (1-2?) b (a + et) (6.3.41-2) where h t = <pt + t t , 6 t = p „ t t + p f t , and M(R, t) - 1 + U + - + J? f c-i - 1 " R t (6.3.42) 1 - R 335 For the case i n which kt are co n t r a c t i b l e events, we have Proposition 6.13: Under the same conditions as Proposition 6.12, i f k i s a co n t r a c t i b l e event, then (6.3.41) become C ( e t ) - Y M ( y 6 , T-t)Bt* [ I + Y M ( Y 8 , r-t) ht] b • 4-i b(l-b) b (6.3.43-1) JL kt - [l + yM(y b,T-t) ht] *• (l-Jb)"* (a + et) (6.3.43-2) I t i s easy to show that the f i r s t - b e s t s o l u t i o n of a multi-period model i s given by (similar to a two-period model) JL k*t - [l+YAf(y«f T-t) ht] b (1-b) (a+et) JL C'(ec) - [l+yM(yb,T-t) ht] b 4-i b(l-b) b 336 which are the solutions to k e [l+yM(y6, T-1) ht] mt-kt-C (e t) Comparing (6.3.41) or (6.3.43) with the f i r s t - b e s t s o l -utions, i t i s obvious that both of them are i n f e r i o r to the f i r s t - b e s t solutions. This conclusion holds even as T goes to i n f i n i t y , i . e . , the employment r e l a t i o n i s ever-l a s t i n g . The incentives created by the a n t i c i p a t i o n of future contract renewal i n a multi-period model have properties s i m i l a r to those i n a two-period model as described by Proposition 6.11. In addition, we have following proposi-t i o n . Proposition 6.14: In a multi-period model, i f we assume that the bargaining power and human asset a c q u i s i t i o n rates are constant over time, i . e . , a l l p a, p, 0 t , f t , n t ' a n d ® t a r e constants, then: (1) the employee's e f f o r t e t i s decreasing i n t ; (2) i f the t o t a l employment period i s long enough, i . e . , T i s large enough, then the employee's e f f o r t l e v e l s are close to a constant over time except when the time i s close to termination; (3) the firm's investment i s decreasing i n t ; (4) i f T i s large enough, the firm's i n -vestment l e v e l s are close to a con-stant over time except when the time i s close to termination. 337 Proposition 6.14 provides some i n t e r e s t i n g r e s u l t s about the nature of employee incentives. F i r s t , the employee's e f f o r t l e v e l i s , i n general, decreasing over time. Of course t h i s r e s u l t i s derived under our assump-t i o n that human asset a c q u i s i t i o n i s proportional to the current production output, but t h i s should be also true when human asset a c q u i s i t i o n i s p o s i t i v e l y c orrelated with h i s e f f o r t l e v e l . The c r u c i a l point i s that when an employee invests e f f o r t into a firm's operation, he w i l l not only a n t i c i p a t e short term benefits but also long term return. When the number of future periods are decreasing, h i s expected return i s decreasing which reduces h i s incen-t i v e to invest e f f o r t . This i s consistent with the f r e -quent observation that senior employees i n an organization work l e s s hard than most juni o r employees, although the former get higher s a l a r i e s . Second, when the expected employment i s long enough, an employee's incentives w i l l be quite stable over time, except when he i s close to retirement. This incentive i s not guaranteed by an e x p l i c i t incentive contingent contract, but i s motivated by the firm's and the employee's r a t i o n a l expectation of future contract renewal. This r e s u l t seems consistent with r e a l world observations that most employee's con-t r a c t s are not a contingent type, but most of them are quite industrious. Third, the firm's investment behaviour 338 i s s i m i l a r to the employees' incentives. In general, the firm invests l e s s for an employee when he i s close to retirement, but i s stable i f the expected employment i s long enough. F i n a l l y , we have the following generalization of Corollary 6.10 i n a multi-period model. Cor o l l a r y 6.15: In a multi-period model, the condition f o r the wage increasing over time i s P.[* tm t-(l -8 ) B t]+p [ t $ t i n t-<l - o)A t] > - P a [ (Jnt+i"-fct+i> - (mt-kt) ] - (1 -pJ [C(ek+1) -C(ek) ] (6.3.44) The general i n t e r p r e t a t i o n of (6.3.44) i s the same as for Corollary 6.10. When the period of employment i s long enough, then based on Proposition 6.14 (2) and (4), the expected production mt i s close to constant over time. This implies that the right-hand side of (6.3.44) i s very close to zero. Hence, condition (6.3.44) w i l l hold f o r any small amount of human asset a c q u i s i t i o n , and the employee's wage w i l l be b i d up. This can explain why we frequently observe that employees' wages are increasing over the employment period. However, t h i s i s not always true. As commented before, i f the employee's production reduction i s large enough, h i s wage may decrease. This i s d i f f e r e n t than the Harris and Holmstrom [1982] r e s u l t s . 339 6 .4 Implications f o r Managerial Accounting System Designs I t has long been recognized that information provided by any accounting system i s only a part of the information c i r c u l a t i n g i n organizations. One p a r t i c u l a r function of an accounting system i s to harden that information. The question of why firms choose to provide hard information has been the focus of accounting research over the l a s t twenty years. One commonly accepted point of view i s Gjesdal's [1981] in s i g h t that accounting information plays a key r o l e i n the stewardship process. Since shareholders of a firm usually delegate decision-making to managers, there i s a demand for information about the manager's actions f o r control purposes. Control i s modelled i n most of the e x i s t i n g l i t e r a t u r e through an agency r e l a t i o n s h i p . Following I j i r i ' s [1971] point of view that stewardship information should be as hard as possible, Gjesdal [1981] and many others claim that s o f t information has no value f o r stewardship processes. Our r e s u l t s show that the claim that hardness i s a necessary c h a r a c t e r i s t i c of stewardship information i s only true f o r high-powered incentive mechanisms. William-son [1985] points out that i n h i e r a r c h i c a l organizations, there may e x i s t d i f f e r e n t mechanisms from those i n the marketplace. In t h i s paper, we formally modelled such a mechanism with respect to incentives. Our analysis shows 340 that there can e x i s t two d i f f e r e n t kinds of incentives i n organizations. On the one hand, high-powered incentives, characterized by e x p l i c i t contingent contracts, depend c r u c i a l l y on hard accounting information. This i s con-s i s t e n t with Gjesdal's insight and most of the e x i s t i n g incentive l i t e r a t u r e . On the other hand, low-powered incentives are i n i t i a t e d by r a t i o n a l expectations of future contract renewal. They make use of a l l a v a i l a b l e s o f t or hard information i n the organization, perhaps providing a cheaper way fo r motivating employees. The merits of low-powered incentives r e l a t i v e to high-powered incentives can be summarized as following. F i r s t , i t can make use of s o f t information so that the costs of harden-ing information are avoided. This economy i n information costs may be s i g n i f i c a n t . Second, since most employees' tasks and t h e i r consequences are multi-dimensional, the design of high-powered incentive contracts may be extreme-l y d i f f i c u l t , i f not impossible. In contrast, low-powered incentives depend on contract renewal, f o r which i t i s easier to subjecti v e l y consider a v a r i e t y of information that pertains to the multi-dimensional factors that a f f e c t the firm's value. Thus, we claim that s o f t information has value i n providing incentives to employees within organizations. Then why do we observe high-powered incentives i n firms, 3 4 1 p a r t i c u l a r l y at some l e v e l s such as top management or d i v i s i o n a l managers? The answer i s : (i) f o r top managers i n a firm, s o f t performance measures are not a v a i l a b l e due to monitoring d i f f i c u l t i e s ; ( i i ) hard f i n a n c i a l accounting data or inside auditable managerial accounting data are a v a i l a b l e at a r e l a t i v e l y low cost; and ( i i i ) given the appropriate hard information, contingent contracts provide more e f f i c i e n t and e f f e c t i v e incentives. While top man-agers are most l i k e l y to be motivated by high-powered incentives, middle rank managers may face both kinds of incentives: some part of t h e i r compensation may be spec