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A microeconomic theory of the financial firm Chinloy, Diana Hancock 1982

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A M I C R O E C O N O M I C T H E O R Y O F T H E F I N A N C I A L F I R M by DIANA HANCOCK CHINLOY B . S c , Un iver s i t y of Santa C l a ra , 1977 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in THE FACULTY OF GRADUATE STUDIES (Department of Economics) We accept th i s thes i s as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December 1982 ° Diana Hancock Chin loy, 1982 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree a t the U n i v e r s i t y of B r i t i s h Columbia, I agree t h a t the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e copying o f t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head of my department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood t h a t copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be allowed without my w r i t t e n p e r m i s s i o n . Department of EffiiOQMlCS  The U n i v e r s i t y of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 3E-6 (3/81) SUPERVISOR - W.E. DIEWERT - i i i -ABSTRACT This research develops a microeconomic theory of the financial firm that is empirically implementable. Financial firms such as banks and savings and loan associations produce intermediation services between borrowers and lenders. User costs per unit of service can be derived for a l l goods. For financial services, these include the effects of reserve requirements, capital gains or losses, deposit insurance, interest rates, and service charges. Items generating more expenditure than revenue for the firm have positive user costs, and are inputs. Those with negative user costs are outputs. Comparative statics on profits, supplies of output and demands for input are derived for interest rates and monetary regulations. Data comprise pooled time series and cross section data for eighteen banks in New York and New Jersey for the years 1973-1978. User cost and quantity data are constructed for loans, demand deposits, time deposits, cash, labor and materials. The f i r s t two are outputs and the last four inputs. A specification is derived for the variable profit function, and the testing of regularity conditions such as monotonicity and convexity described. A test for the existence of a money supply, as a subset of financial goods is developed. The test imposes no prior restriction on the form of the money supply. The empirical results indicate that convexity and monotonicity obtain, at the geometric mean of the sample. E l a s t i c i t i e s of supply for outputs are positive, but less than unity. E l a s t i c i t i e s of demand are negative. Bank response to any monetary policy action can be calculated, - iv -and some experiments are reported on. An alternate model is derived to permit imperfect competition in the financial firm market for outputs and inputs. The model is shown to yield testable predictions, and price taking behavior for these banks is ruled out. The results indicate that i t is possible to develop and implement a model of financial firm behavior. Such a model is required to ensure accuracy in the effectiveness of monetary policy. - V -T A B L E O F C O N T E N T S Page TITLE PAGE I AUTHORIZATION i i ABSTRACT i i i TABLE OF CONTENTS v LIST OF TABLES v i i I ACKNOWLEDGEMENTS x C H A P T E R 1 - I N T R O D U C T I O N A N D S U M M A R Y 1.1 Need of Microeconomic Theory of F i n a n c i a l Firms 1 1.2 Issues i n Technology and Regulation of F i n a n c i a l Firms 5 1 .3 User Cost D e r i v a t i o n 7 1.4 A Model of the F i n a n c i a l Firm 7 1.5 Data and Data Construction 9 1.6 S p e c i f i c a t i o n and Hypothesis Te s t i n g 10 1.7 E m p i r i c a l Results 11 1.8 Imperfect Competition and the F i n a n c i a l Firm 12 Notes 13 C H A P T E R 2 - I S S U E S I N T E C H N O L O G Y A N D R E G U L A T I O N O F  F I N A N C I A L F I R M S 2.1 I n t r o d u c t i o n 14 2.2 Cost Function Approach 16 2.2.1 Output S e p a r a b i l i t y ; 17 2.2.2 Non-joint Technology 18 2.3 P r o f i t Function Approach 20 2.4 Outputs, Inputs and the " C l a s s i f i c a t i o n Problem" 24 2.5 Regulation and the F i n a n c i a l Firm 26 2.5.1 Reserve Requirements 27 2.5.2 I n t e r e s t Rate C e i l i n g s 29 2.5.2.1 Deposit I n t e r e s t Rate C e i l i n g s 29 2.5.2.2 Loan I n t e r e s t Rate C e i l i n g s --Usury Laws 30 2.5.3 Federal Deposit Insurance Corporation Premium Rates 32 2.6 Concluding Remarks 33 Notes 35 - v i -CHAPTER 3 - USER COST DERIVATION FOR FINANCIAL FIRMS 3.1 User Costs for Assets and L i a b i l i t i e s 37 3.2 Implementation Problems 42 3.2.1 Expectations of Future P r i ce s 42 Notes •• 45 CHAPTER - A MODEL OF THE FINANCIAL FIRM 4.1 Introduct ion 4-7 4.2 An Intertemporal Production Model of the Ind iv idua l F inanc ia l Firm 47 Notes 69 CHAPTER 5 - DATA AND DATA CONSTRUCTION 5.1 Introduct ion 72 5.2 Labor Services 75 5.3 Mater ia ls Serv ices 79 5.4 Phys ica l Cap i ta l Serv ices . 84 5.5 User Costs for F inanc i a l Commodities 94 5.5.1 Loans 94 5.5.1.1 Introduction 94 5.5.1.2 Investments 94 5.5.1.3 Real Estate Mortgages 97 5.5.1.4 Instalment Loans 98 5.5.1.5 Credit Card Loans 99 5.5.1.6 Commercial, A g r i c u l t u r a l and Other Loans. . . 100 5.5.1.7 User Cost for Aggregate Loans 100 5.5.2 Cash 105 5.5.3 Demand Deposits 106 5.5.4 Time Deposits 112 5.5.5 Non-deposit L i a b i l i t i e s 115 5.5.6 Net Loans 118 5.5.7 F inanc i a l Cap i ta l 121 5.6 Var iab le P r o f i t s 121 5.7 Concluding Remarks 123 Appendix - Chapter 5 - Funct ional Cost D a t a 126 On Cap i ta l Notes 130 CHAPTER 6 - SPECIFICATION AND HYPOTHESIS TESTING 6.1 Introduct ion 131 6.2 P r o f i t Function and Net Supplies 133 6.3 Regular i ty Res t r i c t i on s 136 - v i i -6.4 Tests of Bank Technology 139 6.4.1 Introduction . 139 6.4.2 Existence of Monetary Subagqregates 142 6.4.2.1 Introduction 142 6.4.2.2 Money Supply Definitions: Cash and Demand Deposits.. 143 6.4.2.3 Money Supply Definition: Cash, Demand and Time Deposits 148 6.5 Econometric Issues.. 149 6.5.1 Exogeneity of Prices and Quantities 149 6.5.2 Pooling Time Series and Cross Section Data -- Bank Effects 151 6.6 Concluding Remarks 153 Appendix - Chapter 6 155 Notes. 158 CHAPTER 7 - EMPIRICAL RESULTS 7.1 Introduction 159 7.2 Ela s t i c i t i e s of Transformation, Demand and Supply.... 161 7.3 Regularity Tests 164 7.4 Tests of Monetary Aggregation 171 7.5 Estimation of Transformation, Supply and Demand El a s t i c i t i e s 178 7.6 Rate of Return on Capital 187 7.7 Policy Implications: Monetary Policy and Bank Behavior 189 7.7.1 Introduction 189 7.7.2 Interest Rate Ceiling Deregulation 190 7.7.3 Reserve Requirement Costs 192 7.7.4 Deposit Insurance -- FDIC Regulation 194 7.8 Concluding Remarks 196 Notes 198 CHAPTER 8 - IMPERFECT COMPETITION AND THE FINANCIAL FIRM 8.1 Introduction 200 8.2 .Noncompetitive Bank Behavior: The Context 201 8.3 Imperfect Competition and the Financial Firm 204 8.4 Specification. 211 8.5 Empirical Results 215 8.5.1 Hypothesis Testing on Competitive Behavior... 215 8.5.2 Output Demand and Input Supply E l a s t i c i t i e s . . 217 8.6 Policy Implications 221 8.6.1 Costs of Noncompetitive Behavior 221 8.6.2 Monetary Policy 224 8.7 Concluding Remarks 225 Notes 226 CHAPTER 9 - CONCLUDING REMARKS 227 BIBLIOGRAPHY 230 - v i i i -LIST OF TABLES Page Table 5.1 O i v i s i a Pr i ce Indices for Labor (Tornqvist s p e c i f i c a t i o n 1973=1.00) 78 5.2 Cross Bank Tornqvist Labor Pr i ces Indices 1973 (Bank 1 normalized at u n i t y ) . . . . 80 5.3 Labor Input and Wage Data 1973-1978, Current Do l l a r s 81 5.4 Pr i ce Indices, Mater ia ls and Intermediate Inputs, 1973-1978 83 5.5 Tornqvist Pr i ce Indices, Mater ia ls and Intermediate Inputs, 1973=1.00 85 5.6 User Cost and Quantity Index, Mater ia l Serv i ces , 1973-1978 86 5.7 Asset Pr ices for Phys ica l Cap i ta l (1972=100) . . . . 89 5.8 Serv ice Lives by Type of Asset 91 5.9 Asset Pr i ce and Quantity Indices, Cap i ta l Stock, 1973-1978 95 5.10A Loan S t a t i s t i c s - User Costs (per cent, net return a f ter discounting) Three Sample Years 101 5.10B Loans Balances Outstanding, M i l l i on s of Do l l a r s Three Sample Years 104 5.11 Reserve Requirements on Demand Deposits of Member Banks November 1972 - November 1978 108 5.12 Reserve Requirements on Demand Deposits of Member Banks, Average Annual 109 5.13 Demand Deposit S t a t i s t i c s 110 5.14 Maximum Interest Rates Payable on Time and Savings Deposits at Federa l l y Insured Commercial Banks 113 5.15 Time Deposit S t a t i s t i c s 116 5.16 Borrowed and Purchased Funds and Other L i a b l i t i e s . . . 119 - i x -5 . 1 7 Net Loans, User Cost and Q u a n t i t i e s . 120 5 . 1 8 V a r i a b l e P r o f i t s , Sample S t a t i s t i c s . 1 2 4 5 . 1 9 V a r i a b l e P r o f i t s 125 Table 6 . 1 Test S t r u c t u r e , R e g u l a r i t y Conditions 140 6 . 2 Testing for Money Supply D e f i n i t i o n s 1 5 0 Table 7 . 1 Test S t a t i s t i c s , Symmetry and E q u a l i t y of V a r i a b l e P r o f i t Function 166 7 . 2 Parameter Estimates, V a r i a b l e P r o f i t Function 168 7 . 3 R e l a t i v e Expenditures, Outputs and Inputs 1 7 0 7.4 Convexity Test 172 7 . 5 Money Supply Aggregates Ml, Parameter Estimates.... 174 7 . 6 Money Supply Aggregates M2, Parameter Estimates.... 175 7 . 7 Estimates of E l a s t i c i t i e s of Transformation and R e l a t i v e Expenditures 1 7 9 7 . 8 Estimates of Own and Cross P r i c e E l a s t i c i t i e s of Supply and Demand 1 8 0 7 . 9 C l a s s i f i c a t i o n of P a i r s — S u b s t i t u t e s and Complements 1 8 5 Table 8 . 1 Parameter Estimates, Bank Supply and Demand Functions 2 1 6 8.2 Parameter Estimates, Tests of Competitive P r i c e Taking i n Separate Markets 2 1 8 8 . 3 Test S t a t i s t i c s , Competitive Behavior in Output and Input Markets (x /OF) 2 19 8.4 Parameter Estimates, Tests of Competitive Bank Behavior, A l l Markets 2 2 0 8 . 5 P r i c e E l a s t i c i t i e s of Demand for Outputs and Supply for Inputs 2 2 2 - X -ACKNOWLEDGEMENTS I would like to acknowledge with gratitude the help of my super-visor, W. Erwin Diewert. His own scholarship has provided me with an example to follow, particularly in duality theory. Further he has generously spent much time making suggestions, comments and developments on the work. > I have learned much on the structure of banking from Ronald Shearer. Kenneth White has also provided input, with his knowledge of econometrics and banking. The data used, on individual New York and New Dersey banks 1973-1978, were supplied by the Federal Reserve Bank of New York. Carl Allen, Anthony Mattia and Ken Behrens of the Bank Services Office of the Federal Reserve provided extensive assistance. I am grateful to the Social Sciences and Humanities Council of Canada (SSHRCC) for providing me with a Doctoral Dissertation Fellowship. The manuscript has been carefully word processed by 3eeva Donahs. Computer f a c i l i t i e s and resources have been provided by the University of British Columbia Computing Centre. CHAPTER 1 INTRODUCTION AND SUMMARY 1.1 Need for Microeconomic Theory of Financial Firms This research develops a microeconomic theory of financial firms. A financial firm is assumed to be a profit maximizing entity engaged in the production of intermediation services between borrowers and lenders. These services are related directly or indirectly to the financial assets and l i a b i l i t i e s held by the firm, such as loans and deposits. The financial firm issues its own l i a b i l i t i e s , typically deposits of various types. Services other than financial intermediation, such as safe deposit provision, estate management and equipment leasing, are excluded from this study. Financial firms include commercial and savings banks and savings and loan associations. Synonymously, "depository institutions" are used to describe these firms. The focus of this research is on national banks subject to regulation by the central bank, though the theory developed can be applied to other financial firms. This permits an examination of money supply aggregates and regulatory policies such as reserve requirements. The need for a microeconomic theory of the financial firm has been pointed out by Tobin [1961] The intellectual gulf between economists' theory of values of goods and services and their theories of value of money is well known and periodically deplored. Twenty-five years after Hicks' eloquent c a l l for a marginal revolution in monetary theory, our students s t i l l detect that their mastery of the presumed fundamental theoretical apparatus is put to very l i t t l e test in their studies of monetary economics and monetary models. As Hicks complained, anything seems to go in a subject where propositions do - 2 -not have to be grounded in someone's optimizing behavior and where shrewd but casual empiricism and analogies to mechanics and thermodynamics take the place of inferences from utility and profit maximization.1 Further, Klein [1971] notes In spite of the importance of commercial banking both as a major financial intermediary and as an important link in the monetary transmission process, there is l i t t l e consensus as to what constitutes a workable and productive theory of the financial firm. Despite this, there remains a paucity of microeconomic analysis of financial firms. There are at least two areas where a thorough understanding of financial firm behavior is essential. First, financial firms are among the most heavily regulated firms in the economy. The motivation for such regulation requires an understanding of the behavior of these firms. Second, money supply determination involves financial firms' decisions. An understanding of financial firm behavior is essential to the development of microfoundations in monetary theory. This research extends the banking literature in two directions. First, the analysis of the firm is built around the concept of user costs. The user cost of a financial good is defined as the net effective cost of holding one unit of services per time period. User costs are constructed per unit of service for both asset and liability items. In the case of a financial firm, a measure of user cost must include not only the interest rate paid to a depositor or received from a loan reci-pient, but also service charges, reserve requirements, deposit insurance and penalties, together with the discount rate. These user costs are the prices, which when multiplied by the quantity in deposit or Loan balances, yield net revenues or expenditures from financial goods. - 3 -User c o s t s are a l s o d e v e l o p e d f o r p h y s i c a l s e r v i c e s . N o t a b l e among t h e s e are l a b o r employed i n m a n a g e r i a l and p r o c e s s i n g f u n c t i o n s , p h y s i c a l c a p i t a l , m a t e r i a l s and s u p p l i e s . The u s e r c o s t s e n t e r the e s t i m a t i o n of the bank t e c h n o l o g y . T h i s p e r m i t s an a n a l y s i s of changes i n r e g u l a t i o n s or monetary p o l i c y on l o a n s , d e p o s i t s and employment i n b a n k i n g . Second, a method of c l a s s i f y i n g o u t p u t s and i n p u t s i s d e v e l o p e d . O u t p u t s are those w i t h n e g a t i v e user c o s t s , or g e n e r a t e more revenue than e x p e n d i t u r e f o r the f i r m . I n p u t s are t h o s e w i t h p o s i t i v e u s e r c o s t s . Hence i t can be r e a d i l y d e t e r m i n e d whether goods are i n p u t s o r o u t p u t s . The model p e r m i t s t h e i n v e s t i g a t i o n o f the e f f e c t s o f monetary p o l i c y on f i n a n c i a l f i r m s , and the r o l e o f i n t e r m e d i a r y d e c i s i o n s i n d e t e r m i n i n g the money s u p p l y . The t h e o r y o f money demand by consumers has been e x t e n s i v e l y s t u d i e d e l s e w h e r e . R e l a t i v e l y l e s s a t t e n t i o n has been g i v e n t o t h e s u p p l y o f money, v i e w i n g banks and o t h e r f i n a n c i a l i n s t i t u t i o n s as f i r m s . E x p l i c i t a t t e n t i o n here has been g i v e n t o whether money s u p p l y a g g r e g a t e s e x i s t , where f i n a n c i a l f i r m d e c i s i o n s d e t e r m i n e t h e money s u p p l y . The method and e f f i c i e n c y w i t h which f i n a n c i a l f i r m s c r e a t e money and i n t e r m e d i a t e between b o r r o w e r s and l e n d e r s i s examined. Though t h e r e i s r e l a t i v e l y l i t t l e m i c r o a n a l y s i s o f the f i n a n c i a l f i r m , t h e r e i s a p l e t h o r a o f l i t e r a t u r e r e g a r d i n g t h e impact of market s t r u c t u r e on perf o r m a n c e . I t may be premature t o ask how f i n a n c i a l f i r m b e h a v i o r i s a f f e c t e d by v a r i a t i o n s i n market s t r u c t u r e when t h e r e i s no t h e o r y t o d e s c r i b e t h a t b e h a v i o r . T h i s r e s e a r c h d e v e l o p s an e m p i r i c a l model which can s t a t i s t i c a l l y t e s t f o r noncom-p e t i t i v e b e h a v i o r i n both o u t p u t and i n p u t m a r k e t s . - 4 -T r a d i t i o n a l l y , the n e o c l a s s i c a l model of the f i rm has been sup-p lanted by p o r t f o l i o theory i n ana l yz ing the behavior of f i n a n c i a l i n s t i -t u t i o n s . Banks have not been t r ea ted as f i r m s , but as r a t i o n a l i n ve s to r s i n an environment c ha r a c t e r i z ed by r i s k or u n c e r t a i n t y . The Markowitz-Tobin p o r t f o l i o theory i s used as the a n a l y t i c a l apparatus. P roduct ion and cost c o n s t r a i n t s , and the r o l e they p lay in determining e q u i l i b r i u m output mix, input demands and s ca le s i z e have been omitted from con s i de r -a t i o n . I t i s u s ua l l y assumed that the f i n a n c i a l f i rm has u n l i m i t e d , r i s k l e s s a b i l i t y to borrow and obta in l eve rage . Extens i ve research has been performed on asset a l l o c a t i o n between a l t e r n a t i v e investments in a p o r t f o l i o . However, the l i a b i l i t y s i de of the balance sheet has rece ived r e l a t i v e l y l e s s a t t e n t i o n . Fu r the r , a theory of f i n a n c i a l f i rms must accomodate monetary r e g u l a t i o n s . These r e g u l a t i o n s are l a r g e l y ignored by those apply ing p o r t f o l i o theory . I t should be noted that t h i s model i s based on the r i s k l e s s neo-c l a s s i c a l theory of the f i r m . I t can be used as a b u i l d i n g block f o r a more complete model which in t roduces u n c e r t a i n t y and po s s i b l y r i s k a ve r s i on . The n e o c l a s s i c a l approach de r i ve s expected user co s t s , but the higher moments of these d i s t r i b u t i o n s may a l so p lay a r o l e . The i n c l u s i o n of such higher moments r equ i r e s data not t y p i c a l l y a v a i l a b l e . I t remains the case that f i n a n c i a l f i rms have expected r i s k premia measurable by expected user c o s t s . Higher r i s k s are compensated by i h igher r e tu rn s . An o b j e c t i v e of the research i s to measure these user c o s t s , dependent not only o n i i n t e r e s t r a te s but a l so reserve requirements, expected c a p i t a l ga ins or" l o s se s and depos i t insurance r a t e s . - 5 -1.2 Issues in Technology and Regulation of Financial Firms Chapter 2 f i r s t discusses the estimation of cost functions for financial firms, where input costs and output quantities are explanatory variables. The problem with the cost function approach is that output is not a predetermined variable. Further, without a classification rule to select between outputs and inputs, outputs cannot be easily determined. Cost functions for financial firms are typically estimated with outputs aggregated, although this is not a requirement. Aggregation of output permits the estimation of economies of scale.** The important issue is what prices are used in the cost function. User costs include interest rates and regulatory and other cost variables. If interest rates only are used, the data are subject to measurement error and the resulting estimates are biased. It is impossible to analyze the effects of reserve requirements and monetary policy on the banking system. The alternative starting point for bank technologies is the profit function. The profit function, as the maximum of profits subject to the production function constraint, is more appropriate for banks and other financial firms. The problems with the profit function arise more in .specification and estimation than in theory. Some of these problems are discussed below. First, i f a second order form such as the translog or generalized Leontief or quadratic is used, i t is necessary to check regularity condi-tions. These include linear homogeneity in output and input •prices, monotonicity and convexity. If the convexity or the linear homo-geneity in prices properties f a i l to hold, then the estimated profit - 6 -function is not consistent with the maintained assumption of profit maxi-mizing behavior. Second, the variable profit function depends on prices, or user costs of outputs and inputs, and the quantities of fixed inputs. There is likely to be substantial multicollinearity in these user costs, whether in time series, cross section or pooled data. This situation can be ameliorated i f demand or supply equations are also included in the system of estimating equations, but otherwise i t is d i f f i c u l t to identify parameters. Third, the argument on user cost data applies to the profit function. If there is measurement error in user cost, biased parameter estimates arise. Furthermore, i f the effects of regulations on user costs are excluded, i t is impossible to analyze monetary policy effects. Chapter 2 examines the principal areas of regulation that affect user costs. For example, reserve requirements, as administered by the Federal Reserve, act as a tax on financial firms so covered. Required reserves earn no return to the financial firm and there is foregone revenue. . Deposit insurance increases the user cost of servicing deposits to the banks. Interest rate regulations place limits on interest rates on time deposits, or prohibit payments on demand deposits during the period studied. Underlying a l l these are the open market operations of the Federal Reserve, and their effects on interest rates and the quantities of financial goods. Chapter 2 reveals that previous work on the estimation of bank technologies is incomplete, and that the regulations require modelling as - 7 -a part of the profit maximizing structure. 1.3 User Cost Derivation Chapter 3 discusses the construction of user costs. These are derived for the services from a l l assets or l i a b i l i t i e s on a bank balance sheet or appearing on the income statement. The user cost formulation permits goods to be classified as outputs and inputs. Those with a positive user cost, where expenditures per unit exceed revenues per unit, are inputs. The unit for financial goods such as loans or deposits is one dollar per period. Goods with a negative user cost, with expenditures falling below revenue per unit, are outputs. L i a b i l i t y items, such as time or demand deposits, involve interest expenditures by banks.5 Further unit costs are incurred for the reserve requirement, in foregone revenue, and deposit insurance, while service and penalty charges are earned. On asset items such as loans, interest revenue is earned. Capital gains or losses are realized on long term loans transferred, such as mortgages, and a provision for bad debts or defaults included. The user costs as constructed, including those for labor and materials, are the data for the profit function estimation. This permits outputs and inputs to be distinguished. 1 A A Model of the Financial Firm A model of producer behavior is developed in Chapter 4 where labor, materials and physical capital demands, and asset and l i a b i l i t y holding decisions are simultaneously determined. The specification differs from previous neoclassical models in that i t is based on the - 8 -theory of intertemporal production of Hicks [1946] and uti l i z e s the user costs derived in Chapter 3. Time plays an essential role in the financial firm's production process, and an intertemporal model is needed, particularly for analyzing asset and l i a b i l i t y decisions. Each financial institution holds an inventory of various financial assets, l i a b i l i t i e s , and capital. There are revenues and costs associated with holding this inventory over time. The financial firm is assumed to choose the input-output combination which maximizes profit during the production period. The model developed considers regulatory controls through their effect on relative user costs. The duality between the production possibility set and the profit function is employed to derive comparative statics yielding testable predictions, and to obtain the functional forms for the estimating equations. It is found that the holdings of an asset do not decrease when the rate of interest payable to the financial firm increases. A similar conclusion obtains If expected capital gains increase, or i f the service charge rate collected increases. However, i f the expected rate of default increases, asset holdings do not increase. On the l i a b i l i t y side of the balance sheet, i t is found that deposits are non-increasing i f their required reserve ratio increases, or i f the interest rate payable increases. A similar conclusion obtains i f the insurance premium increases. However, i f the service charge rate per dollar increases, then deposits are non-decreasing. Comparative -statics for the cross effects of the components of each user costs are indeterminate. It is unknown a pri o r i what the effect on time deposits is when the required reserve ratio on demand - 9 -deposits changes. This is because the off-diagonal elements of the matrix of second order partial derivatives of the profit function evaluated at the optimum cannot be sign-determined using the regularity properties of the profit function. Further analysis of the cross effects of the components of each user cost requires examination of empirical point estimates. Profits for the financial firm are non-decreasing when there is an increase in: (1) the interest rate payable to the firm on assets held; (2) the capital gains on assets held; (3) the service charge rate on loans; and (4) the service charge rate on deposits. Profits are non-increasing i f there is an increase in the following components of user cost: (1) the default rate on loans; (2) the required reserve ratio on deposits; (3) the interest rate payable by the financial firm on l i a b i l i t i e s ; and (4) the insurance premium rate on deposits. 1.5 Data and Data Construction The data and their derivation are described in Chapter 5. The major data source for the study is developed by the Federal Reserve Bank of New York's Functional Cost Analysis Program. The sample comprises yearly data for eighteen commercial banks over the period 1973-1978. The banks are located in the states of New York and New Jersey. Panel data are more appropriate than cross-sectional data for our purposes because they permit variation in user costs over time and permit the testing of specific bank effects. Data are constructed for three physical, or non-financial commodities used in bank production. These are labor input, the services - 10 -of intermediate inputs and raw materials, and the services of capital. User costs and the relevant quantities for financial commodities are constructed. For the specification, four types of financial commodities are distinguished, namely loans, cash, demand deposits and time deposits. With the exception of cash, the quantity of each is an index comprising a number of other financial commodities. For each component a separate user cost must be constructed. Quasi-rents or variable profits are also constructed for each bank in each year. The classification test is then applied to the data. For a l l sample points, loans and demand deposits are outputs. Cash, time deposits, labor and materials are inputs. 1.6 Specification and Hypothesis Testing The functional form used is a translog variable profit function. Prior to testing hypotheses on bank technology, certain conditions must be satisfied. These include symmetry of the quadratic parameters, monotonicity and convexity. Monotonicity requires that variable profits be increasing in output prices, and decreasing in Input prices. Convexity is satisfied i f the Hessian matrix of second derivatives of the variable profit function is positive semi-definite. Chapter 6 derives the e l a s t i c i t i e s of transformation and e l a s t i c i t i e s of supply for outputs and demand for inputs. It is possible to calculate explicitly the response of loan supply by banks when user costs of loans, or of demand deposits, change. This permits a more complete microeconomic analysis of the effects of monetary policy on banks to be derived. - 11 -A s t a t i s t i c a l test is developed for whether a money supply exists, and i f so, what its components are. Candidates for inclusion are cash, demand and time deposits. The test is generalizable to any definition of money. The test is based on a test due to Woodland [1978]. This test is not subject to the bias noted by Blackorby, Primont and Russell [1977] which occurs when the Berndt and Christensen [1974] test for the existence of an aggregate in a translog model is used. Usual application of the Berndt and Christensen test in this context requires the money supply to be Cobb-Douglas, with unit e l a s t i c i t i e s of substitution. The proposed test allows the money supply to have arbitrary substitution possi b i l i t i e s between components. 1.7 Empirical Results The empirical results for the eighteen New York and New Jersey banks 1973-1978 are reported in Chapter 7. Symmetry is imposed on the estimating system. Given this, both monotonicity and convexity hold for a l l data points. The matrix of el a s t i c i t i e s of transformation is well behaved. A l l principal diagonal elements are positive. Own price e l a s t i c i t i e s of supply, for loans and demand deposits, are both less than unity. On the demand side, own price e l a s t i c i t i e s for cash, labor and materials exceed unity, but are relatively close to unity, while that for time deposits is less than one. Responses to changes in monetary regulations are examined. Specifically, the provisions of the 1980 Monetary Control Act are applied to the sample period, by allowing the interest rate ceiling on - 12 -time deposits to increase. Responses to changes in deposit insurance and reserve requirements are also carried out. 1.8 Imperfect Competition and the Financial Firm The theory is extended to account for market imperfections facing financial firms in Chapter 8. The demand for output is permitted not to be perfectly elastic, and similar f l e x i b i l i t y is permitted on the supply of inputs. Previous models impose price-taking in output and input markets. Also, the ela s t i c i t i e s are a l l estimated, and do not require a priori information. The model developed commences from the production function, and is not s t r i c t l y comparable to the variable profit function model. This is because a translog specification is used, and the form is not self-dual. Tests are developed separately for price taking in loans, cash, demand deposits, time deposits and labor. In the empirical results for the eighteen New York and New Dersey banks 1973-1978, price taking is accepted in the labor market, but not accepted in the remaining four markets. However, a l l the price e l a s t i c i t i e s exceed unity. This introduces the issue of the cost of imposing price taking when it is not the case. Price taking is imposed in a l l markets, and the estimates compared with those when price taking is not imposed. The specific simulations are for responses to monetary policy in affecting cash, demand deposits and time deposits. In some cases, the difference in results is small, while in others the error can be as large as 20 percent. NOTES h o b i n [ 1961]. 2 K l e i n [1971]. 3See Barnett [1981]. This i t s e l f i s not a requirement, for economies of scale estimate have been derived for multiple output technology, although there i s no agreement on procedure. One p o s s i b i l i t y i s to evaluate the marginal cost of each output, and to sum. See Caves, Christensen and Swanson [1980] and Panzar and W i l l i g [1977]. 5 I n the case of demand deposits, there may be a p r o h i b i t i o n against p o s i t i v e interest payment. However, p o s i t i v e interest rates apply on negotiable order of withdrawal (NOW) accounts. - 14 -CHAPTER 2 ISSUES IN TECHNOLOGY AND REGULATION OF FINANCIAL FIRMS 2.1 Introduction The s tructure of technology and po ten t i a l s u b s t i t u t a b i l i t y between various assets and l i a b i l i t i e s i s o f in teres t not only from the point of e f f i c i e n c y in the f i n a n c i a l sector , but also for the conduct of monetary p o l i c y . Moreover, such information i s of relevance in the regu la t ion and deregulat ion of the f i n a n c i a l sector . T r a d i t i o n a l l y , the neoc la s s i ca l model of the f irm has been supplan-ted by p o r t f o l i o theory in analyzing the behavior of f i n a n c i a l i n s t i t u -t i o n s . The primary focus of p o r t f o l i o theory i s the a l l o c a t i o n of funds between heterogeneous loans and investments. 1 A number of wr i te r s , Kane and Ma lk ie l [1965], Parkin [1970], Pyle [1971], Hyman [1972], Aigner [1973], Hart and Oaffe [1974], Berndt and McCurdy [1980], have adopted the Markowitz-Tobin p o r t f o l i o theory as the i r a n a l y t i c a l apparatus. P o r t f o l i o theory views firms not as producers, but as r a t i o n a l investors in an environment character ized by r i sk or uncer ta in ty . There are at least two problems with th i s approach. The f i r s t stems from the omission of production and cost cons t ra in t s under which f i n a n c i a l firms operate, and the ro le of these cons t ra in t s in deter-mining equi l ibr ium output mix, input demands and scale s i ze of the f i n a n c i a l f i rm. The second i s the r e l a t i v e neglect in the p o r t f o l i o l i t e r a t u r e of the l i a b i l i t y side of the balance sheet. Further , a theory of f i n a n c i a l firms must take account of po l i cy regu la t ions . Several authors have argued that perfect competit ion may not be the - 15 -relevant behavioral mode in asset and deposit markets.2 Mason [1979] argues that the assumption of quantity-setting behavior is not appropriate for financial firms, and that portfolio theory tends to view prices as exogenous. Hart and daffe [1974] argue that price-setting behavior cannot be adequately treated within a portfolio model. Various studies ut i l i z i n g the concepts of the riskless neoclassical theory of the firm have been proposed to describe the operations of financial firms in order to correct deficiencies of portfolio analysis. Most of these studies do not consider the effects of regulations on financial firms, or imperfectly competitive markets for outputs and inputs. One area of focus has been on the degree to which economies of scale obtain and the implications of increasing returns to scale. 4 Another area relates to the conduct of monetary policy. Specifically, the issue is the relationship between the technology of a financial firm and money creation. 5 Another problem is the relationship between regulations on financial institutions and the theory of money creation. The methodology used has varied. In some cases, a reduced form is derived and estimated without a direct linkage to economic theory'. In other cases, the economic model and underlying technology have been derived. 6 In essence, the research on financial firms can be divided into those using cost functions and those employing profit functions. Section 2 discusses the cost function approach, and section 3 discusses the profit function approach. One of the main confusions in the theory of the financial firm arises from disagreement concerning appropriate measures of outputs - 16 -and inputs. If neither input nor output can be appropriately defined, it is d i f f i c u l t to speak of a production function relating the two. Section 4 discusses this classification problem. Section 5 discusses three types of regulations on financial firms. The chapter closes with some concluding remarks. 2.2 Cost Function Approach Duality theory for production and cost structures permits the specification of any production technology in terms of an eguivalent cost function (McFadden [1978]), assuming cost minimizing behavior. Econometrically, this permits the estimation of the cost structure and the characteristics of the underlying production structure. The short run multiproduct variable cost function can be written as: C = C(z,w,f) (2.1) where C is minimal short run total variable costs,z is a vector of out-puts, w is a vector of variable input prices and f is a vector of fixed inputs, exemplified by capital. The cost function satisfies the properties that i t is a non-negative function, positively linearly homogeneous, concave, continuous and nondecreasing in input prices, w, and s t r i c t l y increasing and continuous in z (Diewert [1982]). Assuming that z and w are exogenous to the firm and i t s stock of capital is given, (2.1) yields unbiased estimates of the underlying technology once an appropriate functional form and stochastic specification have been given. By imposing restric-. tions in the estimation, it is possible to test hypotheses on technology. 17 -The cost func t i on approach has been employed by researchers mainly concerned with the degree of economies of s ca le and the i m p l i c a t i o n s fo r ent ry and branching r e g u l a t i o n . The emphasis i s on whether e x i s t i n g f i n a n c i a l f i rms should be al lowed to expand by branch ing, or i f new f i rms should be al lowed to en te r . To obta in es t imates of economies of s ca le researchers have e i t h e r assumed an output aggregate e x i s t s , or that the f i rm has a non - j o i n t technology. The economies of s ca le were measured for the output aggregate or for each i n d i v i d u a l product. 2.2.1 Output Separability One group of s t ud i e s on the techology of the f i n a n c i a l f i rm p imposes ex ante output aggregat ion. One procedure fo r measuring output q has been to use t o t a l depos i t s as a proxy. An a l t e r n a t i v e measure has been to use t o t a l assets held by the f i n a n c i a l f i r m . 1 0 Goldschmidt [1981] uses both these output p rox i e s . As a t h i r d a l t e r n a t i v e , Greenbaum [1967], Powers [1969] and Schweitzer [1972] cons t ruct output measures that ass ign weights to the var ious components of the earn ing assets p o r t f o l i o . Using the mu l t ip roduct v a r i a b l e cost f u n c t i o n , aggregat ion of outputs imp l i e s the ex i s tence of an aggregator f unc t i on h(z) such that (2.1) can be w r i t t e n S ince = C^h^, where s ub s c r i p t s i n d i c a t e p a r t i a l d e r i v a t i v e s , we have the output aggregation c o n d i t i o n , C = C ( h ( z ) , w , f ) . (2.2) C n h (z) n (2.3) C m h (z) m - 18 -for any outputs n and m independently of w and f. The output aggre-gation condition implies that the ratio of the short run marginal costs for any two outputs must be independent of variable input prices and capital. Since this condition implies restrictions on the variable cost function, it can be tested using (2.1). A rejection of the hypothesis (2.3) would indicate that output cannot be aggregated into a single measure, and that multiproduct specifications must be used in estimating cost structures. 2.2.2 Non-Joint Technology A second group of cost studies uses empirical models based on a more explicit consideration of the structure of the underlying tech-nology (Benston [1965], Bell and Murphy [1968], Dugger [1975] and Long-brake and Merrill [1974]). It is assumed that the transformation function is non-joint in inputs. Let the technology of a multiproduct, multi-input firm be represented by a transformation function T(z,x) = 0 where z and x are M and N dimensional vectors of the quantities of out-puts and inputs respectively. A transformation function is non-joint in inputs i f there exist individual production functions, Z i = f i ( x LT ' " ' X i N ) 1 = 1>--->M (2-4) M such that T(z,x) = 0 i f and only i f z. = f. and Ex.. = x. for 1 1 i = l 1 J J j = 1,...,N where z = ( z ^ , — >z(v|)> x E (x|»-''>x^) a r ,d t n e inputs are so allocated amongst the products that the output of no one product may be increased without decreasing the output of another. Benston [1965] and Bell and Murphy [1968] view the financial - 19 -f i rm as represented by a number of separate production processes in estimating a model of bank behavior. The output of each process i s measured by number of accounts. The products are demand depos i t s , time depos i t s , instalment loans, business loans, rea l estate loans, s e c u r i t i e s , safe deposit boxes and trust business. Overhead costs d iv ided into admin i s t rat ion, business development, and occupancy are analyzed separate ly. The object ive i s to estimate economies of scale for each product. The form of the equation estimated for each of the d i r e c t banking serv i ces , and for each category of i nd i rec t cost i s derived from an underlying Cobb-Douglas production funct ion . Adar, Agmon and Orgler [1975] argue that interdependence may a r i se from the j o i n t use of ce r t a i n inputs by many products. In banks, jo inthess in production i s evident in the j o i n t use of information by d i f f e r e n t departments, e .g . , in evaluat ing a loan app l i ca t i on of a depos i tor . Another example is the jo in t use of general "brand name" type advertisement. A test for the existence of jo intness in production u t i l i z i n g the mult iproduct cost funct ion can be developed. It u t i l i z e s the fo l lowing 12 r e l a t i o n , M C(z.j , . . . ,z^,w,f) { = I C..(z.,w,f) i f F i s non-joint in inputs j=1 M < £ C. (z. ,w,f ) i f F involves jo intness in J J j=1 product ion, j=1,...,M. - 2 0 -3ointness in production has also been called "economies of scope" by Cowing [ 1980]. A logical extehtion of the above research employing the cost function approach is to postulate a flexible functional form for the multiproduct variable cost function and then test for output separability, jointness in production, homogeneity and a Cobb-Douglas structure. These tests would be based on parametric restrictions. Woodland [1978] has developed a test for weak separability. Cowing [1980] has suggested a test for the existence of jointness in production i f a multiproduct transloq variable cost function is postulated. Hall [1973] has derived a functional form for joint cost functions that contains separability and non-jointness as parametric restrictions. The test for output homogeneity using the variable cost function involves non-linear estimation of the degree of homogeneity. Other alternative assumptions can also be considered. 2.3 Profit Function Approach Duality between profit and transformation functions allows the specification of any production technology in terms of an equivalent profit function (Diewert [1974]), assuming that the producer chooses the input-output combination which maximizes profit. For econometric applications it is convenient to introduce the variable profit function due to Samuelson [1953-4]. The variable profit function may be defined as follows: ir(v,w:f) = max {vz-wx : (z,x:f)eS} (2.6) where n is maximized variable profit, z is an M dimensional vector of - 21 -output s , x i s an N dimensional vector of v a r i a b l e i npu t s , f i s a vector represent ing the quant i ty of f i x ed i npu t s , v i s a vector of output p r i c e s , w i s a vector of input p r i c e s and 5 represents the t e c h n o l o g i c a l l y f e a s i b l e set of inputs and output s . H o t e l l i n g ' s Lemma can be used in order to der i ve systems of v a r i a b l e output supoly and input demand func t i on s , i f the v a r i a b l e p r o f i t f unc t i on s a t i s f i e s r e g u l a r i t y cond i t i on s and i s d i f f e r e n t i a b l e with respect to v a r i a b l e 13 output and input p r i c e s . S t a t i c p r o f i t maximizing behavior i s a standard assumption in c on s t r u c t i n g models of f i n a n c i a l i n t e r m e d i a r i e s . Pesek [1970] and Towey [1974] focus on r e c o n c i l i n g the theory of money c r e a t i o n wi th the theory of the f i r m . Mingo and Wolkowitz [1977] and Sealey and L i n d l e y [1977] concent rate on the a l l o c a t i o n of resources and e q u i l i b r i u m l e v e l s of output . A t h i r d group (Adar, Agmon, and Org ler [1975] and Mul l ineaux [1978]) cons ider a l t e r n a t i v e types of p r o f i t f u n c t i o n s . Those i n t e re s t ed i n r e c o n c i l i n g the theory of the f i rm with the theory of money c r e a t i o n (Pesek [1970], Towey [1974]) have the common procedure of s e l e c t i n g the nominal quan t i t y of depos i t s as the output of the banking i ndu s t r y . Roth models assume that banks de s i r e to hold no excess reserves on the depos i t s they expect to r e t a i n . Hence 3 ea = I ( l - k . ) D . (2.7) j = l J 1 where ea = earning assets , and k^ i s the reserve r a t i o on the j t h depos i t type, j =1 , . . . , 3 . Revenues are composed of earn ings on assets and s e r v i ce charges. Pesek [1970] c a l c u l a t e s average cos t s measured per - 22 -d o l l a r of demand deposits using f u n c t i o n a l cost d a t a prepared by the Federal Reserve Bank of Boston for 85 banks i n 1965. Towey [1974] assumes that each bank cost f u n c t i o n can be expressed as a f u n c t i o n of deposit q u a n t i t i e s and a vector of s e r v i c e s per d o l l a r of deposits performed. Sealey and Lin d l e y [1977] and Sealey [1980] consider deposits as inputs i n the production of earning asset output, rather than being the output i t s e l f . The d o l l a r volume of the various types of earning assets i s used as a measure of the output of the f i n a n c i a l f i r m . The f i n a n c i a l f i r m i s viewed as being composed of conceptually d i s t i n c t departments. The i m p l i c a t i o n i s that the transformation f u n c t i o n i s non-joint i n i n p u t s . The transformation f u n c t i o n i s non-joint i n inputs i n the d i f f e r e n t i a b l e case i f and only i f 3 2TT/3V.3V. = 0 1 * 7 i J . 8 I^T ^ 3^TT i=1,... ,M , c > and v. —=• + Z w. = 0 . ' ' (2.8) 1 3v. 1=1 J 3w.3v. J - i , . . . , N i • J i where IT i s the p r o f i t function and v^'s and vv/s are the output and input p r i c e s r e s p e c t i v e l y . Since t h i s i s a necessary and s u f f i c i e n t c o n d i t i o n f o r the c h a r a c t e r i z a t i o n of a non-joint i n inputs technology i t i s amenable to st r a i g h t f o r w a r d e m p i r i c a l t e s t s , though Sealey and Li n d l e y [1977] do not e m p i r i c a l l y t e s t t h e i r model. Mingo and Wolkowitz [1977] and Sealey [1980] also assume a non-joint technology. Most of the econometric studies of bank p r o f i t s are developed without an underlying production s t r u c t u r e . Some contain an incomplete or i n a p p r o p r i a t e s p e c i f i c a t i o n of the p r o f i t f u n c t i o n . 1 1 * One group of - 23 -models contains bank assets as a proxy for bank output. Another uses as output, bank capital, which is highly correlated with assets. These models are theoretically misspecified because output is in the profit function. If output is endogenous and its quantity is correlated with the error term in the profit function then simultaneous equation bias occurs. The estimates of the parameters will be biased and inconsis-tent . Mullineaux [1978] utilizes the theory of the profit function in developing his econometric model. He assumes the technology cons-training bank production can be represented by the transformation function T(z,x,f) = 0. (2.9) The vector of bank outputs, z, includes real estate loans, consumer instalment loans, commercial loans, and safe deposit boxes. Variable inputs x include labor, materials, computer hardware services, and various kinds of deposits. Quantities of fixed factors f are represented by the number of f u l l service branches, limited service branches, paying and receiving stations, and averaqe size of f u l l service branches. A hybrid profit function is tested which is transloq in labor input prices and Cobb-Douglas in the prices of output and other inputs and the quantities of fixed factors of production. Rather than using a specification which utilizes share equations to correct for collinearity in the data, he estimates a single equation usinq ordinary least squares and cross-sectional data. A number of coefficients either f a i l to conform in sign to a pr i o r i specifications or are s t a t i s t i c a l l y insignificant. Mullineaux tentatively interprets these results as - ?A -evidence of non-compet i t i ve behav ior , arquinq that output p r i c e s are not v a r i a b l e s in the monopo l i s t ' s p r o f i t f u n c t i o n . For mu l t ip roduct f i rms such as commercial banks, a f i n d i n g that bank output p r i c e s make no s i g n i f i c a n t c o n t r i b u t i o n to the e m p i r i c a l " e x p l a n a t i o n " of bank p r o f i t s i s c on s i s t en t with the hypothes is that banks are not p r i c e taker s i n any of the markets fo r t h e i r products and s e r v i c e s . Of course, banks may operate c o m p e t i t i v e l y for a subset of t h e i r p roducts , in which case a subset of commercial bank p r i c e s would appear i n the p r o f i t f u n c t i o n . (Mul l ineaux [1978], p. 263) The r e s u l t s may be a t t r i b u t a b l e to annual average i n t e r e s t ra tes used by Mul l ineaux being po s s i b l y poor p rox ies for a c tua l market p r i c e s . They could a l so be caused by m u l t i c o l l i n e a r i t y a s soc ia ted wi th i n s u f f i c i e n t p r i c e d i s p e r s i o n i n the c r o s s - s e c t i o n a l sample to es t imate a f l e x i b l e f u n c t i o n a l form such as the t r a n s l o q . 1 5 The f i x e d f a c t o r v a r i a b l e s , the number and s i z e of va r ious kinds of branches may be subject to e r r o r , and the parameters are not r e s t r i c t e d to ensure the p r o f i t f unc t i on i s homogeneous of degree one i n p r i c e s . The est imated p r o f i t equat ion i s c h a r a c t e r i z e d by i n c rea s i n g returns to s c a l e , but t h i s v i o l a t e s a property of the p r o f i t f u n c t i o n , unless some inputs are held f i x e d . In c o n c l u s i o n , there are seve ra l hypotheses, given the l i t e r a t u r e i n t h i s area, which are of i n t e r e s t i n an econometric model of the f i n a n c i a l f i r m . These i nc lude output s e p a r a b i l i t y , non - jo in tnes s i n i n pu t s , and a Cobb-Douglas s t r u c t u r e . There has been l i t t l e consensus as to what c o n s t i t u t e s the input s and outputs of the f i n a n c i a l f i r m . We now turn to t h i s problem. 2.fr Outputs, Inputs, and the "Classification Problem" Although i t i s w e l l known that f i n a n c i a l f i rms produce - 25 -heterogeneous outputs, there has been l i t t l e consensus on their outputs and inputs. The outputs used by various researchers are: total assets, earning assets, loans, total deposits, demand deposits in dollar terms, the number of deposit and loan accounts, gross operating income and combinations of these measures. Renston [1964] and Mackara [1975] have even suggested that the researcher can adopt any measure of output for the financial firm as long as the measure is consistent with the researcher's goal. The central questions in what we term the "classification problem" are: 1. Which balance sheet items produce services that are outputs and which ones inputs? (e.g. Are demand deposit services outputs or inputs?) 2. How does one measure the outputs and inputs, or put prices on them? The measurement of price is dual to the question "what units is output measured in?" One can be obtained from the other i f the necessary conditions for producer equilibrium are satisfied. Another way of posing the problem is whether stock or flow variables measure the relevant concept of bank output and input. Our approach to tackling the classification problem is to develop complete user costs of balance sheet items for the financial firm. User costs, or rental prices, of balance sheet items are derived in Chapter 3. An input is defined as a good with positive user cost, and an output Is one with a negative user cost. Derivation of user costs not only permits asset input-output classification and develops appropriate - 26 -p r i c e s on inputs and outputs, but also allows examination of key monetary p o l i c y instruments such as reserve requirements, and i n t e r e s t r a t e s and r e g u l a t i o n s such as deposit rate and loan rate c e i l i n g s . Previous researchers have not modelled e x p l i c i t l y these instruments and r e g u l a t i o n s when estimating the f i n a n c i a l firm's technology. 2.5 Regulation and the Financial Firm The a n a l y s i s of r e g u l a t i o n provides a primary motivation for the development of a theory of the f i n a n c i a l f i r m . T y p i c a l l y , r e g u l a t i o n s are not i n t e g r a t e d with the theory of production f o r a f i n a n c i a l f i r m . Three types of r e g u l a t i o n on f i n a n c i a l firms are d i s t i n g u i s h e d . F i r s t , there are r e g u l a t i o n s that are not d i r e c t l y q u a n t i f i a b l e . For example, i n the case of banks subject to r e g u l a t i o n by the c e n t r a l bank, moral suasion i n monetary p o l i c y or s u r v e i l l a n c e and i n s p e c t i o n costs by deposit insurance agencies are not e a s i l y q u a n t i f i a b l e . The second type of r e g u l a t i o n a f f e c t s f i x e d costs or p h y s i c a l c a p i t a l , assumed f i x e d i n the short run i n t h i s a n a l y s i s . Examples are r e s t r i c t i o n s on entry to the industry through requirements on shareholders, and l i m i t s .on the number and extent of branches. The t h i r d type of r e g u l a t i o n a f f e c t s the marginal p r i c e to the firm of o f f e r i n g s e r v i c e s . For banks, these costs include reserve requirements, deposit insurance and c e i l i n g s on i n t e r e s t r a t e s . The focus i s on the t h i r d type of r e g u l a t i o n , for through changes i n marginal p r i c e s , the e f f e c t s on loan and deposit composition can be analyzed. I t permits a microeconomic a n a l y s i s of monetary p o l i c y f o r f i n a n c i a l f i r m s . It i s p o s s i b l e to g e n e r a l i z e the model to accomodate - 27 -the second type of regu lat ion, but that i s not the focus. A model i s derived where regulatory costs are part of marginal p r i ce s or user costs of the serv ices of loans and depos i t s . E m p i r i c a l l y , the model i s formulated for hanks which are members of the Federa l Reserve System. These regulat ions focused upon are summarized, as discussed in the relevant l i t e r a t u r e . In ex i s t i ng research these are not grounded in a theory of product ion, which makes comparative s t a t i c ana lys i s d i f f i c u l t . This study focuses on three types of f i n a n c i a l regulat ion entering user costs. Sect ion 2.5.1 deals with reserve requirements. Section 2.5.2 i s on i n te res t rate c e i l i n g s and sect ion 2.5.3 i s concerned with deposit insurance premium rates . 2.5.1 Reserve Requirements Nearly all depository i n s t i t u t i o n s must keep some minimum port ion of assets in cash or otherwise l i q u i d form. These reserve requirements affect the marginal p r i ce s of var ious f i n a n c i a l commodities. If a commercial bank is a member of the Federal Reserve System, i t must hold its reserves in cash at the Federal Reserve Bank, or in vault c a s h . 1 6 The t r a d i t i o n a l analys i s of reserve requirements i s to view them so le l y as determining the money supply. This neglects other e f f ec t s of the reserve requirement, notably in acting as a tax on f i n a n c i a l f irms and their deposit holders (Kane [1981] p. 357). The existence of required reserves on which no in terest return is received by the f irm reduces revenue. It may also reduce the in teres t rate payable to depos i tors , as pointed out in Laurent [1981]. The neglect of the effect of the reserve - 28 -requirement tax on the user costs of deposits to which they apply, and hence to the structure of bank technology, may have severe effects. The money supply depends on substitutability between financial commodities, their relative user costs, and reserve requirements, rather than on the last named alone. Higher taxes lead to the use of lower reservable instruments as substitutes for deposits in the monetary aggregate. The Monetary Control Act of 1980 specifies uniform reserve requirements against transactions accounts for a l l depository i n s t i -tutions (banks, savings banks, savings and loan associations, credit unions). The term "transactions account" is defined to include demand deposits, NOW accounts, telephone transfers, ATS and share drafts. The purpose of uniform reserve requirements is to give the Federal Reserve better control over the money supply by eliminating changes that occur because of shifts of reserves among different classes of depository institution. It also has the effect of eliminating the primary barrier to wider Federal Reserve membership: higher reserve requirements for member banks. Some authors have proposed that reserves be held against bank assets rather than against deposit l i a b i l i t i e s (Luckett [1976]). Thus a financial firm would hold different amounts of reserves against i t s government securities, or against various kinds of loans. The advantage claimed for this scheme is that by judiciously varying the reserves (taxes) against different types of assets, the Federal Reserve could encourage banks to extend credit to particular sectors of the economy. The user cost framework developed in Chapter 3 can handle this proposal in an analogous manner to reserves on deposits. - 2 9 -2.5.2 Interest Rate Ceilings 2.5.2.1 Deposit Interest Rate Ceilings Financial firms have typically faced price restrictions on both sides of their balance sheets. These include deposit rate ceilings, including the prohibition on paying interest on demand deposits, and loan rate ceilings. For the case of banks, the Banking Act of 1933 made i t i l l e g a l to pay a positive rate of interest on demand deposits. Though banks pay positive rates of interest on time deposits, these are regulated with respect to the maximum rates. The maximum rates are set by the Federal Reserve for member banks and by the Federal Deposit Insurance Corporation (FDIC) for insured non-member banks. The maximum rate structures set by the two agencies are identical. In practice, the Federal Reserve sets maximum rates and FDIC policies are in accordance with these. Estimates of implicit yields and service returns on deposits by Barro and Santomero [1972], Becker [1975], and Startz [1979] a l l suggest that legal interest rate restrictions are binding. The deposit rates are fixed below the equilibrium value that would be set in an unregulated market. The traditional reason given for deposit rate ceilings is that bank competition for deposits allegedly leads to a high rate of bank failures. According to this view, bank competition for deposits led individual banks in the 1920's and early 1930's to offer higher interest rates in order to maintain or increase individual share of the market. The banks were forced to rely on higher yielding riskier assets to - 30 -offset incurred deposit costs. This placed the banks in a vulnerable position. Any adverse economic developments, either national or local, would be sufficient to make these risky assets uncollectable by the bank. Deposit rate ceilings affect consumers, since they receive less for deposits than would otherwise be the case, but the accompanyinq increased monopoly power of financial institutions makes them allegedly more sound. The analysis of interest rate ceilinqs is typically not couched in a production framework. What is required is a model capable of generating demands and supplies for loans and various deposits, as functions of their user costs. The user costs depend on interest rates. If interest rate ceilings are changed, i t is possible to determine the effect on financial firm profits, loans and deposits. This is an objective of this research. 2.5.2.2. Loan Interest Rate Ceilings -Usury Laws As in the case of deposit rate ceilings, the analysis of the effect of usury laws requires the construction of a system where the response of loans and deposits can be calculated. Almost every state limits the interest rate that financial i n s t i -tutions can charge on certain types of loans (Minqo [1977]). Loan rate ceilings have been intended to protect consumers from paying high loan rates. Examples of state usury laws are interest rate ceilings on business and agricultural loans, and mortgage loans on real property or mobile homes. Such ceilings when binding may act to restrict the supply of loans td consumers. This implies that there develops a secondary - 31 -market with unregulated institutions with high risk, high interest rate portfolios. The traditional argument has been that deposit rate ceilings act in concert with loan rate ceilings to reduce loan costs to borrowers. This implies depositors are subsidizing borrowers. It is argued that regulation of deposit rate ceilings in the period from 1966 to 1979 was intended to confer benefits on interests associated with the t h r i f t industry, the housing industry, and construction unions. The underlying regulatory strategy attempted to cartelize competition for household savings deposits to assure a substantial flow of low-cost funds to deposit institutions (savings and loan associations and mutual savings banks) which were restrained by regulatory requirements and tax incentives to hold a high proportion of their assets in the form of mortgages. [Kane [1981], p. 363] Elsewhere Kane [1980] argues that the re-regulation allowed banks and t h r i f t institutions to discriminate effectively between interest-sensitive and interest-insensitive depositors. The marginal penalty that interest rate ceilings imposed f e l l rapidly with depositor wealth and sophistication. It is further argued that the burden of interest rate ceilings f a l l s particularly on the young, the old, and the poor whose adaptive efficiency to financial change is inherently low. The Depository Institutions Deregulation and Monetary Control Act of 1980 permits NOW accounts nationwide after a nine-month waiting period, provides for a six-year phase-out of interest ceilings on time and savings accounts, and overrides state imposed usury ceilings on mortgages, agricultural and business loans. It also eliminates any state restrictions on the rate or amount of interest that may be paid on 1 7 deposits, or accounts, at depository institutions. - 32 -2.5.3 Federal Deposit Insurance Corporation Premium Rates The remaining user cost item examined is the premium rate for deposit insurance. The FDIC insures, effective January 1, 1982, deposits of i t s member commercial commercial banks to a maximum of $100,000. The FDIC is financed by annual insurance premia paid by it s member banks. The premium rate is thus part of the user cost of deposits. By statute, the premium for each bank is set at 1/12 of 1 percent of its total, not only insured, deposits. Out of this premium income the FDIC pays i t s operating expenses, makes an assignment of funds to it s reserves, and returns the remainder to it s member banks on a pro rata basis. In 1977, a year representative of recent experience, this premium reimbursement reduced the net assessment to 1/27 of one percent. 1 8 It is argued by Buser, Chen and Kane [1978] that the FDIC deliberately sets its explicit insurance premium rate below an actuarially fair market rate to entice state-chartered non-member banks to submit themselves voluntarily to FDIC regulatory dominion. To control excess demand for insurance service, or expanded risk-taking, the FDIC is forced to develop an implicit price structure (Merton [1977]). FDIC entry regulation and periodic examination of individual banks balance sheet ratios function in tandem to maintain charter value and to control the moral hazard inherent in insurance. Buser, Chen, and Kane [1978] argue that the FDIC currently employs a pro-rated structure of implicit premia in the form of regulatory interference which varies - 33 -with a bank's portfolio risk. Scott and Mayer [1979] suggest that a risk-rated structure of premia is necessary to offset a structural incentive towards inordinate leverage. The implicit premia are not considered here, but user costs are developed which include as arguments the explicit deposit insurance premium rates. Changes in these rates affect relative prices, and hence the quantities of loans and deposits. It is thus possible to analyze quantitatively the effect of deposit insurance premia given a specified amount of coverage. 1 9 2.6 Concluding Remarks The cost function approach suffers from the major limitation that outputs are assumed to be exogenous. Although it is well known that financial firms produce heterogeneous outputs, there is l i t t l e consensus on what goods constitute their outputs and inputs. The outputs used by various researchers include total assets, earning assets, total deposits, demand deposits, the number of deposit and loan accounts, gross operating income and combinations of these measures. Although i t is not necessary for the application of a cost function, researchers in the banking area have typically assumed either that heterogeneous outputs can be aggregated, or a non-joint technology obtains. These assumptions imply restrictions on the variable cost function that can be tested. Another approach to estimating the financial firm technology involves the profit function. Estimation of this profit function with typically collinear prices as arguments may lead to imprecise parameter estimates. The appropriate specification is to include supply and - 34 -demand equations for outputs and inputs respectively. The instability from not including demand and supply functions appears to affect the results in Mullineaux [1978]. An advantage of assuming profit maximization is that it can accomodate imperfect competition. Most studies on the financial firm assume that the firm operates in a competitive environment. Three exceptions are Klein [1971], Mullineaux [1978] and Sealey [1980]. This environment is largely determined by bank regulation. Klein specifies in his theoretical model that private securities, loans, are in imperfectly elastic supply to the individual bank. Sealey argues that deposit markets are not perfectly competitive. Mullineaux also finds evidence against the assumption of price taking behavior. This 2 0 indicates that the hypothesis of competitive markets should be tested. Financial firms are subject to a myriad of regulations. In order to come to some tentative evaluation of the impact of such regulations, a theory of the financial firm is required. Most studies that have examined financial firm regulations, such as reserve requirements, deposit rate ceilings and deposit rate insurance have concentrated on institutional detail. There has been l i t t l e analysis on their effects on bank substitution, transformation and production. - 35 -NOTES AWhile here user costs for various loans and investments are constructed and the allocation of funds between various assets can be considered, in the empirical specification this is not performed and loans are aggregated. This is both to preserve degrees of freedom and to focus on monetary commodities such as demand and time deposits. 2See Klein, [1971], Hart and Oaffe [1974], Mason [1979] and Sealey [1980]. 3 In Chapter 8 a model of the financial firm is developed which tests for imperfect competition. 4See Schweiger and McGee [1961], Gramley [1962], Benston [1965], Bell and Murphy [1968] and Mullineaux [1978] for results on economies of scale. 5See Pesek [1970], Carleton and Bryan [1971], Towey [1974], Greenbaum, A l i and Merris [1976]. 6See Klein [1971], Towey [1974], Adar, Agmon and Orgler [1975], Sealey and Lindley [1977], and Mingo and Wolkowitz [1977]. 7With the exception of Klein [1971] and Sealey [1980]. Klein assumed that the bank has a preference ordering over P, the rate of return on equity, which can be represented by a u t i l i t y function linear in P. The bank's decision rule is to maximize expected u t i l i t y , or equivalently the rate of return on equity. Sealey [1980] also assumes that the financial intermediary maximizes expected u t i l i t y of profit, but has a general u t i l i t y function in profits, with f i r s t derivative positive. The second derivative depends upon risk preferences. 8See Alhadeff [1954], Horvitz [1963], Schweiger and McGee [1961], Gramley [1962], Grebler and Brigham [1963], Greenbaum [1967], Powers [1969], Brigham and Pettit [1970], and Schweitzer [1972]. 9See Alhadeff [1954], Schweiger and McGee [1961] and Horvitz [1963]. 1 0See Gramley [1962], Grebler and Brigham [1963], Brigham and Pettit [1970] and Murray and White [1981]. nAdar, Agmon and Orgler [1975, p. 239]. 1 2Adar, Agman and Orgler [1975^ p. 240]. 13 One point that should be mentioned is that the assumption of competitive price taking behavior is' not essential in order to apply duality theory: (See Diewert [1982] and Lau [1978]). - 36 -^Examples are in Bryan [1972], Haslem [1968] and Kaufman [1966]. Samuelson [1966] defines jointness in production and suggests a series of tests to determine whether a given neoclassical production function possesses joint production characteristics. The simplest test involved the use of psuedo single product production functions. Another test involves an adaption of Samuelson's approach utilizing a multiple output joint cost function. See Hall [1973, pp. 884-887] for a functional form for joint cost functions that contains separability and non-jointness as parametric restrictions. 15Rather than using share equations to deal with collinearity problems, Mullineaux [1978], enters the average wage of all employees and drops the average wage of officers, and average wage of employees but not their squares and cross products. He then uses OLS to estimate the hybrid translog profit function alone without demand, supply functions or share equations. 1 6Federal Reserve Bulletin [1981] p. A8. After implementation of the Monetary Control Act [1980] non-members may maintain reserves on a pass-through basis with certain approved institutions. Further, a larger group of deposit taking institutions must hold reserves at the Federal Reserve. 17See "Depository Institutions Deregulation and Monetary Control Act of 1980" by the Federal Reserve Bank of Boston. 1 8In 1980 the net annual premium was 1/30th of 1 percent of all deposits for deposit insurance. 19 The maximum level of deposits covered by insurance is another policy variable. Including this information in user costs requires a distribution of deposits into covered and uncovered portions. Typically data are not available that make this distinction. 2 0 See Chapter 8. - 37 -CHAPTER 3 USER COST DERIVATION FOR FINANCIAL FIRMS 3.1 User Costs for Assets and L i a b i l i t i e s The user cost of a financial good is defined as the net effective cost of holding one unit of services per time period. In the context of a consumer decision model Diewert [1974-], Donovan [1978] and Barnett [1978, 1981] have derived user cost formulae for interest bearing and non-interest bearing monetary assets. These models are based on the theory of intertemporal consumer demand of Irving Fisher [1930], and formulated in discrete time. This chapter derives complete user costs for balance sheet items held by financial institutions in the context of an intertemporal producer decision model. Time is decomposed into discrete periods, where the periods are chosen to be sufficiently short so that variations in prices within the period can be neglected. Interest rates, prices, and wages remain constant within the interior of each period, but can change discretely at the boundaries of periods. 1 A l l portfolio transactions are assumed to take place at the boundaries between intervals. Each financial firm holds an inventory consisting of stocks of various kinds of financial assets, l i a b i l i t i e s and capital during each discrete time period. The user cost is the bridge that links the balance sheet at two periods of time. We note that the cost of holding this inventory enters the cost function of a financial firm no less importantly than the cost of labor. 2 - 38 -Consider f i r s t the ith asset. An interpretation of the user cost for the services of one unit of the ith asset during period t is to view the banker as purchasing the asset at the beginning of period t, and then selling i t at the beginning of the following period, possibly to himself. Over one period, one dollar held in asset i produces services earning an interest rate r ^ . 3 The service charge rate per dollar of asset i is s^.1* This rate includes late loan payments and stand-by charges. Capital gains or losses are denoted by c^. 5 The default rate 6^  provides for loan losses per dollar of asset. This includes assets marked down or written off, interest payments forgiven, and collection costs. The financial firm purchases one unit of asset i during the current period, the cost of which is one dollar. If a l l returns arise at the beginning of the following period, the present value of the yield per dollar of the asset one period hence is (1 + r^ + c^ + s. - 6^)/ (1 + R). Here R is the common discount rate applied on a l l assets and l i a b i l i t i e s . The user cost of asset i is the difference between the current value of one dollar of the asset, and the present value of the return one period hence, or _ (1 + r. + c. + s. - 6.) u. = 1 - 1 ( 1 * R ) — i = 1,...,Nr (3.1) An alternative interpretation of the user cost is the net, effective cost per period of holding one unit of asset i , or - 39 -= (cost during period t) - (discounted net revenue in next period). (3.2) If the asset has a positive user cost in period t i t is an input, while i f i t has a negative user cost i t is an output during the period. This is a classifying rule enabling the inputs and outputs to be distin-guished. Financial assets need not permanently be inputs or outputs, given movements in the interest rate return received and the cost of various service charges. Now consider the jth type of deposit. Again assume that interest and service fees are paid at the beginning of the following period. Pesek [1970] has argued that service charges can be expressed in terms of a rate s. that an average dollar of deposit j yields to the J per time period from the deposit holder. In the case of deposits, rather than receiving interest, the financial firm pays interest. Let r.. be the interest payable by the financial firm. A remaining cost is associated with deposit insurance. Consider the case of member banks of the Federal Reserve System. A l l such banks must participate in the deposit insurance system which i s administered by the Federal Deposit Insurance Corporation (FDIC). Non-member state banks and mutual savings banks, at their option, may obtain insurance i f approved by the FDIC. To cover the cost of insurance, each bank pays the FDIC an annual premium equal to a fixed percentage of it s total deposits. From this premium income the corporation f i r s t pays its operating expenses. Two-fifths of the - 40 -r e m a i n d e r i s then added t o the i n s u r a n c e f u n d . The b a l a n c e o f the premium i s c r e d i t e d pro r a t a t o t h e i n s u r e d banks, who a p p l y t h i s c r e d i t t o w a r d payment o f premium payments due i n the f o l l o w i n g y e a r . L e t the premium r a t e per d o l l a r of d e p o s i t be b j . Assume t h a t the premium i s p a i d at the b e g i n n i n g of the f o l l o w i n g p e r i o d . As an example, t h e p e r i o d can be s e l e c t e d t o be one y e a r . D e p o s i t s a r e u s u a l l y s u b j e c t t o r e s e r v e r e q u i r e m e n t s , so t h e f i n a n c i a l f i r m does not g a i n c o n t r o l o v e r t h e t o t a l d e p o s i t b a l a n c e . 6 L e t k j be the r e s e r v e r e q u i r e m e n t r a t e f o r the j t h type of d e p o s i t . C o n s i d e r t h e c a s e o f member banks o f t h e F e d e r a l R e s e r v e System. F o r each, d o l l a r of the j t h t y p e o f d e p o s i t r e c e i v e d by the f i n a n c i a l f i r m , (1-kj) per d o l l a r i s a v a i l a b l e f o r usage. The r e m a i n i n g k j i s t r a n s f e r r e d i n cash t o t h e F e d e r a l R e s e r v e Bank, or i s h e l d i n v a u l t c a s h . 8 The u s e r c o s t o f d e p o s i t j i s based on t h e net amount a v a i l a b l e per d o l l a r f o r usage by the f i n a n c i a l f i r m d u r i n q the c u r r e n t p e r i o d , o r ( 1 - k j ) . A d e p o s i t o r on w i t h d r a w a l r e c e i v e s one d o l l a r , c o m p r i s i n g (1-kj) o f c l a i m on t h e f i n a n c i a l f i r m and k j from r e q u i r e d r e s e r v e s . At the b e g i n n i n g o f t h e f o l l o w i n g p e r i o d , t h e f i r m pays i n t e r e s t and i n s u r a n c e premiums and r e c e i v e s s e r v i c e charge f e e s . T h i s net c o s t i s d i s c o u n t e d t o the c u r r e n t p e r i o d . I n p r e s e n t v a l u e terms i t i s (1 - k j + r j - S J + bj)/(1+R). The u s e r c o s t i s t h e net e f f e c t i v e c o s t of funds per p e r i o d o f h o l d i n g one u n i t of d e p o s i t . So on t h e net d e p o s i t f o r the bank u. = - ( n e t amount r e c e i v e d d u r i n g c u r r e n t p e r i o d ) + ( d i s c o u n t e d net c o s t i n next p e r i o d ) . (3.3) - 41 -or, _ (1-k. + r. - s. + b.) i i - _ (1_k ) + J J J J U j " U V 1 + R - (1+R)(1-k.) + (1-k. + r. - s. + b.) J J J J J 1 + R (1+r. + b. + Rk. - s.) = -1 + 1 1\ R J 1 j=1,...,N2 (3.4) where there are N2 types of deposit and R is the discount rate. The term Rkj has the interpretation of being the cost imposed by the reserve requirement. This is equivalent to the imposition of a tax by the Federal Reserve for one period, for the bank is unable to use the reserve requirement in its loan portfolio. If the deposit has a positive user cost in a period i t is an input, and i f i t has a negative user cost i t is an output. With movements in interest rates and other determinants, a deposit can be either an input or output for the financial firm. Traditionally, there have been two justifications for considering deposit services as outputs of the financial f i r m . F i r s t , since the services which are performed for deposit customers benefit the latter, i t has been argued (Benston [1965], Bell and Murphy [1968], Longbrake [1974]) that possibly these services constitute outputs. Deposit customers derive benefits from the services they receive, and the financial firm produces these services. This does not imply that deposit services are necessarily outputs. One must examine the user - 42 -cost to determine whether particular kinds of deposits are net outputs or inputs. Second, i t has been argued for banks that demand deposits are the most important aspect of bank activity, when one is concerned with the macroeconomic effects of the banking system (Pesek [1970], Towey [1974]). This does not necessarily justify making deposits the microeconomic output of the financial firm or industry. 9 Deposits in financial firms have also been considered as inputs in the production of earning asset output, rather than as outputs. Examples are in Sealey and Lindley [1977] and Mullineaux [1978]. The above derivation for the user cost is applicable not only to deposits, but to any kind of l i a b i l i t y held by the financial firm. Examples are bond obligations or borrowed funds. Usually these l i a b i l i t i e s are not subject to reserve requirements or insurance premia so those terms in (3.4) are set equal to zero. 3.2 Implementation Problems 3.2.1 Expectations of Future Prices In the construction of user costs, i t is necessary to estimate expectations of the producer about asset and capital prices in the next period, given the capital gains term in (3.1). These expected prices are generally unobservable, and thus analysts differ widely on how to estimate them. One approach is to assume that producers have perfect anticipations (Christensen and 3orgenson [1969, 1970]). Another approach is to assume static expectations. Producers expect current - 43 -prices to prevail in the following period (Woodland [1972, 1975]). 1 0 A third alternative is to use a forecasting model to predict asset prices (Epstein [1977], Donovan [1978]). Although the f i r s t two methods for forming expected prices are not generally correct, the third alternative requires extensive econometric modelling. 3.2.2 The Discount Rate The user cost formulae in the previous section both involve a discount rate. Usually i t is argued that i f the firm is a net borrower, then R should be the marginal cost of borrowing an additional dollar for one period, while i f the firm is a net lender, R should be the one-period interest rate i t receives on its last loan (Diewert [1980]). In practice, researchers have taken R to be either an internal rate of return (Oorgenson and Griliches [1967], Christensen and Oorgenson [1969, 1970]) or an exogenous bond rate that may or may not apply to the firm under consideration (Diewert [1980] p. 477). Neither of these last two alternatives appears completely satisfactory from an a priori point of view. 3.2.3 Depreciation Rates User cost formulae for the services of one unit of capital during one period usually involve a depreciation rate. This depreciation rate is related to the finite length of l i f e of the capital stock. It is a function of physical deterioration, usage and vintage. 1 1 It is assumed that financial assets and deposits do not depreciate or deteriorate. Donovan [1978] considers "depreciation" of money due to a positive expected inflation rate. He concludes that the - 44 -user cost of money is unaffected by that kind of depreciation. Anticipated inflation should be taken into account by the (anticipated) capital gains term in the user cost formulae. Since the anticipated capital gains term accounts for nominal price changes in each financial and physical asset the relevant interest rates in the user cost formulae are nominal rates. - 45 -NOTES We also assume that the process of adjustment is essentialy in-stantaneous so that we can ignore stock adjustment problems. See Samuelson [1947]. These assumptions follow Hicks [1946] p. 122, pp. 335-337. 2Pesek [1970] and Sealey and Lindley [1977] recognize that f i -nancial institutions can maintain a stock of deposits or earning assets only by constantly incurring a flow of costs. They reason that this implies that balance sheet items (assets and l i a b i l i t i e s ) could be viewed in terms of flows rather than stocks. This would be analogous to treating capital as a flow because i t has a positive user cost. 3Barnett [1978, 1980] assumed interest was paid at the beginning of the following period when deriving the user cost of interest-bearing money. "See Pesek [1970] p. 371. 5Capital gains are due to discrete jumps in interest rates at the boundaries of intervals. Capital gains would be negative i f inter-est rates rose, positive i f interest rates f e l l . 6Nearly a l l financial firms must keep some minimum portion of assets in cash or otherwise liquid form. These reserve requirements are generally based upon the types of deposit l i a b i l i t i e s the financial firm has. If a commercial bank is a member of the Federal Reserve System, i t must hold its reserves in cash at the Federal Reserve Bank, or in vault cash. 7 Many customers and borrowers are subject to minimum and compen-satory balance requirements, respectively. In their effects on the demanders these are indistinguishable from currency reserve requirements imposed on bankers. They would enter the user cost of money in the same ' way for the customer. Q The user cost formulation below can accomodate the case where the financial firm is allowed to hold reserves in an asset which pays interest. Q For example, labor economists are interested in the determinants of the equilibrium quantity of labor services hired by firms and exchanged in labor markets. However, labor economists do not consider labor to be the output of the firms which they study. (See Sealey and Lindley [1977, p. 1261]). 1 0With the recent upsurge of world-wide inflation and interest rates, i t has become more d i f f i c u l t to ignore capital gains and losses. - 46 -^ C a p i t a l stocks constructed on the basis of d i f f e r e n t deprec ia t ion assumptions can d i f f e r cons iderab ly . See examples tabulated in T ice [1967] and Creamer [1972]. 1 2 S e e Diewert [1974b] p. 510. 1 3 The caveat i s that i f the discount r i s e s due to i n f l a t i o n a r y expectat ions, then the user cost of monetary serv ices w i l l r i s e . - 47 -CHAPTER 4  A MODEL OF THE FINANCIAL FIRM fr .1 Introduction The objective remains the modelling of the optimal behavior of financial institutions, with explicit attention given to regulatory constraints on operations. We develop a model of producer behavior where labor demands, physical capital demands and asset and l i a b i l i t y holding decisions are simultaneously determined. The specification differs from previous neoclassical models (Benston [1965], Bell and Murphy [1968], Klein [1971], Towey [1974], Adar, Agmon and Orgler [1975], Mingo and Wolkowitz [1977] and Mullineaux [1978]) in that i t is based on a theory of intertemporal production introduced by Hicks [1946] and utilizes the user costs derived in Chapter 3 above. Our model is unique in that i t considers regulatory controls through their effect on relative user costs. We employ the duality between the production possibility set and profit function to derive comparative statics yield-ing, testable predictions, and to obtain the functional forms for the estimating equations. fr.2 An Intertemporal Production Model of the  Individual Financial Firm Intertemporal or dynamic optimization problems are distinguish-able from static optimization models by the essential role that time plays in dynamic models. In a dynamic problem the dates that parameters adopt certain values, and the dates that certain choices are made are part of the relevant data for the problem.1 - 48 -Previous researchers have considered static optimization problems. Bell and Murphy [1968] derive a static cost minimization model, and Mullineaux [1978] a static profit maximization model. Time plays an essential role in the financial firm's production process, and an intertemporal model is needed, particularly for analyzing asset and l i a b i l i t y holding decisions. Each financial firm holds an inventory consisting of stocks of various financial assets, l i a b i l i t i e s and capital. There are revenues and costs associated with holding this inventory over time. We follow Hicks [1946] by formulating the model in discrete time. Producers make a production plan at the beginning of period t that extends to period t+1. The plan consists of a l i s t of input demands and output supplies for the period. Since the model is in discrete time, a structure of assumptions is required regarding the timing of interest rate, wage rate and price changes, payments and of portfolio transactions. These are: (1) Interest rates, prices and wages remain constant within the interior of each period, but can change discretely at the boundaries of periods. (2) A l l portfolio transactions are assumed to take place at the boundaries between intervals. (3) The producer is assumed to s e l l a l l financial assets and l i a b i l i t i e s at the end of the period (possibly to himself) and to buy new issues, so that the market value equals the face value within the interior of each period and the new issue interest rate equals the seasoned rate. 5 - 49 -(4) Interest and service fees are paid at the beginning of the following period. 6 (5) Insurance premiums are paid at the beginning of the follow-ing period. The model is short-run in that we consider only two time periods. 7 With active secondary markets in each period, the financial firm can review its past decisions in light of the current market situation and alter its input demands and output supplies accordingly. Although we shall not fix the time interval in the theoretical model, it a could be set as short as one day. The financial firm is assumed to choose the input-output combination which maximizes profit during the production period. The assumption of profit maximizing behavior under-li e s the models of Pesek [1970], Towey [1974], Adar, Agmon and Orgler [1975], Greenbaum, A l i , and Merris [1977], Sealey and Lindley [1977], Mingo and Wolkowitz [1977] and Mullineaux [1978].9 Assume that producers take prices, wage rates, and user costs as given, and optimize with respect to quantity variables they cont r o l . 1 0 The producer's profit maximization model for period t may be written as follows, with the dot denoting an inner product ir = max - {u*y - V»z + w^ x : Cx/y,z)eS x'/y/z, _> 0, w » 0, v~C 0} "x,7,z~ (4.1) with T J an N1 + N2 dimensional vector of user costs for the financial firm's balance sheet holdings during period t. The f i r s t Ni - 50 -user costs will be for the types of assets held by the firm. The last N2 user costs will be for the N2 types of l i a b i l i t i e s held by the firm. User costs are positive for in-puts and negative for outputs. w a non-negative N3 dimensional vector of period t (purchase) prices for variable inputs, exemplified by wage rates. "v a non-positive dimensional vector of period t prices for outputs which are not balance sheet holdings, such as safe-deposit rentals. y a non-negative + N2 dimensional vector representing balance sheet holdings (inputs and outputs) where there is an Hi dimensional vector representing the assets held by the financial firm and an N 2 dimensional vector representing the l i a b i l i t i e s held by the firm during period t. x a non-negative N3 dimensional vector of period t inputs such as labor. z a non-negative Ni+ dimensional vector of period t outputs which are not balance sheet holdings such as safe-deposit boxes. S the financial firm production possibility set, which is assumed to be a closed, non-empty, and convex. The above formulation does not follow the convention of Debreu [1959] which indexes outputs with a positive number, inputs with a nega-tive number, and measures a l l prices p o s i t i v e l y . 1 1 We can rewrite ( 4 . 1 ) above using the convention of Debreu as follows, - 51 -- max {u«y +• v z + w x : (x,y,z)e S, z >^ 0, x <_ 0, > • • • ), y. > 0 i f u. < 0 and ' J l l ^ < 0 i f u. > 0, v » 0, w » 0, u » 0} = T T ( U , V , W ) (4.2) with u w v y a non-negative Nj_ + N2 dimensional vector of transformed user costs for the f i n a n c i a l f irms balance sheet holdings during period t . a non-negative N3 dimensional vector of period t (purchase) p r i ce s for var iab le inputs (e.g. wage rates) (w = w). a non-negative dimensional vector of period t pr ices for outputs which are not balance sheet holdinqs (v = v ) . an Ni + N2 dimensional vector represent ing balance sheet ho ld-ings . Outputs are measured p o s i t i v e l y (y > 0 i f u « 0). Inputs are measured negatively (y <^  0 i f u >> 0) . Once so determined, the qoods are renumbered so that the f i r s t Hi components of the vector y represent assets held by the f i n a n c i a l f i rm, while the las t N2 components represent the l i a b i l i t i e s held by the firm during period t . a non-pos i t ive N3 dimensional vector of period t inputs (x = - x ) . - 52 -z a non-negative N 4 dimensional vector of period t outputs which are not balance sheet holdings such as safe-depos i t boxes (z = 7). S the f i n a n c i a l firm production p o s s i b i l i t i e s set, which i s assumed to be convex, c losed, non-empty, and contains the 0 vector . Equation (4.2) i s the producer 's p r o f i t f unc t i on , I T . Maximum p r o f i t s are a funct ion of the pr ice vector (u,v,w) which we denote by n(u,v,w). Given the production p o s s i b i l i t i e s set S, the p r o f i t funct ion def ined by (4.2) w i l l s a t i s f y the fo l lowing r e g u l a r i t y cond i t ions : ( i ) ir i s non-negative i f (u,v,w) » 0 N + N 2 + N 3 + r V t h e N1 + N 2 + dimensional 0 vector, ( i i ) ir i s non-decreasing in output p r i c e s , ( i i ) IT i s non-decreasing in output p r i ce s , ( i i i ) TT i s non- increas ing in input p r i ce s , ( iv) TT i s a (proper) convex funct ion and (v) TT i s homogen-12 eous of degree one in input and output p r i c e s . We are now in a pos i t ion to state a resu l t which w i l l enable us to der ive funct iona l forms for systems of input demand equations, and output supply equations consistent with p r o f i t maximization. Suppose we are given a funct iona l form for a p r o f i t funct ion T T ( U , V , W ) which s a t i s -f i e s the above f i v e condit ions and i s , in add i t i on , d i f f e r e n t i a b l e * * * with respect to output and input pr ices at the point (u,v,w ) » (0 ,0 ,0 ) . Then we have, 9 T r ( u % ! w * ) = y . ( u %V) i = 1 , . . . , N 1 + N 2 - 53 -# * * (-±^= zAu%W) j = 1,...,N J J (4.3) and * * * ( u , v , w ) , * * *\ = x k ( u , v , w ) k = 1,...,N where y^(u,v,w ) is the profit maximizing amount of output i (of input i * * * *• * * i f y.(u,v,w ) < 0), z.(u,v,w ) is the profit maximizing amount of output # * * j , and xk(u,v,w ) is the profit maximizing amount of input k given posi-* * * tive prices (u,v,w ). This result is due to Hotelling [1932, p. 594]. Profit maximizing labor and other input demands, asset and l i a b i l i t y holding decisions, and output supplies are simultaneously determined in our model of the financial firm given exogenous prices and user costs. Hotelling's lemma is useful from an econometric point of view since i t permits the derivation of functional forms for demand and supply functions consistent with profit maximization simply by choosing a functional form for and differentiating i t with respect to input and output prices, including user costs. Also, this lemma and duality theory permit the derivation of comparative 1static results. Using the duality between the production possibilities set and the profit function, we know the profit function is a proper convex function. Let p = (p 1 ,.. - ,PN) = (u 1,...,u N + N , v 1,...,v N , w^...^ ) - 54 -denote the vector of pos i t i ve transformed user costs and prices for outputs and inputs, where N = Ni + N 2 + N 3 + Mi+. Then u(u,v,w) = ir (p ) . Denote the N by N matrix of second order p a r t i a l de r i va t i ve s with respect to p of the funct ion TT by [ 3 2 TT( p) / 9p^3p,. ], i , j = 1 , . . . , N . 1 5 If TT i s a twice continuously d i f f e r e n t i a b l e funct ion over the convex set S*, then TT i s a convex funct ion over S i f and only i f the Hessian matrix of ir i s pos i t i ve semi -def in i te for a l l p £ S * . That i s i f [3 2ir (p) /3p^3pj ] i s a pos i t i ve semi -de f in i te m a t r i x 1 6 (4.4) t h i s impl ies , [8 2Tr (p ) /8p.8p i ] >_ 0 for i = 1 , . . . , N . (4.5) A l t e r n a t i v e l y , s ince p = (u,v,w) 3 2 ir(u,v,w)/3u.3u. _> 0 for i = 1,.. . ,N 1 + N 2 3 2ir(u,v,w)/3w.3w. >_ 0 for j = 1 , . . . ,N 3 (4.6) 3 J 3 2 T T ( U , V , W ) / 3 V 3v > 0 for k = 1,'...^^ . Using (4.3) which we obtained by applying H o t e l l i n q ' s lemma and the convexity condit ions (4.6) we have the fol lowing comparative s t a t i c r e s u l t s , 3y.(u,v,w ) y. _> 0 ( i . e . i f u. < 0) i = 1 , . . . ,N : +N2 1 — > 0 i f 1 1 (4.7) 3u i yL < 0 ( i . e . i f u. > Q ) * * * 3z.(u,v,w ) — — 5 > 0 where z . i s an output ( i . e . z . > 0) (4.8) 3v. - j J -j = 1,...,N3 - 55 -3 w. k 2^  0 where x, i s an input ( i . e . x. < 0) (4.9) k = 1 Equation (4.7) summarizes the response of the i th balance sheet item with respect to a change in i t s own user cost . If balance sheet item i i s an output, or has a negative user cost , and i t s transformed user cost increases ( i . e . the untransformed user cost becomes more negat ive) , holdings of balance sheet item i do not decrease, and the supply of the i th output does not d e c l i n e . If the balance sheet item has a po s i t i ve user cost , and hence i s an input, and i t s user cost increases , holdings of the balance sheet item do not increase, or the demand for the input does not r i s e . Equation (4.8) impl ies that i f the pr i ce of output j increases then the supply of output j by the f i n a n c i a l firm does not decrease. S i m i l a r l y , (4.9) impl ies that i f the pr ice of input k increases, the demand for that input by the f i rm does not increase. We now turn our at tent ion to cross e f f e c t s , or response of output supply or input demand when the pr i ce of another output or input changes. We begin by def in ing the e l a s t i c i t y of transformation between commodities m and n as Tf(p*)3 2Tr(p*)/3p 3p n [ 3 T T ( p * ) / 3 p m ] [ 3 T T ( p * ) / 3 p n ] (4.10) - 56 -* * * Reca l l p* = (u,v,w ). If the mth p r i c e corresponds to u. then n is a 1 mn normalization of 3y.(p*)/3p m, the chanqe in the supply of the i t h output i f y . >_ 0 or chanqe in demand for the i th input i f y . < 0 with res-pect to a chanqe in the nth p r i c e or user c o s t . If the nth p r i c e corresponds to v. then n i s a normalization of 3z.(p*)/3p or the J mn J n change in the supply of output j with respect to a chanqe i n the nth p r i c e . If the mth pr i ce corresponds to w, then n i s a normaliza-k mn t ion of 3 x k ( p * ) / 3 p n , the change in demand for the kth input with respect to a change in the nth p r i c e . The normal izat ions have been chosen so that n i s invar iant to scale changes in un i t s and so that n = n mn •—•> mn nm * * * Assuming T T ( U , V , W ) = Tr(p*) s a t i s f i e s the f i ve regu la r i t y cond i -t ions above, T T ( p * ) > o, the f i r s t order p a r t i a l de r i va t i ve s of rr evalua-ted at p* are non-zero, and that * is twice continuously d i f f e r e n t i a b l e at p*: ( i ) the symmetric e l a s t i c i t y of transformation matrix [n 1 L mnJ pos i t i ve semi -def in i te of rank at most e q u a l to N - l ; i n , i s mn • p a r t i c u l a r n > 0 for every m, mm — J ' N ( i i ) for every m, T n 9 = 0 - mn n n=1 (4.11) where the nth commodity r a t i o of r e l a t i v e expenditure to var i ab le p r o f i t 9 n i s defined as - 57 -M p * [ a T r(p*)/9p ] / i r ( p * ) for n = 1 , . . . , N . Also T 9 =1, and 9 N 0 if n n n n n= I commodity n is an output but 8 < 0 i f commoditv n is an input. 1 7 The financial firm has many inputs and outputs, so the compara-tive statics for cross-effects are indeterminate. 1 8 The above theorem, however, does provide an addinq up property for the cross-effects. If we consider input k, its commodity share of value added 6^  is negative. We know from (4.11(1)) that n k ) < _> 0, so nk|<ek_< 0. Now using (4.11(ii)) we obtain N ^, k^m^ m + ^kk^k ~ ^  m= l m*k which implies N ^ nkmem= " V k ^ 0 (4.12) m*1 Similarly for output j , N I n 4 m e m = -n..e. < o. rn*1 Although the comparative statics for cross effects are indeter-minate, we can test to determine whether the above adding up properties and symmetry conditions are satisfied in an econometric estimation of - 58 -the model. For f u r t h e r a na l y s i s of cross e f f e c t s we have to examine e m p i r i c a l po int e s t imates . Above we developed a model of f i n a n c i a l f i rm behavior that s imu l taneous ly determines input demands, output s u p p l i e s , and asset and l i a b i l i t y ho ld ing d e c i s i o n s . Equation (4.7) summarized the response of an i n d i v i d u a l balance sheet item with respect to a change in i t s own user co s t . Now we cons ider how changes in the components of the user cost of a p a r t i c u l a r balance sheet item a f f e c t the f i n a n c i a l f i r m ' s d e c i s i o n to hold that i tem. We are e s p e c i a l l y i n t e r e s t e d in adjustments i n response to a change i n regu la to ry requi rements, such as reserve requirements and FDIC insurance premium r a t e s . In Chapter 3 we der ived user cost s fo r balance sheet items held by f i n a n c i a l f i rms i n the context of an i n t e r t empo ra l producer d e c i s i o n model. The user cost of ho ld ing asset i dur ing pe r i od t was found to be a f u n c t i o n of r^, the i n t e r e s t payable to the f i n a n c i a l i n s t i t u t i o n on one d o l l a r , c^ , the expected c a p i t a l ga ins or l o s se s dur ing pe r iod t on asset i , s^, the s e r v i ce charge ra te that an average d o l l a r of asset i y i e l d s to the f i n a n c i a l f i r m , 6., the p ropo r t i on of loans expected to d e f a u l t dur ing per iod t , and R the d iscount ra te used by the f i r m . R e c a l l ( 3 . 1 ) , {1 + r. + c, + s. +• 6.} — . i i l i u i = 1 ( T T D = u . ( r . , c . , s , 6., R ) . l l l i l We can c a l c u l a t e the f o l l o w i n g p a r t i a l d e r i v a t i v e s w i th i n d i c a t e d s i gn s , 59 -9u i/3r. = 3u./3c. = 3u./3s. = -9u./36. = -1/(1 + R) < 0 3u./3R = (1 + R)"^[1 + r t + c . + s. - 6.] (^.13) = (1 + R)"1[1 - u.l with 3Uj./3R > 0 unless u^ > 1, implying a period user cost exceeding 100 per cent. The transformed user cost of asset i , u^, equals u. i f u. is positive, and equals -u^ i f is negative, or u i u. > 0 u i = i _ i f J i = 1,...,Ni. (4 .14 ) -u^ u^ < 0 Using this definition and (4.13) we obtain the following results, yL > 0 < u. > 0 y. < 0 3 u 1 / 3 r 1 5 0 i f {_ i.e. i f { 1 U j < 0 v " < u. > 0 3u./3c. > 0 i f {_ 1 u. < 0 l i = 1, ,Nx < u. > 0 3 u , / 3 s . > 0 i f u < 0 u > 0 a i ^ / a f i j i o i f {_ U j < o . Similarly, the user cost of holding deposit j during period t was found - 60 -to be a functi o n of k., the reserve r a t i o on the j t h tvpe of d e p o s i t s , r ^ , the i n t e r e s t pavabLe by the f i n a n c i a l i n s t i t u t i o n on one d o l l a r of de p o s i t s , b , the insurance premium rate per d o l l a r of d e p o s i t s , s., the s e r v i c e charge rate that an average d o l l a r of deposit j >ields to the f i n a n c i a l i n s t i t u t i o n during period t, and R, the discount rate used bs the f i r m . R e c a l l ( 3 . 3 ) (1 t r. t b. t Rk. - s . ) U j = " 1 + 7 (1 I R) J 1 1=1, . . . ,N 2 = u . ( r . , b., s., k., R). We can ca l cu l a te the fo l lowinq p a r t i a l der i va t i ves with indicated siqns usinq (3.3) , 8lTj/3k. = R/(1 + R) 3u /3r . = 3u./3b. = -3u./3s = 1/(1 + R) > 0 (4.15) 3u./3R = (1 + R)~2(1 + r. + b. f Rk. - s.) J •} <T J «7 and 3u./3R < 0 unless s. > I r r . + b. + Rk., an extremelv im p l a u s i b l e J J J J ,T occurrence. The user cost u. i s c l e a r l y increasinq in reserve requirements k. and insurance premium leve l s by both of which may be mandated. The i n te res t rate payable r^ is a lso subject to regu la t i on , such as - 61 -cei.Li.ng r e q u i r e m e n t s on r a t e s p a i d and p r o h i b i t i o n o f i n t e r e s t payment on c e r t a i n d e p o s i t s . N o t e t h a t d e r e g u l a t i o n o f r . , w i t h u . r e p r e s e n t i n g a p e r f e c t l y e l a s t i c s u p p l y , may r a i s e t h e u s e r c o s t o f t h e g i v e n d e p o s i t , and r e d u c e t h e demand by a g i v e n b a nk. However, i f t h e i n d u s t r y f a c e s an upward s l o p i n g s u p p l y , t o t a l d e p o s i t s o f j i n t h e f i n a n c i a l s y s t e m i n c r e a s e , e v e n i f t h e s h a r e o f e a c h f i r m d e c r e a s e s , so d e r e g u l a t i o n o f i n t e r e s t r a t e c e i l i n g s i s f a v o r a b l e f o r e x p a n s i o n o f t h e f i n a n c i a l s e c t o r as a w h o l e , i f n o t f o r e a c h f i r m . F u r t h e r , t h e u s e r c o s t , by way o f c r o s s - s u b s t i t u t i o n e f f e c t s , e n t e r s t h e n e t s u p p l i e s o f o u t p u t s and o t h e r i n p u t s , and d e r e g u l a t i o n e n g e n d e r s a more e f f i c i e n t a l l o c a t i o n o f f u n d s . The t r a n s f o r m e d u s e r c o s t o f d e p o s i t j , u . , c a n be d e f i n e d , u u . > 0 uf = { J i f _J j = 1,...,N2 ( 4 . 1 6 ) J - u . u . < 0 j J U s i n g t h i s d e f i n i t i o n and ( 4 . 1 4 ) and ( 4 . 1 5 ) , 3 u . / 3 k , I 0 i f u . I 0 j j J 3 u . / 3 r ^ 0 if uJ 0 J J J 3 u . / 3 b . I Ifu.U ( ^ 1 7 ) 3Uj/3s^ 5 i f u.Z 0 - 62 -3Uj/3FL i i f I K < 0 and I + r^ * * Rk^ > , j=1,...,N2. Using the notation u as a N L f N 2 vector of normalized user costs, we can rewrite the profit function ir(u,v,w). From (4.3) which we obtained by applying Hotelling's lemma, the convexity condition (4.6) and the signs of the above partial derivatives (4.14) and (4.17), we have the following comparative static results. If the ith asset is an input and has a positive user cost, 3y.* 3y.* 3u. 3 2* 3u. l 3r. 3u. 3r. 3r. 3y.* J l 3u. l 3u. l 3c. L 3u. l 3c. l 3u. 2 l 3c. l 3y.* 3u. l 32* 3u. l 3 S i ' 3 u i 3u.2 l 3s. l 3y.* 3y.* 3u^ 3 2» 3u^ 3 6 i _ 3 U i 9 5 i 3 u.2 l 3 2 TT 9 U > > 0, — < 0 (4.18) 3u. 3 r i a 2* 9 u -<0 since ^ - > 0 , — ± <0 (4.19) 3 u / 3c. i l 3 2* 3 u -> 0, — < 0 (4.20) 3u 2 3s. l 3 2 TT 9 U ' >0 s i n c e — ^ - > 0 , — > 0.(4.21) 3 u / 36. ~ i l If, however, the ith asset is an output and has a neqative user cost then, >0 since 7 2.0, — 1 > 0 (4.181) 3u. 2 9 r . 3y.* 32w 3Uj 3r. 3u^ 2 3r. *y* 3 2* 3 u i SCj S u j 2 SCj a 2 i r 9 u s >. 0 since ±-!L. > 0, — i >_ 0 ( 4 19 I ) 3u. 3 C l - 63 -3 2TT 3 u i 92 3u. L _ ^ U since • > o — - < 0 /, ,,i 3u.2 35. - 3 u . 2 ~ ' 36 ~ ( ^ 2 1 1 ! 1 If the jth deposit is an input and has a positive user cost, 3y * 3u. 2 3u. .2, 3u. _ J _ ._J. = UL_ — 1 >_ o since 0, - J 3u. 3k. 3u.2 3k. 3u.2 3k. J J J J T T - —*- >_[) since ^-^^O, — i >_ 0 (4.22) 2 - } 3k. J J 3y.* 3u, 2 3u. 2_ 3u. = _ J _ _ 1 = i_L_ __1 > o since UL_ > 0 , - J - >0 (4.23) 3u. 3r. 3u.2 3r. 3u.2 3r. J J J J J J 3y* 3u. .2 3u. 2 3u. = — J - — i = - — - — J - >_ 0 since -2-1- > 0, — i >0 (4.24) 3u. 3b. 3u.2 3b. 3u.2 3b. J J J J J J 3y * 3u. 3u. g 2 3u. = — — i = — i £ 0 since > 0, — i £ 0. (4.25) 3u, 3s. 3u 2 3s. 3u 2 3s j J j J j J If, however, the jth deposit is an output and has a negative user then, 3 2TT 3 U 3 u 2 9 k > since — > 0, - J - , o J 3 u / 3k. J J I!! !!1 3 2TT 3 U -3u 2 9 r . 1 0 since — > 0, - J . < 0 (4.231) J j 3^ 4 3r 3 2TT 3 U i g2 3 u 3 | 2 " ^ ° since - J l - > 0, _ 1 < 0 (4.241) 3 u j 3 r i 3u.2 3r x ~ - 6k -3y.* 3 2TT 3u. a 2 3u. — — = — >0 s i n c e — _>0, — _> 0. (4.251) 3r. 3u2 3r. 3u.2 3r. The response of asset i with respect to a change in its own rate of interest is summarized by (4.18) and (4.18 1). If the rate of interest payable to the financial institution increases on asset i , an input, the demand for that input does not decrease. From (4.18 1), i f the rate of interest payable to the financial institution increases on asset i , an output, then the supply of asset i is non-decreasing. Hence, we conclude that i f the rate of interest payable to the financial institution increases on asset i , then holdings of asset i do not 1 9 decrease. In (4.19) and (4.191) are the responses of asset i with respect to a change in the expected capital gains on asset i , c^. If asset i is an input, and i t s expected capital gains increase, or expected capital losses decrease, the demand for that input i s non-decreasing. From (4.19), i f asset i is an output and i t s expected capital gains increase, or expected capital losses decrease, then the supply of asset i is non-decreasing. Consequently, i f expected capital gains increase, or expected capital losses decrease, on asset i , then holdings of asset i do not decrease. The response of asset i with respect to a change in the service charge rate are in (4.20) and (4.201) for an average dollar of asset i yields S j to the financial firm. If s^ increases, then holdings of asset i are non-decreasing. In (4.21) and (4.21") are summarized the response of asset i with respect to a change i n the expected d e f a u l t rate 6.. If the expected default rate on asset i increases, and asset i i s an input, then the demand for that input i s non-increasing. If asset i i s an output, (4.21l) implies that i f the expected default rate 6 increases, then the supply of asset i is non-increasinq. Hence, i f the expected rate of default on asset i increases, then holdinqs of asset i do not increase. We now turn to the l i a b i l i t y side of the financial firm balance sheet. In (4.22) and (4.221) are the responses of the j t h type of deposit l i a b i l i t y to a chanqe in the required reserve ratio k.. The required reserve ratio is under direct control of the requlatory body governing the financial institution. The requlatory body for national commercial banks in the United States is the Federal Reserve Board. 2 0 If the reserve ratio on the jth type of deposit is increased, and these deposits are inputs, then the demand for that input does not increase. If deposit j is an output, and the reserve ratio k. increases, then the supply of deposit j does not increase. Hence, i f the required reserve ratio on the jth type of deposit increases, then holdinqs of the jth type of deposit do not increase, and may f a l l . This i s an important result because reserve ratios are used in controlling the aqqreqate money supply which is defined in terms of currency and bank l i a b i l i t i e s 21 such as demand deposits and time deposits. In (4.23) and (4.231) are the responses of the jth type of deposit to a change in the interest rate payable per dollar to the deposit or l i a b i l i t y holder. If the interest rate payable per dollar of - 66 -the jth type of deposit increases, then holdinqs of those deposits are non-increasing. This r e s u l t i s important in anal y z i n g the e f f e c t of the Depository Institutions Deregulation Act of 1980 on i n d i v i d u a l f i n a n c i a l 22 mst ltutions. In (4.24) and (4.24 1) are contained the responses of the j t h tyoe of deposit l i a b i l i t y to the insurance premium rate per d o l l a r . A l l member banks of the Federal Reserve System, i n c l u d i n g both n a t i o n a l and state banks, must participate in the deposit insurance system which i s administered by the Federal Deposit Insurance Corporation (FDIC). Virtually a l l commercial banks are insured with the FDIC. Other finan-c i a l institutions such as savings and loan associations and credit unions have similar insurance schemes where a premium is paid dependent on deposits held. The insurance premium rate is thus another potential regulatory control variable. From (4.24) i f the jth deposit l i a b i l i t y is an input, and its premium b^ increases, the demand for that input is non-increasing. If deposit j is an output, and i t s premium increases, then (4.241) implies that its supply is non-increasing. Consequently, i f the premium on the jth deposit increases, i t s holdings are non-increasinq. In (4.25) and (4.251) are summarized the response of the j t h category of deposit to the service charge levied per dollar per time period. If the jth type of deposit, is an input, and its service charge rate, s^ increases, then its demand is non-decreasing. If deposit j i s an output, and its service charge rate increases, (4.25) implies that its supply is non-decreasing. Hence, i f the service charge rate per - f>l -dollar per unit time increases, then holdinqs of the j t h type of deposit are non-decreasinq. Comparative s t a t i c s for the cross e f f e c t s of the components of each user cost are indeterminate. It i s unknown, for example, what i s the e f f e c t on time deposits when the required reserve r a t i o on demand deposits chanqes. This i s because the o f f - d i a q o n a l elements of the matrix of second order partial derivatives of IT evaluated at p* cannot be siqn-determined using the regularity p r o p e r t i e s of the p r o f i t func-tion. We can test to determine whether addinq up p r o p e r t i e s (4.12) and symmetry conditions hold in econometric estimation. Further analysis of the cross effects of the components of each user cost requires examina-tion of empirical point estimates. Consider the interrelationship between profits and the various components of the user costs. Using (4.3), obtained by applying Hotelling's lemma, and (4.14) and (4.17) which employ the user costs, the following comparative static results are obtained: a* 3 * 3 u i 8r. " 3u. 3r. - U i l l 3ir dir 3 u i 3c. 3u. 3c. -i i i > 0 3 ir 3* 3 u i 3s x = l u j 3sT- 0 1 = If.-.N! - 68 -37r_ _ 3TT 3 u j 3k. " 3u. 3k7 - 0 J J J 3TT _ 3TT 3 u j 3r. " 3uT 8771 0 J J J 3TT_ _ 3TT_ 3 u j 3b. " 3 U. 3bT- 0 J = J J J 3TT_ _ 3TT_ 3 u j 3s. " 3 U. 377 - 0 J J J Profits for the financial institution are non-decreasing when there is an increase in: (1) the interest rate payable to the financial institution on assets held; (2) the capital gains on assets held; (3) the service charge rate charged on loans; and (4-) the service charge rate charged on deposits. Profits are non-increasing i f there i s an increase in the following components of user cost: (1) the default rate on loans; (2) the required reserve ratio on deposits; (3) the interest rate payable by the financial institution on l i a b i l i t i e s ; and (4) the insurance premium rate on deposits. The comparative static predictions yield qualitative results from user costs embedded in a profit maximizing framework. Many of these results follow a priori expectations. The value of the results is that exact quantitative measures of responses can be obtained once a functional form for the variable profit function is specified and estimated. - 69 -NOTES See Schworm [1980] p. 1. 2 Financial firms also use durable equipment such as computer hardware, furniture, equipment and bank buildings which also have user costs. q See Chapter 3 for a more complete discussion on the d i s c r e t e periods. Note dynamic problems do not necessarily require d i f f e r e n t mathematical techniques than those used for s t a t i c problems. Lf time i s treated as taking on discrete values, then calculus can be used to char-acterize optimal time paths for choice variables. Let x(t) be a vector of choice variables at time t and let a(t) be a vector of parameters at time t. Let x(») and ot(«) denote the sequence of values x(t) and a(t) respectively for t = 0,1 ,...,+°°, where we use inteqers to index the per-missible values of t. Let * be an objective function that maps the functions (s(»), a(«)) into the real numbers. A necessary condition for optimal choice of x(«) relative to the objective for $ is that 3 »(x(«), <»(•)) „ i- n 1 -a T x T t n — = 0 t = 0,1,...,+-This procedure can be used as long as the domain of x(») is countable. See Schworm [1980] for further discussion: pp. 1-3. Formally, we define the time period to to be the time interval [t,t+D, closed on the left and open on the right. The instant t is in-cluded in interval t, but the instant t+1 is not. 5Producers realize expected capital gains (losses) at the end of each period. 6This occurs at time t + 1. A long-run Hicksian intertemporal model would consider a l l time periods until the financial firm is dissolved. The point is that with active secondary markets or rental markets, the long-run problem can be decomposed into a series of short-run problems. This can be done even i f the secondary markets do not exist. However, the long-run model w i l l be required in order to determine the correct shadow rental rates of the short-run model. 0 Because of data constraints, our time interval in the empirical model wi l l be set at one year. - 70 -3 The assumption of cost min imiz ing behavior i s out of voque mainly because of the d i f f i c u l t y in j u s t i f y i n g the exoqeneity of the vector of outputs . The vector of bank outputs w i l l chanqe in composit ion as r e l a t i v e user co s t s vary . Rank cost f unc t i on s t ud i e s were plagued by se r i ou s d i f f i c u l t i e s in d e f i n i n g the outputs of commercial banks. 1 0 O u a l i t y theory can be u t i l i z e d even i f there is monopsonistic or monopo l i s t i c behaviour on the part of f i n a n c i a l f i r m s . A model of a hank or f i n a n c i a l f i rm under imperfect compet i t i on i s developed in Chapter 8. See Diewert [19S21. 1 d e b r e u [1959] p. 38. 12 Actually, convexity of the production p o s s i b i l i t y set may be omitted and the profit f u n c t i o n , T T , w i l l s a t i s f y the above f i v e c o n d i -t i o n s . See Diewert [1973, p. 289]. Note, however, i f we assume the production possibility set is closed, non-empty, convex and has the properties of (i) free disposal and ( i i ) contains the zero v e c t o r , then TT completely characterizes S. 1 3See also Diewert [1973, pp. 290-294]. We note that i f the profit function i s not differentiable at the point (u,v,w) but i s f i n i t e in a neighborhood of (u,v,w) then the convexity of the p r o f i t function wi l l imply that the profit function has a non-empty set of supportinq hyperplanes (y,z,x) at (u,v,w) and thus the profit maximizing derived input demand and output supply functions become set valued functions or correspondences. l Exogeneity of prices and user costs w i l l be relaxed i n Chapter 6. l 5 i r defined by (4.2) using (u,v,w) = p. 1 6See Diewert's [1977, p. 11] fourth characterization of concavity. 1 7See Diewert [1974a] pp. 142-146. Proofs pp. 163-164. 18 For one input-output the cross effect term can be signed using the above theorem. See Diewert [1974a], p. 143. 1 9 Loan rate ceilings have been intended to protect consumers from paying high loan rates. Such ceilings, when binding, may r e s t r i c t con-sumer loans. These ceilings are adjusted periodically. I n t e re s t rates on specific loans have been influenced by "moral suasion" imposed fo r short periods by the regulators. This affects loan supply i n the short-run. 2 0Under the United States Monetary Control Act of 1980 a l l de-pository institutions (saving banks, savings and loans, credit unions) will be required to maintain reserves in a ratio prescribed by the Fed-eral Reserve Board. Previously regulatory bodies differed between - 7 1 -depos i tory i n s t i t u t i o n s ( e .q . The Federa l Home Loan Bank regu lated savings and loan a s s o c i a t i o n s ) , in other c oun t r i e s each tyoe of depos i tory i n s t i t u t i o n may have i t s own r e q u l a t i n g body determin ing the reserve r a t i o on each k ind of l i a b i l i t y . 21 The theory of money c r e a t i o n has been c r i t i c i z e d by Curies and Shaw [1960] and Tobin [1963] f o r i qnor ing that banks, c r e d i t un ions, sav ings and loan a s s o c i a t i on s are f i rms . We have desc r ibed f i n a n c i a l f i rm operat ions e x p l i c i t l y with a model of the i n d i v i d u a l f i rm a p p l i c a b l e to ther producers. 2 ? I n teres t rates on depos i t s in the United S ta te s have been r e gu l a t ed . Payment of i n t e r e s t on demand depos i t s was p r o h i b i t e d , and Regu la t ion 0 set depos i t rate c e i l i n g s on other c a t e g o r i e s of depo s i t s . The Depository I n s t i t u t i o n s Deregu lat ion Act of 1980 r e q u i r e s the Deregu la t ion Committee to exe rc i s e i t s au thor i t y to prov ide for the order l y phase-out and u l t i m a t e e l i m i n a t i o n of i n t e r e s t ra te c e i l i n q s as r a p i d l y as economic cond i t i on s warrant. I t se t s out t a r q e t s for i n c r ea s i n g the ra te c e i l i n q s by at l ea s t ha l f a percentaqe po int not l a t e r than the end of each of the t h i r d , f o u r t h , f i f t h and s i x t h years a f t e r the date of enactment. - 7 2 -CHAPTER 5 DATA AND DATA CONSTRUCTION 5.1 Introduction To estimate the parameters of the model developed in Chapters 3-4, it is necessary to have observations on a wide variety of variables. The major data source for the study is developed by the Federal Reserve Bank Functional Cost Analysis (FCA) program. This program is a co-operative effort of the Federal Reserve Banks and the member banks, designed to develop and maintain a uniform income and cost accounting system as a tool for bank management. The FCA develops individual bank income and cost along functional lines and provides comparisons of these data within each bank by year and with groups of other banks. It is designed "to help a participating bank achieve the objective of increasing overall bank earnings as well as increasing the pr o f i t a b i l i t y and efficiency of each bank function." 1 The three primary sources of bank funds are demand deposits, time deposits, and non-deposit funds. Non-deposit funds include common and preferred stock, capital, notes and debentures, borrowed money, and federal funds purchased. There are six asset categories: cash, investments, real estate mortgages, instalment loans, credit card loans, and "commercial, agricultural and other loans". Other bank functions include the provision of safe deposit boxes, trust and estate services, and on-premises computer services. Data also exist on non-banking functions. A non-banking function is defined as a specific activity contributing to earnings, which has no balance sheet - 73 -2 e n t r y . Some examples .ire the operat ion of insurance agenc ies , t r a v e l bureaus and t r u s t and safekeepinq s e r v i c e s . These f unc t i on s prov ide f o r the i s o l a t i o n of income and expenses generated by non-bankinq, non-fund us inq a c t i v i t i e s other than from safe depo s i t s , t r u s t s , and computer s e r v i c e s . Due to the s i q n i f i e a n t d i f f e r e n c e omonq banks in the extent o f non-banking a c t i v i t i e s , i t i s important that income and expense generated by them not be minqled with the income and expenses of the s t r i c t l y banking f u n c t i o n s . The appendix prov ides a d e t a i l e d example of F u n c t i o n a l Cost Ana l y s i s data. Periodic reviews were conducted by the Federal Reserve Bank of New York to ensure comparable, uniform and precise reporting. Care was taken to ensure accuracy, s ince the information is used both for cost account-ing and performance comparisons between banks. Other s t a t i s t i c a l s e r i e s reported both to the Federal Reserve and federal government lack such incentives, and are probably more subject to error than Functional Cost data. The Functional Cost data also use arbitrary rules to allocate joint costs, for example for labor and material supplies, among outputs. These are not followed here, and rather these are viewed as inputs in the production possibility set at the financial firm. Use of the Functional Cost data is important in the estimation of the model because they contain a salary breakdown between officers, or skilled workers, and processors, or unskilled workers, thus allowing them to be treated as separate factors of production. The FCA data a l s o contain information on the use of computers, details on number and types of branch offices, account characteristic information, balance sheet and income and expense information. - 74 -The s a m p l e c o m p r i s e s y e a r l y F u n c t i o n a l C o s t d a t a f o r e i g h t e e n c o m m e r c i a l b a n k s i n New Y o r k and New D e r s e y o v e r t h e p e r i o d 1973 t o 1978. T h e s e a r e a l l members o f t h e F e d e r a l R e s e r v e . T h e s e b a n k s a r e assumed t o f a c e s i m i l a r demand c o n d i t i o n s and f a c t o r m a r k e t s . They l i e i n F e d e r a l R e s e r v e D i s t r i c t 2, s e r v e d by t h e F e d e r a l R e s e r v e Bank o f New Y o r k , and h e n c e d i f f e r e n c e s i n D i s t r i c t s u p e r v i s i o n and e x a m i n a t i o n h a v e b e e n l a r g e l y e l i m i n a t e d . P a n e l d a t a a r e b e t t e r t h a n c r o s s - s e c t i o n a l d a t a f o r o u r p u r p o s e s b e c a u s e more v a r i a t i o n i n p r i c e s , o r u s e r c o s t s , t h a n i n t y p i c a l c r o s s -s e c t i o n s i s r e q u i r e d t o e s t i m a t e a v a r i a b l e p r o f i t f u n c t i o n w i t h a f l e x i b l e f o r m . S i n c e t h e r e a r e d i f f e r e n c e s i n s t a t e r e g u l a t i o n o f c o m m e r c i a l b a n k s , s u c h as u s u r y l a w s f o r m o r t g a g e s , t h e s a m p l e h a s b e e n c o n s t r a i n e d t o come fr o m o n l y two s t a t e s , New Y o r k and New 3 e r s e y , w h i c h h a v e s i m i l a r r e s t r i c t i o n s on b r a n c h e s . D a t a on r e s e r v e r e q u i r e m e n t s on d e p o s i t s come f r o m t h e F e d e r a l  R e s e r v e B u l l e t i n o f t h e F e d e r a l R e s e r v e B o a r d o f G o v e r n o r s , a s do t h e maximum i n t e r e s t r a t e s p a y a b l e on t i m e and s a v i n g s d e p o s i t s . I m p l i c i t p r i c e d e f l a t o r s a r e t h o s e u s e d i n t h e N a t i o n a l Income and P r o d u c t A c c o u n t s as p u b l i s h e d i n t h e S u r v e y o f C u r r e n t B u s i n e s s o f t h e U.S. D e p a r t m e n t o f Commerce, B u r e a u o f E c o n o m i c A n a l y s i s . T h e s e i n c l u d e d e f l a t o r s on a s s e t p r i c e s o f c a p i t a l , p a r t o f t h e c a l c u l a t i o n o f u s e r c o s t s f o r c a p i t a l . The c h a p t e r i s o r g a n i z e d i n t h e f o l l o w i n g m a n n e r . S e c t i o n s 2, 3, and 4 d e v e l o p t h e d a t a c o n s t r u c t i o n f o r t h e p h y s i c a l , o r n o n - f i n a n c i a l c o m m o d i t i e s u s e d i n bank p r o d u c t i o n . T h e s e a r e l a b o r i n p u t , t h e s e r v i c e s o f i n t e r m e d i a t e I n p u t s and raw m a t e r i a l s , and t h e s e r v i c e s o f c a p i t a l . - 75 -Section 2 on labor input constructs two wage variables for skilled and unskilled workers from FCA data. A T'ornqvist price index is then calculated for the price of labor. 3 In section 3 we construct price data for materials. Included in materials expenditures are outlays on stationery and office supplies, telephone, teleqraph, advertisinq, postage and delivery. User costs for capital are constructed in section 4 using implicit price deflators, and information on service lives of various capital assets. Utilizing income and expense statement informa-tion and user costs for capital, quantities of capital are obtained. Section 5 deals with the construction of user costs and relevant quantities for financial commodities. For the specification, four types of financial commodities are distinguished, namely loans, cash, demand deposits and time deposits. With the exception of cash, the quantity of each is an index comprising a number of other financial commodities. For each component, a separate user cost must be constructed. As indicated in Chapter 3, these rely on extensive information on reserve require-ments, interest rates, deposit insurance rates and service charges on the deposit side, and interest rate returns, loan loss provisions and service charges on the loan side. Section 6 explains the construction of quasi-rents or variable profits for each bank in each year. Data are tabulated in summary form in each subsection. The information is obtained for eighteen banks over 1973-1978, and user costs and quantities of services consumed constructed for each. 5.2 Labor Services Average compensation is calculated for processing employees and officers for each bank and year. Compensation includes salary and fringe - 76 -benefits. FCA data distinguish processing salaries, officers' salaries and fringe benefits by function, implying that the allocation to demand and time deposits can be separated. Processing employees and officers are also allocated to each function. Where fringe benefits are not specified to processors or officers for a function, they are allocated on a person basis. Average compensation is obtained by dividing total compensation for each kind of labor by the number of workers. Hence Wt(PE) E SPE^ + FBPE i=l l t : *t NPE t=1973,...,1978 (5.1) Wt(OE) = F I i=l E SOE. + FBOE, i t i t NOE t-1973,.,.,1978 ( 5 . 2 ) where i - 1,..., F represents the various functions, such as demand deposits and investments in the FCA data, with S P E i t t h e s a l a r l e s o f processing employees in function i at time t S 0 Ei t the salaries of officers in function i at time t FBPE the fringe benefits of processing employees In function i at time t FBOEit the fringe benefits of officers in function i at time t NPE^ the number of processing employees at time t NOEt the number of officers at time t. - I l -ka aggregate price of labor input is then constructed using the Divisia Indexing procedure for each bank. Let EXLt denote labor compen-sation at time t, or EXL = P «L = W (PE)«NPE + W (OE)«NOE (5.3) C L. C t t t t t where P and L denote respectively the price and quantity of aggregate L i t t * i. L labor at time t. The Divisia index for the price of labor is t W.(PE) t W (OE) P l t - « p [ S j(PE, ^ <j . . ( O E j J ^ d j l ( 5 . 4 ) with base value P L ( 1 9 ? 3 ) = 1, and W (PE)'NPE s t(PE) = — _ 1 ( 5 > 5 ) W (OE)'NOE S t ( 0 E ) " ^ E X l ~ (5.6) where s(PE) and s(OE) represent the relative shares in total compensation of processing employees and officers respectively. A quantity index can be derived analogously, or by dividing the expenditure on labor by the Divisia index for the price of labor. The calculated Divisia price indices for labor using a moving two period arithmetic mean share weight on s(PE) and s(OE), are in Table 5.1 for each bank. Similar Tbrnqvist indices were also calculated across banks using Bank 1 in 1973 as the base bank and 1973 data for the other seventeen - 78 -TABLE 5.1 J K v i s i a Price indices for Labor (Tornqvist Specification 1973 = 1.00) Bank Number4 1 2 3 4 6 12 13 14 15 16 19 21 2? 23 25 27 28 29 1974 1.166436 1.052673 1.034380 0.9839331 1.031076 1.057684 1.347334 1.093831 1.069191 1.189604 1.046269 0.872930 1.057668 1.043968 0.967494 1.049748 1.091673 1.173486 1975 1.218487 1.120276 1.183816 1.123774 1.157491 1.134845 1.297000 1.128340 1.170598 1.192038 1.175020 0.895532 1.111585 1.071801 1.121230 1.141093 1.139794 1.231121 1977 1978 1.290430 1.220815 1.138518 1.330551 1.203251 1.277678 1.494361 1.376768 1.276689 1.240170 1.019742 1.012204 1 . 174525 1.027639 1.271021 1.342566 1.292020 1.428588 1.152978 1.315380 1.425856 1.30639 1.075691 1.3291 15 1.426364 1.390473 1.188653 1.356224 1.250883 1.113594 1.2605 34 1.067936 1.261261 1.330654 1.331671 1.407685 Number coding is as supplied by the Federal Reserve Bank of New York. - 79 _ banks. These were used to weight the p r i c e i nd i ce s for labor in Table 5.1 s ince data on Rank 1 in 1973 are used as r e spec t i ve numerai res. The c ros s bank i n d i c e s are in Table 5.2. These cross-bank adjusted p r i c e i nd i ce s are used in the study for the p r i c e of l a bo r . The data for l abor s e r v i c e s are tabu la ted in summary form in Table 5.3 for three sample year s . 5.3 Materials Services The FCA data inc lude expenditures on s t a t i o n e r y , p r i n t i n g and s u p p l i e s , te lephone and te leg raph , p u b l i c i t y and a d v e r t i s i n g , and postage, f r e i g h t and d e l i v e r y . In order to use these data i n e s t i m a t i o n , it is necessary to decompose them i n to p r i c e s and q u a n t i t i e s . The hanks in the study are geograph ica l l y l o ca ted in the same Federa l Reserve D i s t r i c t , and so can be assumed to face the same p r i c e s i n f a c t o r markets. I m p l i c i t p r i c e i nd i ce s con s t ruc ted by the U.S. Departments of Commerce and Labor are used for the va r i ou s m a t e r i a l components. T o t a l expenditures in each category are d i v i d e d by the re l evan t p r i c e index to y i e l d a quant i t y index. The p r i c e used for p r i n t i n q , s ta t ionery and s upp l i e s i s the s e r i e s on o f f i c e suppLies and acces so r ie s from the Wholesale P r i c e Index of the Department of Labor. The base year used i s 1972, when the index i s set at 100. For telephone and te leg raph , the i m p l i c i t p r i c e d e f l a t o r in the n a t i o n a l accounts , as publ i shed in the Survey of Current Bus iness f o r telephone and te legraph i s u s ed . 5 For p u b l i c i t y and a d v e r t i s i n q , the . i m p l i c i t p r i c e d e f l a t o r for se rv i ce s in the n a t i o n a l accounts from the Survey of Cur rent Bus iness is used. A p r i c e index, w i th the base 100 i n - 30 -TABLE 5.2 Cross Bank Tornqvist Labor P r i c e I n d i c e s , 1973 (Bank 1 normalized at uni ty) Bank Number Index 1 1 2 1.014 3 1.129 4 1.077 6 1.184 12 1.056 13 0.881 1 4 0.962 15 1.054 16 1.033 19 1.412 21 1.224 22 1.062 23 1.362 25 1.281 27 1.094 28 0.923 29 1.030 - SI -TABLE 5.3 L a b o r I n p u t and Wage D a t a 1973-1978, C u r r e n t D o l l a r s 1 * ? 7 3 _ Variable Mean Standard Deviation Minimum Maximum Annual wage, officers W(0E) ($) 19,159 3,811.7 1fr,fr52 30,1fr0 Annual wage, processing employees, W(PE) ($) 7,661.6 1,000.7 6,286.8 9,88fr.2 Labor cost, EXL ($) 2,432,700 2,824,800 136,620 8,586,800 Labor quantity, L 2,308,600 2,700,900 120,520 9,325,900 Labor price, 1.0522 0.13882 0.8fr3fr2 1.3587 1 9 7 5 Annual wage, officers W(0E) ($) 22,011 3.648.0 17,877 30,730 Annual wage, processing employees, w(PE) ($) 8,765.0 1,070.fr 7,151.fr 11,907 Labor cost, EXL ($) 2,786,000 3,15fr,20O 159,900 9,frfr1,600 Labor quantity, L 2,337,400 2,666,200 122,010 9,099,000 Labor price, P L 1.1990 0.1fr67 1.0062 1.59fr6 1 9 7 8 Annual wage, officers W(OE) ($) 23,902 3,fr56.1 19,260 31,060 Annual wage, processing employees, W(PE) ($) 9,909.0 1,323.2 7,905.3 1fr,29fr Labor cost, EXL ($) 3,722,000 fr,36fr,200 159,280 12,582,000 Labor quantity, L 2 '7,680,000 32,578,000 130,070 9,769,100 Labor price, P. .L 1.3412 0.1fr76 1.1083 1.7069 Note: Labor quantity Is measured in index units. - 82 -1972, is constructed using the U.S. domestic rate for f i r s t class postage. This index for postage, freight and delivery along with the other price data for materials is in Table 5.4 below. An aggregate price of materials is then constructed using the Tornqvist indexing procedure for each bank. Let EXM^  denote the total expenditure on materials at time t. Hence EXM = P «M = PSS «SS + PTT «TT + PPA «PA + PPD «PD (5.7) t M t t t t t t t t t t where P and M denote respectively the price and quantity of Mt t aggregate materials at time t. Stationery, printing and supplies quantity is denoted by SSt with PSSt the corresponding price at time t. The quantity of telephone and telegraph services is TT and PTT^ i t s price at time t. Similarly, PAfc represents publicity and advertising quantity, and PD^  denotes the postage and delivery quantity with PPAt and PPD^ their respective prices at time t. The Divisia index for the price of materials is t PSS. t PTT S P PA . t P P D . 1973 P A p -pAT d j + S P D P T O T d J ] (5.8) with base value P (t) = I, and PSSt-SSt PTTt-TTt PPA -PA PPD •PD 'PS = EXMt ' STT = ~EXM^  ' SPA = ~EXM^  SPD = " ( 5' 9> $1 -TABLE 5.fr Price Indices, Materials and Intermediate Inputs, 1973-1978 Printing, Stationery 4 Supplies Telephone 4 Telegraph Publicity 4 Advertising ostage, Freight 4 Delivery 100 100 100 100 106.5 102.6 105.fr 106.25 131.88 106.9 113.7 125.0 1fr3.fr 110.fr 128.0 162.5 1frfr.76 11fr.3 136.6 162.5 1fr6.70 115.6 1fr7.3 162.5 151.8fr 117.0 158.9 162.5 Spc;' ^ T X ' ''Vv 1 1 n r * ^PD r t " P r e s e n ( l h ( ' r e l a t i v e shares in t o t a l expend i ture on m a t e r i a l s of s t a t i one ry and s upp l i e s , telephone and t e l eq raph , p u b l i -c i t y and a d v e r t i s i n g , and postage and de l i v e r y r e s p e c t i v e l y . The quant i ty index can be der ived analogously or by d i v i d i n g the t o t a l expendi ture on m a t e r i a l s , F.\M t, by P . The c a l c u l a t e d D i v i s i a p r i c e i nd i ce s fo r m a t e r i a l s are in Table 5.5 f o r each bank under the Tornqv i s t s p e c i f i c a t i o n . The data for m a t e r i a l s e r v i c e s are tabu la ted in summary form in Table 5.6. 5.1- Physical Capital Services I n format ion reqard ing p h y s i c a l c a p i t a l can he obta ined e i t h e r from the balance sheet or the income and expense statement. On the balance sheet, c a p i t a l i s l i s t e d at book value l e s s accumulated d e p r e c i a t i o n . Balance sheet data are not an appropr ia te source fo r c o n s t r u c t i n g p r i c e s and q u a n t i t i e s fo r two reasons. F i r s t , the c a p i t a l expend i tures are measured by h i s t o r i c cos t s and are not adjusted for post-purchase asset p r i c e chanqes. Each f i n a n c i a l i n s t i t u t i o n may have purchased i t s c a p i t a l in a d i f f e r e n t time p e r i o d . Second, c a p i t a l co s t s are aqqreqated a r b i t r a r i l y on the balance sheet. "Bank Premises " , as an asset on the balance sheet i nc lude i n i t i a l expenditures on bank b u i l d i n g s , r e a l e s t a t e , and f u r n i t u r e and equipment less accumulated d e p r e c i a t i o n . The costs are added together . income and expense statement in format ion on c a p i t a l are p r e f e r -ab l e . The data capture the flows r e l a t ed to the c a p i t a l s tock . The occupancy expense of bank premises inc ludes d e p r e c i a t i o n , maintenance - 85 -TABLE 5.5 Tornqvist Price Indices, Materials and Intermediate Inputs 1973 =1.00 ' Bank Number 1 2 3 4 6 12 13 14 15 16 19 21 22 23 25 27 28 29 1974 1.134208 1.111802 1.118852 1.128526 1.169465 1.131352 1.114799 1.127663 1.126246 1.110494 1.121184 1.138339 1.128845 1.126066 1.128423 1.129817 1.111448 1.143240 1975 1.249685 1.230382 1.243437 1.255438 1.297721 1.253476 1.226566 1.236259 1.256294 1.228877 1.239348 1.271443 1.250466 1.244310 1.254958 1.242663 1.226302 1.270928 1977 1.371 134 1.377210 1.403031 1.413953 1.418836 1.395110 1.356195 1.358282 1.422896 1.362099 1.367394 1.428530 1.38292 I 1.382432 1.397117 1.364757 1.368730 1.411747 1978 1.414840 1.423199 1.443664 1.466109 1.461923 1.440034 1.401012 1.394968 1.466637 1.416199 1.418753 1.463575 1.430213 1.426618 1.451547 1.406885 1.412366 1.447325 TABLE 5.6 User Cost and Quantity Index, Material Services, 1973-1978 1— 1 9 7 3 Variable Mean Standard Deviation Minimum Maximum Price of Materials, P M 0.95715 0 0.95715 0.95715 Quantity of Materials, M 539,770 601,430 18,229 1,786,600 Expenditure on Materials, EXM ($ current) 516,640 575,650 17,448 1,710,100 1 9 7 5 Variable Mean Standard Deviation Minimum Maximum Price of Materials, P u 1.1938 0.0174 1.1723 1.2406 Quantity of Materials, M 516,620 566,950 19,144 1,569,900 Expenditure on Materials, EXM ($ current) 612,450 671,740 23,751 1,876,700 1 9 7 8 Variable Mean Standard Deviation Minimum Maximum Price of Materials, P M 1.3770 0.0224 1.3409 1.4098 Quantity of Materials, M 569,230 658,560 20,829 2,088,300 Expenditure on Materials, EXM ($ current) 777,230 898,470 29,270 2,870,900 - S7 -cos t s , rent, i n te res t , and taxes for bank bu i l d ing s , land, f ixed equip-ment and parking l o t s . 5 The furn i ture and equipment expense includes deprec i a t i on , maintenance, rent, interest and tax charges on movable bank fu rn i tu re and equipment. There is also a computer or computer serv ice expense. Let E n denote the expense on c a p i t a l asset n. There are three kinds of c a p i t a l : s t ructures (n=1), fu rn i tu re and equipment (n=2), and computers (n=3). 8 Then, E n = U n V n K n n=1,...,3 (5.10) where U i s the user cost of c a p i t a l asset n, V i s i t s u t i l i z a t i o n rate n n and i s the quantity of c a p i t a l serv ices from asset n. U t i l i z a t i o n data are not ava i l ab le for bank structures and f u r n i t u r e and equipment. For banks who have on-premise computing f a c i l i t i e s there are data on average cent ra l processing unit (CPU) hours per week. It is assumed that the u t i l i z a t i o n rate i s the same for a given c a p i t a l asset over time. The user cost of c a p i t a l asset n in period t i s constructed in the framework of 3orgenson and G r i l i c h e s [1967]. The user cost i s derived as though a l l firms lease the i r c a p i t a l qoods from a " l e a s i n q " f i rm. Competition presumably forces the " l ea s ing " firm to earn the going rate of re turn , or nominal discount rate R, on i t s leas inq a c t i v i t i e s . The purchase cost of one unit of the cap i t a l good less the renta l received during the period is equal to the discounted depreciated value of the c a p i t a l good in the rent per iod. In symbols we have, P - U = }(1 - d ) P . .}/(! + R). (5.11) nt nt n nt+1J Rewrit ing (5.11) we obtain - S3 -Unt = < R P n t + d n P n U l " ( P n t + , " V ^ 1 + R ) (5",?) n = 1,2,3 t = 1973 , . . .,1978 where P is the purchase price of capital good n in period t, P . i s i t s expected purchase price in period t *- 1, d i s i t s one-period combined economic depreciation and obsolescence rate and R i s the nominal discount rate. Data on purchase prices for capital are obtained from the U.S. national accounts, as published in the Survey of Current Business. It is assumed that the banks face competitive physical capital markets, and hence the same capital prices. The implicit price deflator for purchases of commercial structures is used for structures. For furniture and fixtures and for computing machinery we use the respective implicit price deflator for private purchases of producers' durable equipment. These prices are in Table 5.7. Information on service lives of capital assets is limited. Detailed information on the average service lives of the equipment and structures that make up the stock of fixed capital, is unavailable, as is information on how the service lives of individual items depart from the average. There are differences in the basic p h y s i c a l c h a r a c t e r i s t i c s of capital assets, variations among the practices of their owners with respect to use and retirement, and technological changes which make for a large dispersion of service lives. For fixed non-residential business capital, estimation of average service lives has relied on data compiled in connection with the - 3 9 -TABLE 5.7 Asset Prices for Physical Capital [1972 = 100] 1973 1974 1975 1976 1977 1978 1979 Structures 108.4 127.9 138.3 139.1 147.6 163.20 186.5 Furniture & Equipment 106.6 122.4 134.8 140.3 150.7 166.1 182.2 Computers 100.2 101.3 102.3 102.6 102.1 102.4 102.5 Source: U.S. Department of Commerce, Bureau of Economic Analysis, Survey of Current Business. 3uly national accounts issues, various years. a d m i n i s t r a t i o n of f ede r a l income tax l a w s . 9 This study u ses the asset working l i v e s app l ied in a l l na t i ona l accounts and U.S. c a p i t a l s tock s t u d i e s . They are publ i shed in Fixed R e s i d e n t i a l and Non -Re s i den t i a l Bus iness C a p i t a l in the United States 1929-1976, and are l i s t e d in Table 5 . 8 . 1 0 I f L i s the se r v i ce l i f e of c a p i t a l asset n, then d , the n ii one-per iod d e p r e c i a t i o n r a te , i s dn ~ E~ n=1 ,2,3 n assuming a constant geometric rate of d e p r e c i a t i o n . 1 1 The user cost of c a p i t a l (5.12) and the user co s t s (3.1) and (3.3) i n Chapter 3 a l l i n vo l ve the discount rate R. The app rop r i a te d i scount r a t e i s the marg ina l opportun i ty cost of borrowing or lend ing the marg ina l d o l l a r . Economic theory p red i c t s that the f i rm w i l l engage in s ho r t - r un p roduct ion i f qua s i - r en t s are p o s i t i v e . I f q u a s i - r e n t s are negat ive the f i rm i s not cover ing i t s v a r i a b l e ope ra t i n g c o s t s and i t i s more app rop r i a te not to produce than to p r o d u c e . 1 2 Quas i - r en t s have been c a l c u l a t e d us ing as d i scount r a te s a l l the va r i ou s major i n t e r e s t rates f a r i n a the banks. I f loan i n te re s * rates are used as the d i scount r a t e , there is no spread to cover v a r i a b l e i n p u t c o s t s . Th is i s confirmed by apply ino t h i s procedure to a l l the data p o i n t s , and qua s i - r en t s are negative throughout the sample. Th is imp l i e s that the d i scount ra te should be one on a depos i t category . Demand depos i t s have a zero or n e g l i g i b l e i n t e r e s t r a t e , the non-zero component coming from the i n t r o d u c t i o n of Negot iab le Orders of Withdrawal (NOW) accounts in 1978. This leaves the time depos i t i n t e r e s t r a te as the remaining candidate for use as the discount r a t e . - C I -TABLE 5.8 Service Lives by Type of Asset Type of Asset Life (years) Commercial Buildings 36 Furniture and Fixtures 15 Office, Computing, and Accounting Machinery 8 As calculated in the Functional Cost d a t a , the time deposit rate is a blended rate of the savings deposit rate and the certificate of deposit rate. Certificates of deposit are in large denominations, freguently in excess of $100,000, hence the> are not marginal dollars. Therefore a blended rate includes marginal and non-marginal dollars. For this reason it is assumed that the marginal opportunity cost of funds is the lowest time deposit rate paid in the sample in each year. This rate is likely to have the lowest ratio of certificates of deposit. 1 3 The rates are 4.477 percent in 1973, 5.0514 percent in 1974, 4.6036 percent in 1975, 4.465 percent in 1977 and 4.0327 percent in 1978. This completes the user cost calculations including capital gains. If capital expenditure data were available on a net basis, as "occupancy cost and service outlays less capital gains", then the quantity of capital services would be obtained as Q = TE /U n _ i , n n n n- 1 »• • • >' where TE n is true expenditure on capital services. In the FCA capital expenditures data, as in most published series in financial statements, capital qains are excluded. Measured expenditures are consequent \ r* . n=1,...,3. These are obtained from the income statements, and separate series exist for structures, furniture and fixtures and computers according to (5.12). Correspondingly, the quantity of capital services is derived as Q = M E /U* n n n n=1,...,3 (5.13) - 93 -where i f = (RP + P n U , ) / ' ! + n = 1 , . . . , 3 , t = 1 9 7 3 , 1 9 7 8 or the user cost e x c l u s i v e of c a p i t a l qa in s . This procedure i s used to cons t ruc t c a p i t a l s e r v i ce f lows. From the 0 and the assumption that u t i l i z a t i o n ra tes of c a p i t a l are cons tant , the c a p i t a l stocks K can be cons t ruc ted as 0 /V , n n n n=1,...,3. The quant i ty of c a p i t a l i s assumed to be f i x ed in the short run. E q u i l i b r i u m i n the c a p i t a l s e r v i ce s market, with demand downward s l o p i n g , and the p e r f e c t l y i n e l a s t i c supply determines the user c o s t . E i t h e r the c a p i t a l i s used at a zero or constant ra te of u t i l i z a t i o n , and the l a t t e r may be normal ized at u n i t y . The expendi ture on c a p i t a l s e r v i c e s i s thus the product of the f i xed c a p i t a l quan t i t y and the e q u i l i b r i u m user c o s t . This imp l ie s that i n the H i c k s i a n short run, no response to tax changes, fo r example, takes p l a ce . A p h y s i c a l c a p i t a l aggregate i s then c o n s t r u c t e d , (5.14) K = K ( K r K 2 , K 3 ) us ing the Tbrnqv i s t s p e c i f i c a t i o n . In growth form, t h i s i s 3 A£n K = z S ^ A£n K 1 n=1 n t n t ( 5 . 1 5 ) where S . = 0.5 nt nt nt-1 3 E E n=1 3 n t + n=1 E ^ - 1 n=1 , . . .,3 t=1973, .. ., 19.78 (5.16) a n d Ent = Pnt Knt i s t h e d S S e t V d i u e o f C d P i t a l stock of type n i n year t. The p r i c e fo r aggregate c a p i t a l can be computed ana logous l y , or the - 9k -total expenditure on c a p i t a l c a n be d i v i d e d by a g g r e g a t e c a p i t a l , yielding 3 P^ . = C E E ]/K t=1973, . . . , 1978. (5.17) n= 1 The data f o r c a p i t a l a r e tabulated i n summary i n T a b l e 5.9. 5.5 User Costs for Financial Commodites 5.5.1 Loans 5.5.1.1 Introduction There are five types o f l o a n s considered, namely i n v e s t m e n t s , real estate mortgage loans, instalment loans, credit card l o a n s , and commercial, agricultural and other loans. There are FCA d a t a on each o f these five loan categories. The user cost o f loan i is constructed according to (3.1) which is , _ 1 + (r.+-s. + c.-6.) u. = 1 - { " ( 1 / R ) 1 -} 1=1 ,... ,5 (5.18) where r^ is the mathematical expectation of interest payable t o the financial instituion, s^ is the service charge rate that an average dollar of asset i yields per t i m e p e r i o d , c^ refers t o c a p i t a l g a i n s o r losses, and 6. i s the p r o p o r t i o n o f l o a n s e x p e c t e d t o d e f a u l t o f c a t e g o r y i . The term (r. + s^ + c. - 5.) represents t h e expected income f r o m o n e dollar of loan i per time period. In the empirical m o d e l i t i s assumed that the bank expects the actual income that i t r e c e i v e s . Alternative expectation specifications are outlined in Chapter 3. As there a r e five observations per bank, a lagged expectations model was not feasible. Static expectations were not appropriate during this time period. - 96 -5.5.1.2 I n v e s t m e n t s I n v e s t m e n t s i n c l u d e U n i t e d S t a t e s s e c u r i t i e s , t a x exempt s e c u r i t i e s and l o a n s , f e d e r a l f u n d s s o l d , and o t h e r l i q u i d i t y l o a n s . The m a j o r p o r t i o n o f t h e i n v e s t m e n t p o r t f o l i o f o r FCA b a n k s s t u d i e d i s i n v e s t e d i n U n i t e d S t a t e s s e c u r i t i e s and t a x - e x e m p t s e c u r i t i e s and l o a n s . F e d e r a l f u n d s s o l d and o t h e r l i q u i d i t y l o a n s n o r m a l l y r e p o r t e d a s l o a n s a r e i n c l u d e d as i n v e s t m e n t s i n t h i s a n a l y s i s . 1 4 They a r e r e s t r i c t e d h e r e t o f e d e r a l f u n d s s o l d , p u r c h a s e d c o m m e r c i a l p a p e r , b a n k e r s ' a c c e p t a n c e s , p u r c h a s e d c e r t i f i c a t e s o f d e p o s i t , and Commodity C r e d i t C o r p o r a t i o n c e r t i f i c a t e s o f i n t e r e s t . I n c l u d e d i n t h e i ncome f o r t a x - e x e m p t s e c u r i t i e s and l o a n s i s t h e c a s h f l o w g e n e r a t e d f r o m n o t p a y i n g t a x on t h i s i n c o m e . M u n i c i p a l b o n d s e x e m p l i f y t h i s t y p e o f i n v e s t m e n t . Tax s a v i n g s on t a x - e x e m p t s e c u r i t i e s a r e c a l c u l a t e d by t h e FCA d i v i s i o n o f t h e F e d e r a l R e s e r v e Bank o f New Y o r k i n t h e f o l l o w i n g manner. The a p p l i c a b l e f e d e r a l i n c o m e t a x r a t e on b a n k s t h r o u g h o u t t h e 1973-1978 p e r i o d f o r t h e f i r s t $ 2 5 , 0 0 0 o f t a x a b l e i n c o m e i s 20 p e r c e n t . The t a x r a t e on t h e s e c o n d $ 2 5 , 0 0 0 i s 22 p e r c e n t . On t a x a b l e i n c o m e i n e x c e s s o f $50,000 t h e m a r g i n a l t a x r a t e i s 48 p e r c e n t . Most b a n k s h a v e an a v e r a g e t a x r a t e w h i c h i s a p p r o x i m a t e l y e q u a l t o 48 p e r c e n t s i n c e t h e i r a c c o u n t i n g income s u b s t a n t i a l l y e x c e e d s 1 5 $ 5 0 , 0 0 0 . A f t e r t a x , p r o f i t s a r e t h e r e f o r e a p p r o x i m a t e l y 0.52TT, where n i s p r o f i t s b e f o r e t a x , s i n c e t h e m a r g i n a l t a x r a t e and a v e r a g e t a x r a t e a r e e s s e n t i a l l y t h e same. G i v e n t h i s , e s t i m a t i o n r e s u l t s a r e r o b u s t t o w h e t h e r £mr r a t h e r t h a n An[(1-T)ir] = £ n ( 1 - t ) + Jinn i s t h e d e p e n d e n t v a r i a b l e , and T i s t h e m a r g i n a l and a v e r a g e c o r p o r a t e i n c o m e t a x r a t e . - 97 -It is noted that £n(1-t) = -x is a constant and will be subsumed in the intercept term. The banks in the stud> face similar state and local taxes and are in the same geographical market. An analogous argument holds for state and local taxes as a consequence. There are also data on realized securities gains or losses. These dollar values are transformed into a capital qains rate by dividing them by total investments. The user cost of investments is calculated in the following manner UINV = M M + UNCINV/INV) + (TAX/INV) + (GAINS/INV) ]/(1+R)} (5.19) where INV is total investment volume in dollars, and INCINV is interest income received, (INCINV/INV) is the interest rate, (TAX/INV) denotes tax savings on tax-exempt securities and loans in rate form, (GAINS/INV) is the capital gains rate, and R is the discount rate. 5.5.1.3 Real Estate Mortgages There are three categories of real estate mortgage loans, namely loans made and serviced, loans sold but serviced, and loans purchased but not serviced. Loans sold but serviced do not appear on the balance sheet. This subcategory, representing mortgaqes sold to other financial firms, is deleted from the analysis because it constitutes a negligible portion of the real estate portfolio during the period under study. Loans purchased but not serviced generate interest income, but not service fees and late charges to the bank. The FCA data l i s t separately service fees on loans sold but serviced, interest on loans made and serviced, their late charges and service fee income, and interest on loans purchased but not serviced. - ?S -I t i s assumed in the emp i r i c a l model that each bank has e x p e c t e d income equal to the actua l income received on i t s rea l e s t a te mortqaqe p o r t f o l i o . As a proxy for the expected default: r a t e , the f i v e year average net l o s s rate i s c a l c u l a t e d . The user cost of r e a l e s t a te mort-qaqe loans i s c a l c u l a t e d in the f o l l ow ing manner U R E = 1 - {[1 + (ItlCREM/REML) + (FF.ESRE/RF.ML) - (L0SSRE/REML)]/(1+R)} (5.20) where REML i s equal to the sum of loans made and s e r v i c ed and loans purchased but not serviced, INCREM/REML is the interest ra te charged on rea l estate loans, FEESRE/REML i s the service fee and l a t e charge income, LOSSRE/REML i s the expected default rate, and R is the discount r a t e . 5.5.1.4 Instalment Loans Instalment loans consist of d i rect consumer l oans , i n d i r e c t consu-mer loans, check c red i t , commercial and eguipment loans, and f l o o r p lan loans which refer to advances made for financinq i n v e n t o r i e s of durable goods such as automobiles, equipment and appliances. It i s customary fo r most banks having f loor plan loans to record them in the insta lment loan department, since the sa le of these items to the consumer usua l l y gener-ates instalment paper for the bank. Typical c r e d i t ex tens ions in the commercial and equipment category are single payment loans, t r a i l e r loans, commercial instalment loans and farm and other heavy equipment loans. Income from instalment loans comprises interest and a discount. To obtain an interest rate, th i s income i s divided by the t o t a l do l l a r - 99 -volume of instalment loans or INCIN/iNSTAL. The expected default ra te i s approximated by the dollar volume of f i v e year average net l o s se s d i v i d e d by the total dollar volume, or LOSSIN/INSTAL, so U 1 N = 1 - {[1+(INCIN/IHSTAL) - (LOSSIN/INSTAL)]/(1+R)} (5.21) where again R is the discount rate. 5.5.1.5 Credit Card Loans Credit card function data are collected for card banks. A card bank fully funds the credit card outstanding balances and has records to report the number of accounts, account usage and volume of credit losses. Merchandise or retail volume is average assets reported by credit card business generated from sales slips, dealer discounts and r e t a i l loans to pay for the sales s l i p s . The cash advance volume is the average volume outstanding for direct cash advances to card holders. Merchandise or r e t a i l volume and cash advance balances summed equals total credit card balances outstanding. The income earned on total credit card balances outstanding, CRC, includes merchant discount, net intercharge fees, merchant charge loan interest, and cash advance interest and fees. There are also data on the five year average net credit losses which are used to approximate the default rate. The user cost for credit card loans is calculated as U C R C = 1 - {[1+(INCCC/CRO - (LOSSCC/CRC)]/(1+R)} (5.22) where UQ^Q is the user cost of credit card loans, CRC is total credit card balances outstanding, INCCC/CRC is the interest rate plus the service charge rate and LOSSCC/CRC is the expected default rate proxy for credit card loans. 5 . 5 . 1 . G Commercial, A g r i c u l t u r a l , ann1 Other Loans Commercial, agr icu 1t ur.i i and leas e d eguipment loan ha I duces and r e l a t e d incomes are reported separately in the commercial, a g r i c u l t u r a l and other loan f u n c t i o n . Leased >'qu i pment loans an- ! i s l e d at hook value and include bank-owned equipment leased to other f i r m s , other than data processing equipment. The a g r i c u l t u r a l loans include a l l to the farm sector except those c a r r i e d in the re a l estate loan or instalment loan departments. Commercial loans include o v e r d r a f t s . The income from commercial, a g r i c u l t u r a l and other loans i s mainly i n t e r e s t income. Again, there are also data on the f i v e year averaqe net losses in d o l l a r terms. The user cost for commercial, a g r i c u l t u r a l , and other loans, IL , i s c a l c u l a t e d L A U U C A A = 1 - {[1 + (INCCAO/COMAOL) - (LOSSCAO/COMAOL)]/(1+R) } where COMAOL i s the t o t a l d o l l a r volume of commercial, a g r i c u l t u r a l and other loans, INCCAO/COMAOL i s the in t e r e s t rate earned on them, I.0SSCA0/ COMAOL i s the c a l c u l a t e d d e f a u l t rate proxy and R i s the discount r a t e . 5.5.1.7 User Cost f o r Aggregate Loans Oata on user costs are tabulated in summarv form in Table '> . ' A f o r three sample years. Investments, real estate mortgage l o a n s , i n s t a l -ment loans, c r e d i t card loans and commercial and other loans a l l have negative user costs and hence c o n s t i t u t e outputs for each bank. This was also the case for the other years i n the sample p e r i o d . The average user cost of loans, i j L O a N> w d S " 3.107 percent in 1973, -3.782 percent in 1975 and -4.666 percent in 1978. Conseguently the mean net return a f t e r TABLE 5.10A - 1 0 1 -Loan Statistics - User Costs (per cent, net return after discounting) Three Sample Years 1 9 7 3 Variable Mean Standard Deviation Minimum Maximum User cost of investments, UT1_, 1NV -2.803 0.473 -4.082 -2.187 User cost of mortgages, U R £ -2.462 0.330 -3.355 -2.089 User cost of instalment loans UIN -5.230 1.058 -6.939 -3.069 User cost of credit loans, UCRC -11.379 12.091 -16.559 -1.902 User cost of commercial and other loans, U ^ -3.062 0.683 -4.273 -1.390 User cost of loans, average U1 = UL0AN -3.107 0.346 -3.698 -2.354 1 9 7 5 Variable Mean Standard Deviation Minimum Maximum User cost of investments, U ' INV -3.631 0.58o -4.747 -2.634 User cost of mortgages, U D r RE -2.775 0.271 -3.245 -2.333 User cost of instalment loans UIN -5.792 1.167 -7.825 -2.729 User cost of credit loans, UCRC -6.873 4.657 -13.217 -4.831 User cost of commercial and other loans, U C Q L -3.844 0.782 -5.138 -1.415 User cost of loans, average U1 = UL0AN -3.782 0.451 -4.829 -2.862 - 102 -T a b l e 5.10A c o n t i n u e d 19 7 8 Variable Mean Standard Deviation Minimum Maximum User cost of investments, Ur..., INV -4.242 0.742 -5.639 -2.222 User cost of mortgages, U R £ -3.944 0.507 -5.672 -3.305 User cost of instalment loans UIN -6.718 0.827 -9.171 -5.194 User cost of credit loans, UCRC -10.945 3.981 -17.710 -4.300 User cost of commercial and other loans, UQQ^ -4.504 0.858 -5.642 -2.138 User cost of loans, average U1=UL0AN -4.666 0.509 -5.283 -3.326 - 103 -d iscount ing ranged from 3.107 percent to 4.666 percent on loans. Balance sheet entr ies for investments, rea l estate mortgages instalment loans, c red i t card loans, commercial and other loans are in Table 5.10B. The sample includes both small and large loan p o r t f o l i o s varying from $8.5 m i l l i o n to $850 m i l l i o n over 1973-1978. Let REVLOAN(t) denote the net revenue from loans in period t, or REVLOAN(t) = U,(t) N(t) = -{U T *INV + U *REML + I 1NV Hh U I N*INSTAL + U C R C *CRC + IJ *C0MA0l_} (5.24) where U(t) and N(t) denote respect ive ly the user cost and quantity of aggregate loans at time t . The user cos t s , Uj^yj '-*RE' ^IN' ^CRC a n c ' U C A Q are for period t and INV, REML, INSTAL, CRC, and CAO are the d o l l a r volumes of investments, real estate mortgages, instalment loans, c r e d i t card loans, and commercial, a g r i c u l t u r a l and other loans r e s p e c t i v e l y . It i s noted that a l l the d i f f e ren t loan quant i t i e s are measured in d o l l a r s . D i f fe rent user costs r e f l e c t d i f f e rences in c h a r a c t e r i s t i c s of the type of loan. These c h a r a c t e r i s t i c s include r i s k ine s s and length of matur i ty . For these two reasons, using the Tornqvist indexing procedure is inappropr iate. This procedure would weight the aggregate user cost toward higher user cost loans which may also be more r i s k y . For aggregate loans, the user cost i s constructed as fo l lows . Let LOAN(t) denote t o t a l outstanding loan balances at time t . Then, LOAN(t) = {iNV + REML + INSTAL + CRC + C0MA0L}. (5.25) The aggregate user cost i s - 105 -U l ( t ) = ULOAN ( t ) * f UINV* I N V + URE* R E M L + U I N * I N S T A L + UCRC* C R C + U C A O * C O M A ° L ^ / L ° A N (5-26) or, substituting (5.24) into (5.25) U l ( t ) - " L O A N ^ ) = -REVLOAN(t)/LOAN(t). (5.27) The aggregate quantity of loans at time C is total outstanding loan balances LOAN(t). Summary statistics on the aggregate user cost for loans, U^Q^J, and the aggregate quantity of loans, LOAN are in Tables 5.10A and 5.10B respectively for three sample years. 5.5.2 Cash The user cost of cash, an asset on the balance sheet of the finan-c i a l firm, is constructed according to ( 3 . 1 ) and ( 5 . 1 8 ) . The holding of cash during the Hicksian period does not yield revenue to the firm, but has an opportunity cost. Consequently, the user cost of cash is " C A S H " 1 - { i / C i * ) } . < 5- 2 8> where R is the discount rate. This user cost is applicable to excess reserves. Nearly a l l financial firms must keep some minimum portion of assets in cash. These reserve requirements are generally based upon the types of deposit l i a b i l i t i e s the financial firm possesses. The banks in this study are members of the Federal Reserve System and hence must hold their reserves in cash at the Federal Reserve Bank, or in vault cash. The required reserves on deposits are accounted for in the user cost calculations for - 106 -depo s i t s below. These reserves are the property of the Federa l Reserve Bank and do not have an opportunity cost to the bank as in (5.28) because of the p r o h i b i t i o n on use of t h i s cash. Fu r t he r , s i n ce the cost of reserve requirements i s accounted for by type of d e p o s i t , a double count ing a r i s e s i f the cost i s a l so a s c r i bed to ca sh . For example, the user cost of demand depos i t s inc ludes the cost of the reserve requirements on such depo s i t s , to be held i n cash. 5.5.3 Demand Depos i t s The user cost on the j t h type of depos i t i s c a l c u l a t e d accord inq to (3.3) which i s , _ (1 - k. + r. - s. + b.) u. = -(1 - k.) + ' ^ I R ) J j=DD,TD (5.29) 1 + r. + b. + Rk. - s. - 1 + f J j J .71 wi th DD and TD r e s p e c t i v e l y denotinq demand and time d e p o s i t s . In the case of depo s i t s , ra ther than r e c e i v i n g i n t e r e s t , the f i n a n c i a l i n s t i t u t i o n pays i n t e r e s t . I n te re s t payable by the bank i s denoted by r^. The depos i t insurance r a t e , b^, i s expressed i n terms of a premium ra te per d o l l a r of depo s i t . The reserve requirement r a te fo r the j t h type of depos i t i s k., wh i le s^ i s the s e r v i c e charge ra te that an average d o l l a r of depos i t j y i e i d s to the bank per time p e r i o d , w i th R being the discount r a t e . For most of the sample pe r i od , 1973 to 1978, f e d e r a l l y insured f i n a n c i a l i n s t i t u t i o n s were p r o h i b i t e d from paying i n t e r e s t on demand d e p o s i t s . Negot iab le orders of withdrawal (NOW) accounts , which are - 107 -essentially demand deposits with interest payments, were authorized in only a few states. Massachusetts and New Hampshire were f i r s t permitted to offer NOW accounts on January 1, 1974. Authorization to issue NOW accounts was extended to similar institutions throuqhout New England on February 27, 1976, and in New York State on November 10, 1978. Our study considers banks in New York and New 3ersey which are located in Federal Reserve District 2. For those banks which reported NOW interest expense in 1978 we used for r^p the actual interest expense incurred. For the rest of the sample equalled zero. The FCA data include information on the dollar amount paid for Federal Deposit Insurance Corporation (FDIC) premiums on demand deposits. These are converted to a premium rate by dividing their dollar value by total demand deposits dollar volume. Information on reserve requirements comes from the Federal Reserve  Bulletin. Demand deposits subject to reserve requirements are gross demand deposits minus cash items in process of collection and demand balances due from domestic banks. Demand deposit balance data in the FCA are these net balances. Reserve requirement schedules are graduated, and each deposit interval applies to that part of the deposits of each bank. The reserve requirement schedules for the period 1973 to 1978 have been compiled in Table 5.11. For those years in which reserve requirements changed, an averaqe reserve requirement is calculated to apply to average demand deposits listed in the FCA data. These are in Table 5.12. Income is earned on demand deposits by levying service and penalty charges. The service charge rate on demand deposits is calculated by dividing this income by total demand deposits. - 1 0 8 -TABLE 5.11 Reserve Requirements on Demand Deposits of Member Banks November 1972 - December 1978. (Deposit Intervals are in Millions of Dollars. Requirements are in percent of deposits.) Effective Net Demand Deposits ($M.) Date 0-2 2-10 10-100 100-400 over 400 1972 - November 9 8 10 12 16.5 17.5 November 16 - - - 13 -1973 - Duly 19 - 10.5 12.5 13.5 18 1974 - December 12 - - - - 17.5 1975 - February 13 7.5 10 12 13 16.5 1976 - December 30 7 9.5 11.75 12.75 16.25 Requirements in effect 1978 - December 31 7 V.5 11.75 12.75 17.25 Sources: Federal Reserve Bulletin, Board of Governors of the Federal Reserve System, Washington, D.C. 20551, No. 1, Vol. 62, January 1976, p. A7 and No. 1, Vol. 65, January 1979, p. A9. - 109 -TABLE 5.12 Reserve Requirements on Demand Deposits of Member Banks, Average Annual (Deposit Intervals are in Millions of Dollars. Requirements are in percent of deposits). Year Net Average Yearly Demand Deposits ($M.) 0-2 2-10 10-100 100-400 over 400 1973 8 10.25 12.25 13.25 17.75 1974 8 10.5 12.5 13.5 18 1975 7.5625 10.0625 12.0625 13.0625 16.625 1976 7.5 10 12 13 16.5 1977 7 9.5 11.75 12.75 16.25 1978 1 7 9.5 11.75 12 16.25 ... _ i TABLE 5.13 Demand D e p o s i t S t a t i s t i c s T h r e e Sample Y e a r s Variable Mean Standard Deviation Minimum Maximum Penalty rate, (PEN/DD)1 0.1657 0.1438 0 0.6060 FDIC Insurance premium rate 1 (FDIC/DD) 0.0347 0.0062 0.0110 0.0400 Reserve effect (R*RESREQ)1 0.5547 0.0775 0.4589 0.7947 Service charge rate (SERVJ/DD1 0.6128 0.2917 0.1760 1.322 Return on $1 of demand deposit2 0.9981 0.0043 0.9866 1.0061 Return on $1 discounted3 0.9553 0.0041 0.9443 0.9630 Quantity of demand deposits,^DO 107.68 153.39 3.845 422.07 User cost of demand deposits,1  UDD -4.4662 0.4100 -5.567 -3.7054 19 7 5 Variable Mean Standard Deviation Minimum Maximum Penalty rate, (PEN/DD)1 0.1957 0.1376 0.036 0.6285 FDIC Insurance premium rate 1 (FDIC/DD) 0.0410 0.0030 0.0343 0.0463 Reserve effect (R*RESREQ)1 0.5502 0.0521 0.4632 0.6014 Service charge rate (SERVJ/DD1 0.6301 0.2962 0.17505 1.422 Return on $1 of demand deposit2 0.9977 0.0042 0.9854 1.0037 Return on $1 discounted3 0.9538 0.0040 0.9420 0.9596 Quantity of demand deposits,1*DO 101.62 142.61 3.457 388.97 User cost of demand deposits,1  UDD -4.6253 0.4047 -5.7973 -4.0451 111-•able 5.13 continued 19 7 8 Variable Mean Standard Deviation Minimum Maximum Interest rate, (NOWINT/DO)1 0.0006 0.0014 0 0.0046 FDIC Insurance premium rate 1 (FDIC/DD) 0.0392 0.0035 0.03235 0.0449 Reserve effect (R*RESREQ)1 0.4750 0.0660 0.3831 0.6553 Service charge rate (SERVJ/DD1 0.7167 0.3309 0.2158 1.6776 Return on $1 of demand deposit2 0.9980 0.0036 0.9884 1.0046 Return on $1 discounted3 0.9593 0.0035 0.9501 0.9656 Quantity of demand deposits,**DD 110.41 150.48 4.065 400.86 User cost of demand deposits,1  UD0 -4.071 0.3495 -4.991 -3.436 'Percent. Return on $1 of Demand deposits = {1 - (N0WINT/D0) + (FDIC/DO) + R*RESREQ - ((SERV + PEN)/DD)}. 3Return on $1 discounted = {1 - (N0WINT/DD) + (FDIC/DD) + R*RESRE( (SERV • F-N)/DD}/(1 + R). ^Millions of dollars - ]}? -The user cost of demand deposits is calculated as follows: u D D = - l + { i+(NnwiNT / n n ) + (FDIC/OD) + R*RESREO) -(SERV+PEN)/D0) }/(HR) (5.30) where DD is total demand deposits, M0W1NT/DD is the interest rate payable by the financial institution, FDIC/DD is the insurance premium rate, RESREQ is the reserve requirement as in Table 5.12 and (SERV+PEN)/DD is the service charge rate on an average dollar of demand deposits. The data for demand deposits are tabulated in summary form in Table 5.13 for three sample years. The user cost for demand deposits is always negative for each bank in all years of the sample, hence demand deposits are an output from the financial firm viewpoint. Even when a zero discount rate is used, negative user costs are obtained, so this result is robust to the discount rate. It is contrary to several papers in the literature, notably Mullineaux [1978] who estimates a profit func-tion using demand deposits as an input. This indicates the importance of having a criterion for determining whether financial goods are inputs or outputs. 5.5.4 Time Deposits During the sample period 1973 to 1978, Requlation Q was in effect. This sets an upper bound for the interest rate payable on time and savings deposits by member banks. These maximum rates are established by the Board of Governors of the Federal Reserve System, and are in Table 5.14. The FCA data include the interest expense paid to holders of time deposits at each bank. An interest rate is obtained by dividing the interest expense by the dollar volume of time deposits. Maximum Interest Rates Payable on Time and Savings Deposits at Federally Insured Commercial Banks (percent per annum) - 113 -Type and Maturity of Deposit On Effect Dec. 31/1978 Previous Maximum Percent Effective Date Percent Effect i v e Date 1. Savings Other time deposits (multiple & single maturity unless otherwise indicated) 30 - 89 days 5 7/1/73 4.5 1/21/70 2. Multiple-maturity 3. Single-maturity 90 days to 1 year 5 7/1/73 4.5 5 1/21/70 9/26/66 4. Multiple-maturity 5. Single-maturity 5.5 7/1/73 5 7/20/66 9/26/66 6. 1 to 2 years 7. 2 to 2-1/2 years 6 7/1/73 5.5 5.75 1/21/70 1/21/70 8. 2-1/2 to 4 years 6.5 7/1/73 5.75 1/21/70 9. 4 to 6 years 7.25 11/1/73 a -10. 6 to 8 years 7.5 12/23/74 7.25 11/1/73 11. 8 years or more 7.75 6/1/78 b -12. Issued to govern-mental units ( a l l maturities) 8 6/1/78 7.75 12/23/74 13. Individual r e t i r e -ment accounts and Keogh (H.R.10) plans 8 6/1/78 7.75 7/6/77 Between July 1, 1973 and October 31, 1973, there was no c e l l i n g for c e r t i f i c a t e s maturing i n 4 years or more with minimum denominations of $1,000. However, the amount of such c e r t i f i c a t e s that an i n s t i t u t i o n could issue was limited to 5 percent of i t s t o t a l time and savings deposits. Sales ln excess of that amount, as well as c e r t i f i c a t e s of less than $1,000 were limited to the 6-1/2 percent c e i l i n g on time deposits maturing i n 2-1/2 years or more. N o separate account category. S o u r c e : Federal Reserve B u l l e t i n , Board of Governors of the Federal Reserve System, Washi jton, D.C. 20551, No. 1, Vol. 62, January 1976, p. A10 and No. 1. Vol. 65, January 1979, p. A10. - 114 -This interest rate is used to represent the expected interest rate cost of obtaining these funds. The FCA data include information on the dollar amount paid for Federal Deposit Insurance Corporation (FDIC) premiums on time deposits. As was the case for demand deposits, these are converted to a premium rate. This is done by dividing their dollar value by total time deposits dollar volume. The required reserve rate varies not only with respect to the quantity, or dollar volume, of time deposits held, but also with respect to their maturity. The FCA division of the Federal Reserve Bank of New York has calculated the required reserves on time deposits for each bank. The cash and due from banks item in the time deposit function data is equal to required reserves on time deposits plus one percent of such depos i ts . 1 6 Some income is earned on time deposits by levying service charqes 17 and fees. The service charge rate on time deposits is calculated by dividing this income by total time deposits. The user cost of time deposits is U T D = -1 + {l + (TDINT/TD) + (FDICT/TD) + R^RESREOT -(SERVT/TD)}/(UR) (5.31) where TD is total time deposits, TDINT/TD is the interest rate payable by the financial institutions, FDICT/TD is the insurance premium rate pay-able on time deposits, RESREQT is their reserve requirement, and SERVT/ TD is the service charge rate on an average dollar of time deposits. - 115 -The data for time deposits are tabulated in summary form in Table 5.15 for three sample years. The data are s imi lar for the other years in the sample. The user cost for time deposits i s always pos i t ive for each bank in a l l years of the sample. This indicates that time deposits are an input from the viewpoint of the f inanc ia l f i rm. With a zero discount rate a l l of the user costs for time deposits are pos i t i ve for each bank over the sample period, so th i s result is robust. 5.5.5 Non-Deposit L i a b i l i t i e s Total l i a b i l i t i e s represent the sum of deposits, in the form of demand and time categories, and non-deposit l i a b i l i t i e s . The two main categories of non-deposit l i a b i l i t i e s dist inguished in the FCA data are borrowed and purchased funds and other l i a b i l i t i e s . The borrowed money category represents loans made to the bank. Purchased funds refer to federal funds purchased. Other l i a b i l i t i e s are the t o t a l of f i nanc i a l obl igat ions not elsewhere c l a s s i f i e d . The main component i s other deposit funds purchased. The user cost of borrowed and purchased funds i s U = - 1 t {l + BPFINT/BPF} / (HR) (5.32) where BPFINT represents the interest paid by the bank for borrowed and purchased funds, and BPF the to ta l balance outstanding. I f U^ p^ . i s po s i t i ve , th i s category represents an input. The t o t a l expenditure on borrowed and purchased funds i s Uppp *BPF. Analogously, the user cost of other l i a b i l i t i e s i s = - 1 + { 1 + OLINT/OL} / (HR) (5.33) - 116 -TABLE 5.15 Time D e p o s i t S t a t i s t i c s T h r e e S a m p l e Y e a r s 19 7 3 Variable Mean Standard Deviation Minimum Maximum Interest rate (TDINT/TD)1 4.9070 0.3240 4.477 5.515 FDIC insurance premium rate (FDIC/TD) 0.0347 0.0062 0.0110 0.0400 Reserve effect (R*RESREQT)1 0.1557 0.0159 0.1343 0.1782 Service charge rate (SERV/TD)1 0.0151 0.0226 0 0.1000 Return on $1 of time deposit2 1.0508 0.0034 1.0464 1.0572 Return on $1 discounted3 1.0058 0.0033 0.0015 1.0119 Quantity of time deposits,^TD 100.44 108.46 4.60 316.92 User cost of time deposits,1  UTD 0.5794 0.3268 0.1526 1.1906 19 7 5 Variable Mean Standard Deviation Minimum Maximum Interest rate (TDINT/TD)1 5.204 0.2484 4.604 5.612 FDIC insurance premium rate (FDIC/TD) 0.0411 0.0030 0.0343 0.0463 Reserve effect (R*RESREQT)1 0.1725 0.0247 0.1381 0.1964 Service charge rate (SERV/TD)1 0.0159 0.0247 0 0.1091 Return on $1 of time deposit2 1.0540 0.0027 1.0477 1.0584 Return on $1 discounted3 1.0076 0.0026 1.0016 1.0118 Quantity of time deposits,^TD 112.96 117.82 5.10 333.58 User cost of time deposits,1 TD 0.7630 0.2562 0.1623 1.1807 Table 5.15 continued - 117 -19 7 8 Variable Mean Standard Deviation Minimum Maximum Interest rate (TDINT/TD)1 5.073 0.4175 4.0327 5.6856 FDIC insurance premium rate (FDIC/TD)1 0.0392 0.0035 0.0324 0.0449 Reserve effect (R*RESREQT)1 0.1404 0.0150 0.1210 0.1645 Service charge rate (SERV/TD)1 0.0166 0.0261 0 0.1040 Return on $1 of time deposit2 1.0524 0.0043 1.0414 1.0585 Return on $1 discounted3 1.0116 0.0042 1.0010 1.0175 Quantity of time deposits,**TD 117.88 132.15 5.41 425.71 User cost of time deposits, U * TD 1.1565 0.4164 1.0350 1.7512 APercent. Return on $1 of Time deposits = {l • (TDINT/TD) + (FDIC R*RESREQT - (SERVT/TD)}. 3Return on $1 discounted = {1 + (TDINT/TD) + (FDIC/TD) + R*RESREQT - (SERVT/TD)}/(1 + R). ^Millions of dollars. - I I S -where the t o t a l i n t e r e s t paid by the bank in t h i s category i s 0L1NT and the amount of other l i a b i l i t i e s i s OL. Expendi tures are U*OL. Summary data on other l i a b i l i t i e s and borrowed and purchased funds are tabu la ted in Table 5 .16 . 5 .5 .6 Net Loan s The c a l c u l a t i o n of user cost s f o r borrowed and purchased funds and o t h e r l i a b i l i t i e s permits the d e r i v a t i o n o f t he u s e r c o s t o f net l o a n s . F o r l o a n s and i n v e s t m e n t s , t he bank can be e i t h e r a b o r r o w e r or l e n d e r . As l e n d e r , t he bank r e c o r d s l o a n s o f v a r i o u s c a t e g o r i e s and investments on t h e a s s e t s i d e o f t h e b a l a n c e s h e e t . As b o r r o w e r , s i m i l a r f i n a n c i a l c o m m o d i t i e s a r e i n d i c a t e d as l i a b i l i t i e s . Net l o a n s a r e t h e d i f f e r e n c e between t h e two. The net l o a n p o s i t i o n o f the bank i s NLOAN = INV + REML + INSTAL + CRC + COMAOL - EPF - OL. ( 5 . 34 ) Loan and i n v e s t m e n t a s s e t s i n c l u d e s e c u r i t i e s , r e a l e s t a t e m o r t g a g e s , i n s t a l m e n t , c r e d i t c a r d and c o m m e r c i a l and o t h e r l o a n s . L i a b i l i t i e s a r e bo r rowed and pu r cha sed funds and o t h e r l i a b i l i t i e s . T o t a l net r evenue f rom t h e l o a n and i n v e s t m e n t p o r t f o l i o i s EXNLOAN = -UJ..... * INV + U D C *REML + U... * INSTAL + U - D „ *CRC INV RE IN CRC + t l C A 0 *C0MAOL) - (Uppj. *BPF + IJ * 0 L ) ( 5 . 35 ) where t he n e g a t i v e s i q n b e f o r e t he a s s e t c a t e g o r i e s c o n v e r t s t h e u s e r c o s t s t o p o s i t i v e numbers. Hence EXNLOAN i s p o s i t i v e . The u s e r c o s t o f net l o a n s i s UL = EXNLOAN/NLOAN ( 5 . 36 ) o r t o t a l ne t r e venue s d i v i d e d by b a l a n c e s o u t s t a n d i n g . D a t a on t h e u s e r c o s t and b a l a n c e o f net l o a n s , and t h e i r net r e v e n u e s , a r e i n d i c a t e d i n T a b l e 5 . 17 . - 119 -Table 5.16 Borrowed and Purchased Funds and Other L i a b i l i t i e s , Sample S t a t i s t i c s Three Sample Years 1 9 7 3 Mean Standard Dev iat ion Min imum Maximum User Cost, Borrowed and Purchased funds 0.040 0.041 0.012 0.208 Quant i ty, Borrowed and Purchased funds ($m.) 7.040 16.743 0 63.885 User Cost, Other L i a -b i l i t i e s 0.025 0.068 0.018 0.032 Quant i ty , other l i a b i l i t i e s ($m.) 0.923 2.216 0 9.022 1 9 7 5 Mean Standard Deviat ion Minimum Maximum User Cost, Borrowed and Purchased Funds 0.011 0.004 0.0004 0.016 Quant i ty , Borrowed and Purchased Funds ($m.) 10.924 30.670 0 127.640 User Cost, Other L i a b i l i t i e s 0.019 0.010 0.009 0.041 Quant i ty , Other L i a b i l i t i e s ($m.) 6.099 15.087 0 54.061 1 9 7 8 Mean Standard Deviat ion Minimum Maximum User Cost, Borrowed and Purchased Funds 0.035 0.005 0.030 0.042 Quant i ty , Borrowed and Purchased Funds (Sm.) 7.706 18.420 0 68.996 User Cost, Other L i a b i l i t i e s 0.032 0.009 0.012 0.061 Quant i ty , Other L i a b i l i t i e s ($m.) 44.815 67.230 0.517 228.220 - 120 -Table 5.17 Net Loans, User Cost and Q u a n t i t i e s (revenue measured as negative net expend i tu res ) 1 9 7 3 Mean Standard Dev i a t i on Min imum Maximum User Cost s , Net Loans Q u a n t i t y , Net loans ($m.) Revenue, Net loans ($m.) -0.032 202 .440 6.140 0.004 250.310 7.546 -0.037 8.598 0.202 -0.024 728.640 24.556 1 9 7 5 Mean Standard Dev i a t i on Minimum Maximum User Cos t s , Net Loans Quan t i t y , Net Loans ($m.) Revenue, Net Loans ($m.) -0.038 219.960 8.264 0.005 265.190 9.886 -0.048 9.178 0.269 -0.029 800.550 27.230 1 9 7 8 Mean Standard Dev i a t i on Minimum Maximum User Costs , Net Loans Quan t i t y , Net Loans ($m.) Revenue, Net Loans ($m.) -0.047 265.390 6.099 0.005 306.560 8.576 -0.053 10.643 0.302 -0.033 854.110 30.354 - 121 -5.5.7 F i n a n c i a l C a p i t a l On the balance sheet, a l l items i n v o l v i n g user costs are now completed. Assets include f i n a n c i a l goods, and the c a t e g o r i e s included are cash and various loans and investments. F i n a n c i a l assets l e s s f i n a n c i a l l i a b i l i t i e s together are equal to p h y s i c a l assets and shareholders' e q u i t y . The l a t t e r two categories c o n s t i t u t e the c a p i t a l of the bank. Fu r the r , i f f i n a n c i a l assets and l i a b i l i t i e s are repor ted in cur rent d o l l a r s , then t o t a l c a p i t a l i s measured in cu r ren t d o l l a r s . A l s o , s ince t h i s i s a balance sheet i tem, i t i s a s tock . T o t a l c a p i t a l i s CAPITAL = CASH + INV + REML + INSTAL + CRC + COMAOL - BPF - OL - DO - TD (5.37) or cash , loans and investments l e s s borrowed and purchased funds and d e p o s i t s . C a p i t a l in p h y s i c a l and f i n a n c i a l form i s assumed to be f i x e d i n the short run . Th is c a p i t a l d e f i n i t i o n (5.37) i s used i n the e s t i m a t i o n of the model. 5.6 Variable Profits The v a r i a b l e p r o f i t s , or quas i - ren t s f o r each bank i n each year are constructed u t i l i z i n g the c a l c u l a t e d user costs for balance sheet i tems, t h e i r d o l l a r va l ue s , and expenditures on l abo r and m a t e r i a l s . V a r i a b l e p r o f i t IT* i s * * = ~ ' U 1 N V * I N V + U R E * R E M L * » 1 N * I N STAL + U C R C * C R C + U C A Q*COMAOL} - ( U C A S H * C A S H ) - (U D D *™> ) - ( n T D * T D ) - [(EXL + EXM)/(1 + R)] (5.32) where L l ^ y , " p p > l ' [ N ' ' V R C " c A O a r e t : ^ e u s e r c o s t s °f investments, r e a l e s t a t e mortqaqes, instalment loans, c r e d i t card loans and commerc ia l , a g r i c u l t u r a l and other loans r e s p e c t i v e l y . The v a r i a b l e s INV, Rf ML, INSTAL, CRC and COMAOL denote the d o l l a r va lues of investments , r e a l e s t a te mortgages, instalment loans, c r e d i t card loans , and commercial a q r i c u l t u r a l and other loans held on the balance sheet dur inq the H i c k s i an time p e r i o d . The term - { U T *INV + U *REML + U , *INSTAL + INV Kh IN U^R*CRC + U^^COMAOL} represents the net revenue from loans held by the f i n a n c i a l i n s t i t u t i o n . The user costs of borrowed and purchased funds and other l i a b i l i t i e s r e s p e c t i v e l y are U^pp and UQ^' A N C' A N (^ ^ A R E the balances held of these l i a b i l i t y i tems. So t o t a l expend i tu res on these are subt racted from asset loan revenue to y i e l d net revenue from loans and investments. The term -(U^A(.^*CASH) r e f l e c t s the cost of ho ld ing funds i n cash form. S ince demand depos i t s are an output of the f i n a n c i a l f i rm -(U^^DD) i s the net revenue of ho ld ing demand d e p o s i t s . Time depo s i t s are an i npu t , so -(IJ *TD) i s the net cost of ho ld i ng them. The expend i tures on labor and mate r i a l s are denoted by EXL and EXM r e s p e c t i v e l y , and are d i scounted to r e f l e c t the i n t e r p r e t a t i o n that payments are made at the end of each pe r i od . V a r i a b l e p r o f i t s do not inc lude the expend i ture on c a p i t a l because c a p i t a l i s assumed to be f i x e d . Consequently, v a r i a b l e p r o f i t s i n c l ude a l l re tu rns to c a p i t a l , and indeed the e l a s t i c i t y of p r o f i t s to c a p i t a l , and the ra te of return on c a p i t a l can be con s t ruc ted d i r e c t l y . - I,M -The c a l c u l a t e d v a r i a b l e p r o f i t s for each bank in each year are a i l p o s i t i v e . The sample s t a t i s t i c s for each vear are in Tables 5.IS and 5.19, 5.7 Concludinq Remarks Th i s concludes the d e s c r i p t i o n of procedures for c o n s t r u c t i n q the da t a . The data conta in v a r i a b l e p r o f i t s and user cos t s and q u a n t i t i e s f o r f i n a n c i a l and p h y s i c a l qoods. The user cost method on f i n a n c i a l qoods can be qene ra l i z ed to a wider and f i n e r c l a s s i f i c a t i o n than that app l i ed here. On the p h y s i c a l qoods s i de , l abor , c a p i t a l and raw m a t e r i a l s q u a n t i t i e s are a l l adjusted fo r q u a l i t y change. 124 -TABLE 5.18 Sample S t a t i s t i c s V a r i a b l e P r o f i t s ( i n current m i l l i o n s of d o l l a r s ) Year Mean Standard Dev i a t i on Minimum Maximum 1973 5.863 7.705 0.221 23.788 1974 6.468 8.472 0.240 23.968 1975 7.337 9.618 0.253 26.968 1977 7.824 10.529 0.252 29.901 1978 6.099 8.576 0.335 36.168 - 125 -TABLE 5.19 V a r i a b l e P r o f i t s ( i n current m i l l i o n s of d o l l a r s ) Bank Number Year 1973 1975 1978 1 0.9722 1.3403 1 .571 1 2 2.2341 3.0301 3.4816 3 0.3317 0.4429 0.7192 4 2.1091 2.5942 3.0837 6 0.2402 0.2528 0.3168 12 0.8931 1.0258 1.3903 13 1.6276 1.9843 2.1204 14 16.5993 22.5702 16.1216 15 0.7838 0.8623 1.1788 16 8.9842 7.3421 12.2611 19 23.9684 24.2464 19.7758 21 1.6483 1.7289 2.0880 22 22.7611 26.9681 30.3280 23 20.6998 22.9954 22.7969 25 1.6247 1.7934 2.4202 27 2.2408 2.7473 1.7589 28 S.4024 9.8374 10.6488 29 0.2963 0.3043 0.4247 APPEN01X-CHAPTER 5 FUNCTIONAL COST DATA ON CAPITAL A. R u i l d i n q s , f u r n i t u r e , jnd f i x t u r e s 1. "Bank premises " as an asset on ha Lance s hee t 1 a. Entered i s the value of hank premises, f u r n i t u r e and equipment at book value less accumulated d e p r e c i a t i o n or V I I t Z <t> .k .- d. $ k = E (1 -D ) <b k v=1 1=1 V 1 V 1 1 V l v l 1=1 1 v l v i where <J> i s the purchase p r i c e of c a p i t a l qood i of v v i n t aqe , k. i s c a p i t a l qood i of v in taqe v - q u a n t i t v , IV D. i s the accumulated d e p r e c i a t i o n ra te for c a p i t a l qood i , 1=1,...,I A. Included in bank premises: 1. Bank premises that are a c t u a l l y owned by the bank and i t s con so l i da ted s u b s i d i a r i e s and that are e n t i r e l y or p a r t l y occupied (or are to be occupied i f under con s t ruc t i on ) by the bank or i t s branches and con so l i da ted s u b s i d i a r i e s . 2. Leasehold improvements, v a u l t s and f i x e d machinery and equipment. 3. Remodeling cos t s to e x i s t i n g bank premises. ' k. Real e s ta te acquired fo r f u tu re expans ion. 5. Park inq l o t s , whether ad jo i n i nq or not a d j o i n i n g bank premises, that are owned by the bank and that are used by customers or emp] oyees -»f the bank. See Reports of Cond i t i on and Income by S ta te Member Banks of the Federa l Reserve System that Have Only Domestic O f f i c e s that Have Less Than S100 M i l l i o n i n T o t a l A s se t s , [1978], p. 22 - 127 -R. Included in f u r n i t u r e and f i x t u r e s : 1. A l l movable f u r n i t u r e and f i x t u r e s of the bank, i t s branches, and i t s conso l idated s u b s i d i a r i e s . 2 . The amounts assigned to leases acqu i red in purchase and assumpt ion t ransact ions. 3. The amount of s tocks , bonds, or other assets that i n d i r e c t l y represent hank premises or f u r n i t u r e and of non-major its-owned cornorat ions. C. D e p r e c i a t i o n : 1. Any method of dep rec i a t i on conforminq to acceptab le account ing p r i n c i p l e s may be used. D. Cost 1. Amount reported should represent the amount before deduct ion of mortgages or other l i e n s . 2. Occupancy Expense of Bank Premises, Net a. Th i s item r e f l e c t s the net expense (or i n some cases net income) of bank premises occupancy. The amount of "occupancy expense of bank premises, net " represents the gross occupancy expense of bank premises l e s s r e n t a l income. A. The gross occupancy expense of bank premises i n c l u d e s : 1. Compensation ( i n c l u d i n g supplementary b e n e f i t s ) of those o f f i c e r s and employees of the bank and i t s con so l i da ted s u b s i d i a r i e s who spend the major p r opo r t i on of t h e i r working time on bank b u i l d i n q and r e l a t e d "housekeeping" f u n c t i o n s . 2 . Normal and recu r r i ng dep rec i a t i on or j m o r t i7 a t ion charges app l i c ab l e to the current: pe r i od , whether represent ing d i rec t reduct ions in the c a r r y i n g va lue of the a s se t s , i nc lud ing c a p i t a l lease a s s e t s , or add i t i o n s to accumulated d e p r e c i a t i o n or a m o r t i z a t i o n accounts. 2See Ibid., p. 70. - P s -3. Ord inars i v na i rs to hank premi ses and leaseho ld improvement $, and the c>st i f leasehold i i n n n i v c n t c i i t r. not placed o n the bank ' s hooks as an a s se t . 4. M l current expenses, not included above, connected with the use o f bank premises, e . g . , the cost o f heat, e l e c t r i c i t y , water, ou t s ide . jan i tor s e r v i c e s and s upp l i e s , f i r e insurance. 5. A l l operat ing lease rents paid on bank premises and park ing Lots. 6. i n t e r e s t on mortgages, Liens or other encumbrances on bank premises owned, i n c l ud i n g the po r t i on of c a p i t a l lease payments represent ing i n t e r e s t expenses, but not such expense on " r e a l e s t a t e " other than bank premises. 7. A l l property and other taxes paid or accrued r e l u t i n q to bank premises and leaseho ld improvements. 8 . Any po r t i on of c a p i t a l lease payments r ep re sen t i ng executory cos t s e.g. insurance, maintenance, and taxe s . H. Renta l Income Inc ludes : 1. A l l r en t a l s charged for the use of b u i l d i n g s not i nc ident to the use of the premises by the r epo r t i n g bank, and i t s con so l i da ted s u b s i d i a r i e s . a. r e n t a l s from regu la r tenants of the bat ik ' s b u i l d i n g . b. shor t - term r e n t a l s of other bank f a c i l i t i e s except safe depos i t boxes. 3. F u r n i t u r e and Equipment Expense a. Inc ludes: A. Normal and r e cu r r i n g dep rec i a t i on or amo r t i z a t i on charges a p p l i c a b l e to the report pe r i od , whether represent inn d i r e c t reduct ions in the ca r r y i n g value of the assets i n c l u d i n q c a p i t a l lease as set s , or add i t i o n s to accumulated d e p r e c i a t i o n or amor t i z a t i on accounts . 3 See I b i d . , p. 71. ]?.? -B. A l l operjti.no, lease rents paid on o f f i c e machines, i nc l ud ing data process ing equipment. C. Ordinary r epa i r s to f u r n i t u r e and o f f i c e machines, i n c l ud i n g s e r v i c i n g co s t s . 0. The po r t i on of c a p i t a l lease payments represent ing i n t e r e s t expense and executory c o s t s . E. Taxes on f u r n i t u r e and equipment. - 130 -NOTES 1 F u n c t i o n a l C o s t A n a l y s i s - Average Banks [1979] p. i . 2 I b i d . , p. 18 3 T h e T o r n q v i s t s p e c i f i c a t i o n f o r c o n s t r u c t i n g s u b a g q r e q a t e s and i t s r e l a t i o n t o f l e x i b l e f u n c t i o n a l forms i s d e v e l o p e d i n D i e w e r t [ 1 9 7 6 ] . The same p r i c e s a re used i n the n a t i o n a l a c c o u n t s . See Survey  o f C u r r e n t B u s i n e s s [ 1 9 7 7 ] , The N a t i o n a l Income and P r o d u c t A c c o u n t s o f  t h e U n i t e d S a t e s 1929-74 [ 1 9 7 5 ] , and W h o l e s a l e P r i c e s and P r i c e Indexes",  Supp lement [ 1 9 7 4 - 1 9 7 8 ] , 5 S e e T a b l e 7.12 ' I m p l i c i t P r i c e D e f l a t o r s f o r P e r s o n a l Consumpt ion E x p e n d i t u r e s by Type o f P r o d u c t ' , S u r vey o f C u r r e n t  B u s i n e s s , S upp l emen t , 3u l y 1981 , p. 6 7 . 6 T h e model w i l l use economic d e p r e c i a t i o n r a t e s . •7 F o r more d e t a i l e d i n f o r m a t i o n see t h e A p p e n d i x t o C h a p t e r 5. o S t r u c t u r e s c a p i t a l i n c l u d e s s t r u c t u r e s , l a n d and f i x e d e q u i p m e n t . F u r n i t u r e and equ ipment c a p i t a l r e f e r s t o moveab le f u r n i t u r e and equ i pmen t . Q S p e c i f i c a l l y , t h e 1942 e d i t i o n o f B u l l e t i n F o f t he T r e a s u r y D e p a r t m e n t . 1 0 8 5 p e r c e n t o f B u l l e t i n F l i v e s . ^ T h e h a l f - l i f e f o r a g e o m e t r i c s e r i e s i s e q u a l t o 1 / d n > hence d = 2/L . H u l t e n and Wyko f f [ 1977 ] e s t i m a t e d economic d e p r e c i a t i o n f o r n n v a r i o u s t y p e s o f s t r u c t u r e s used i n the U.S. m a n u f a c t u r i n g s e c t o r . I n most c a s e s they found t h a t a c o n s t a n t g e o m e t r i c r a t e o f d e p r e c i a t i o n c o u l d a p p r o x i m a t e t he economic d e p r e c i a t i o n w e l l , w i t h the e x c e p t i o n o f t h e e a r l i e s t y e a r s o f t h e a s s e t l i f e . 1 2 The d e c i s i o n t o c l o s e down and have a z e r o p r o d u c t i o n l e v e l i n t h e s h o r t run may depend on q u a s i - f i x e d c o s t s o r s p e c i f i c c o s t s a s s o c i a t e d w i t h c l o s i n g o r o p e n i n g . T h i s i s p a r t i c u l a r l y t he c a s e where t h e bank e x p e c t s n e g a t i v e v a r i a b l e p r o f i t s to o b t a i n as a t e m p o r a r y s h o r t te rm phenomenon. Among t h e s e c o s t s a r e s e v e r a n c e pay and d i s c h a r g e c o s t s f o r emp l o yee s , l e a s e p e n a l t i e s and t h o s e f o r a s s e m b l i n g and m a i n t a i n i n g a s k i l l e d work f o r c e . G i v e n t he r e g u l a t o r y and a d m i n i s t r a t i v e c o s t s o f o p e n i n g a bank, t h e s e may be a v o i d e d by o p e r a t i n g w i t h s h o r t term n e g a t i v e v a r i a b l e p r o f i t s . These i s s u e s a r e r e c o g n i z e d , bu t no d a t a a r e a v a i l a b l e t o q u a n t i f y t h e s e c o s t s . - 131 -The time depos i t rate for each bank m each year i s a l so t e s t e d . Those bdnks with a hiqh propor t ion of c e r t i f i c a t e s of deposit have d high time depos i t rate and quas i - ren t s for these i n s t i t u t i o n s ar negat ive us ing the time depos it rate as the d i scount r a t e . 1 4 S e e Func t i ona l Cost Ana ly s i s [1978], p . 10. 1 5 I b i d . , p. 19b. 1 6 S e e Federa l Reserve B u l l e t i n [1979]. See Func t i ona l Cost Ana l y s i s [19781, p. 8. - H i -CHAPTER 6 SPECIFICATION AND HYPOTHESIS TESTING 6.1 I n t r o d u c t i o n The e s t imat ina system c o n s i s t s of a p r o f i t f u n c t i o n and a s c r i e s of net suppLies for outputs and inputs. The convention adopted is that p o s i t i v e net supp l i e s obta in for outputs and negat ive net supnLies for i npu t s . A l t e r n a t i v e l y , i f a l l q u a n t i t i e s of inputs and outputs are def ined to be non-neoat ive, neqative user costs ob ta in for outputs and p o s i t i v e user cos t s for i npu t s . Hence net demands for outputs are neqa-t i v e , and net demands f o r inputs p o s i t i v e . The former convent ion y i e l d s non-neqat ive p r i c e s , the appropr ia te form for s p e c i f i c a t i o n and t e s t i n g w i th a v a r i a b l e p r o f i t f u n c t i o n . Sec t i on 2 develops the e s t imat ing system. There i s a p r o f i t func-t i o n and net supp l i e s fo r two types of v a r i a b l e p h y s i c a l input , namely labor and raw ma te r i a l s or in termediate i npu t s . P r o f i t a l so depends on the quan t i t y of c a p i t a l , assumed f i xed dur inq the d e c i s i o n p e r i o d . There are four types of f i n a n c i a l commodities: ( i ) loans, ( i i ) cash, ( i i i ) demand depos i t s and ( i v ) time depo s i t s . Whether these four are inputs or outputs i s not known a p r i o r i , but the s iqn test applied • •> t he l a t a , is i n d i c a t e d in Chapter 5, concludes that a l l sample points are uniguelv c l a s s i f i a b l e . The nonparametric siqn test shows that loans and demand depo s i t s are outputs of the banks throughout 1 q 7 l - r ? 7 R , while cash and time depos i t s are i npu t s . The p r o f i t f u n c t i o n , two p h y s i c a l input demands and two f i n a n c i a l input demands and the loans and demand depos i t s upp l i e s c o n s t i t u t e seven equat ions . S ince v a r i a b l e p r o f i t s or quasi-- U:> _ rent s .ire defined .is the d i f f e r e n c e between revenues fro " t f i n . i n c i . i l . o u t -puts and expenditures on v ar i able f i n a n c i a l and ph\s i c a l i nputs , there is a L inear dependence, reducino the system to s i x indepeudent equat ions . Sect ion 3 descr ibes the s t r uc tu re of t e s t s on the e s t i m i t i n g equa-t i o n s . The v a r i a b l e p r o f i t funct ion is s p e c i f i e d to have the transLoq form, with the Logarithm of p r o f i t s quadrat i c in the Logarithm of p r i c e s of v a r i a b l e qoods and q u a n t i t i e s of f i xed goods. The f i r s t group of t e s t s determines whether the p r o f i t f unc t i on and the net supp l i e s s a t i s f v some r e g u l a r i t y c o n d i t i o n s . The f i r s t is eguaLity and symmetry. For the t r a n s l o g f u n c t i o n , i t i s regu i red that the second order mat r i x of p a r t i a l d e r i v a t i v e s w i th respect to p r i c e s be symmetric. The e g u a l i t y r e s t r i c -t i o n s are between the demand func t i on s and the v a r i a b l e p r o f i t f unc t i on parameters. Under symmetry and eguaL i ty , the var iabLe p r o f i t f unc t i on may be obta ined by i n t e g r a t i n g the net supply f u n c t i o n s . A f u r t he r regu-l a r i t y te s t i s for monoton ic i t y , that increases in input p r i c e s reduce p r o f i t s , and increases in output p r i ce s increase p r o f i t s . 1 \ te s t for convex i t y of the p r o f i t f unc t i on in p r i ce s i s d e t a i L e d . Tests for monoton ic i t y and convex i ty are der ived both at a Local po int of approx imat ion and for a l l the data in the sample. The l a t t e r are sample-wide te s t s of convex i ' y and monoton ic i t y . These require " v a l u -a t i o n at each data po i n t . Once the r e gu l a r i t y t e s t s are performed, the s t r u c t u r e o f bank inn technology can be examined in more d e t a i l for t e s t s on performance and behav io r . This inc ludes t e s t s on response of banks to monetary poLicy and t e s t s on the ex i s tence of monetary subaggregates. For example, the - in -ex i s t ence of var ious d e f i n i t i o n s of nones depends on whether cash, demand depo s i t s and time depos i t s can be aqgreg at ed. The r<>lev .ml Vest for s e p a r a b i l i t y i s whether the r e l a t i v e user costs of an\ pai r of f inane i a l commodities w i t h i n a subaqqreqate is independent of the quant i t y of r i \ commodity ou t s i de i t . The t»*sts for ex i s tence of monetary subaqqreqat "s are desc r ibed in sec t i on 4, point inq to the mos: important potent, i a l po l i c y a p p l i c a t i o n s of the model. P r i o r e s t imat i on s t r u c t u r e s for the p o r t f o l i o s of f i n a n c i a l i n s t i t u t i o n s (Pa rk in [1970], Berndt and McCurdy [1990] ) , apart from incomplete con s t r uc t i on of user c o s t s , do not i n t e -g rate the markets for f i n a n c i a l commodities with those for other inputs such as l abo r , c a p i t a l and raw m a t e r i a l s . In s e c t i on 5 some econometric i ssues are de s c r i bed , together with the e s t ima t i on procedure. The data involve l o n g i t u d i n a l obse rva t ions on the f i n a n c i a l performance of banks in the New York Fede ra l Reserve D i s t r i c t over 1973 - 1978. There e x i s t s the p o s s i b i l i t y of sys temat ic bank e f f e c t s , a f f e c t i n g the l e ve l s of p r o f i t s and net s u p p l i e s . The s t r u c t u r e of e s t ima t i on with bank e f f e c t s i s developed. The other p r i n c i p a l econometric issue i s the p o t e n t i a l presence of contemporaneous cova r i ances w i t h i n each hank, in the d i s turbance terms. 6.2 Profit Function and Net Supplies The bank has a technology i nvo l v ing two outputs , loans, and demand d e p o s i t s , and f i v e input s , namely cash, time depo s i t s , l abor , c a p i t a l and raw m a t e r i a l s . User cost s of a l l v a r i a b l e goods are p o s i t i v e . Q u a n t i t i e s of v a r i a b l e outputs are a l so p o s i t i v e , and q u a n t i t i e s of v a r i a b l e input s negat ive . The q u a n t i t i e s and p r i c e s of these commodities a re : - 134 Uj) loans: service quant ity and user cost per unit of s e r v i ce (x^, U^) demand depos i t s : s e r v i ce quant i ty and user cost per un i t of serv ice (x^, U^) cash: s e r v i ce quant ity and user cost per un i t of s e r v i ce (x^, U^) time depo s i t s : s e r v i ce quant i ty and user cost per un i t of serv ice (x^, IJ^) l abo r : e f f i c i e n c y un i t s of p roces s inq and manager ia l l abo r , and wage per e f f i c i e n c y u n i t . (x^,, Ug) in termediate inputs and raw m a t e r i a l s : e f f i c i e n c y index and p r i c e per un i t of s e r v i c e w i th c a p i t a l f i x e d dur ing the per iod of product ion at l e v e l x^. The ob se r va t i on s are a l so indexed by bank and year, but these are suppressed for n o t a t i o n a l convenience. Among the f i n a n c i a l commodities X j , . . . , x ^ , the s ign t e s t fo r the sample i n d i c a t e s loans and demand depos i t s c o n s t i t u t e output s . whiLe cash and time depos i t s c o n s t i t u t e i npu t s . Net loan revenue x^Uj i s non-negat ive wh i l e the analogous demand depos i t term i s x-,U^ • Expendi tures on cash and time depos i t s are X..U-, and x, U, and these are 3 3 4 4 4 negat ive s i nce inputs are measured nega t i ve l y . Hence 7. \.:> v i e Ids i = i ! p r o f i t from f i n a n c i a l ope ra t i on s . The s ub t r a c t i on of physical input co s t s f o r l abo r and raw mate r i a l s y i e l d s v a r i a b l e p r o f i t s as 1 1 5 -and t h i s i s the dependent v a r i a b l e in the \ a r i a b l e p r o f i t f u n c t i o n . i n -v a r i a b l e p r o f i t f unc t i on i s ir + ( U , \ ) where II = (IJ . , . . . ,l I.) c o n s t i t u t e s k I n the vector of user cos t s for v a r i a b l e commodities. The t r an s l oq s p e c i f i c a t i o n for the v a r i a b l e p r o f i t f unc t i on i s , where a and g w i th appropr ia te sub sc r i p t s denote parameters 6 6 6 Jlnir* = a + E a. fcnU. + a, Inx + 1/2 E E 0 £ntl 2nlJ 0 1 = ] v i K K 1 = 1 J = 1 i i i t + I 3 . K £nl). £nx K + 1/2 B K | <( £ n x R ) 1 . (6.2) A property of such a f unc t i on i s homogeneity of deqree one in p r i c e s of v a r i a b l e inputs and outputs imply ing the r e s t r i c t i o n s E a. = 1 ' < r>\ and 6 E 8 = 0 f o r i = 1 , . . . f 6. (6.4) .1=1 J The output share supp l i e s of loans and demand depos i t s are The exp lanatory v a r i a b l e s are the user costs of f i n a n c i a l commodit ies, l abor and raw m a t e r i a l s , in logar i thms, and the l oga r i thm of the quant i ty of c a p i t a l . 136 Demand shares fo r inputs are 3* Tf * aInTr- - i p r = a i * ^  3..4nU t . i = l , . . . , 6 (6.6> r e s p e c t i v e l y fo r cash, time depos i t s , Labor and raw m a t e r i a l s . Also 9 An ir*/9fcnU. i s neqat lve for inputs , with x^ measured neqa t i veLv . The equat ions ( 6 . 2 ) , (6.5) and (6.6) c o n s t i t u t e the e s t ima t i n g system. From these seven, i t i s p o s s i b l e to est imate the p r o f i t f u n c t i o n . Excluded i s the ma te r i a l s demand share, reducing the number of e s t ima t i n g equat ions to s i x , s ince the seven equat ion system i s depen-dent. However, a l l parameters i n vo l v i n g m a t e r i a l s can be recovered, g iven the r e s t r i c t i o n s imposed by (6.3) and (6.4) f o r l i n e a r homogeneity. 6.3 Regularity Restrictions The f i r s t set of t e s t s i s to determine whether the v a r i a b l e p r o f i t f u n c t i o n and i t s a s soc ia ted supp l i e s obey c e r t a i n r e g u l a r i t y c o n d i t i o n s . I f these are s a t i s f i e d , t e s t s on the ex i s tence of a monetary subuggre-gate, and bank behavior with respect to monetary p o l i c y can both he examined. The v a r i a b l e p r o f i t f unc t i on has ?% f ree parameters once the l i n e a r homoqeneity r e s t r i c t i o n s i n (6.3) and (6.4) are imposed. F u r t he r , the parameters est imated in the v a r i a b l e p r o f i t f unc t i on (6.2) need not be i d e n t i c a l to those i n the net supply f unc t i on s (6.7) below: ^hJT=X-P-= Y i + \ 6 i j ' " " j + 5 i K £ n X K i = l 1=1 1 - 137 -The v a r i a b l e p r o f i t f unc t i on s a t i s f i e s the t r an s l o g p roper ty of symmetry i f 6 ^ = 6 ^ i , j = l , . . . ,6. (6.8) Aga in , i n e s t ima t i on only f i v e of these equations are used. The f i v e supply equations have seven parameters each, or 35 i n t o t a l . The symmetry r e s t r i c t i o n s (6.8) are ten i n number. I f both symmetry and e q u a l i t y o b t a i n , then, " i = Y i - « l . j - l 5 (6.9) g = <5 i K i K and there are 35 such r e s t r i c t i o n s . The s a t i s f a c t i o n of a l l of these cond i t i on s imp l i e s that the p r o f i t f unc t i on may be obta ined by i n t e g r a t i n g the supply f u n c t i o n s . The next sequence of t e s t s i n the de te rm ina t i on of r e g u l a r i t y p r o p e r t i e s i s f o r monoton ic i ty and convex i ty i n p r i c e s . Mono ton i c i t y r equ i r e s that the p r o f i t f u n c t i o n be i n c r ea s i n g i n output p r i c e s and decreas ing i n input p r i c e s . For the t r an s l o g s p e c i f i c a t i o n , the form under l i n e a r homogeneity may be viewed as a second order l o c a l approx imat ion around the po int u n i t y . The homogeneous of degree one ve r s i o n approximates TT*(U,X ) around U=l, f o r U = (U ,... ,U ) and x = 1, K 1 6 K w i t h Jlnu = 0 and £nx =0 . At the same t ime, the t e s t s of monoton i c i t y JT\. and convex i t y are a l so developed fo r a l l po s s i b l e data p o i n t s , once the parameters are e s t imated . - 13ft -L o c a l monotonic i ty at the point of expansion i s te s ted by o, , a 2 > 0 a 3 , a , a , a < 0 . (6.10) Th i s te s t fo r monotonic i ty does not reduce the number of parameters in the v a r i a b l e p r o f i t f u n c t i o n , but r e s t r i c t s the parameter space. The sample-wide tes t of monotonic ity requ i re s that output and demand depos i t revenues be p o s i t i v e . S ince the input expend i tu res are expressed neqa t i ve l y in ( 6 .7 ) , sample-wide monoton ic i ty i s determined from x .U./n* > 0 i=1,2 l l ' - x . U i / i r * > 0 i=3 ,6. (6.11) These are not parametr ic r e s t r i c t i o n s , and thus cannot be subjected to s t a t i s t i c a l i n f e r ence . The remaining r e g u l a r i t y c o n d i t i o n i s convex i ty i n p r i c e s . As i n the case of monoton i c i t y , there are l o c a l at the expansion po int and sample-wide v a r i a n t s . In both cases, the Hessian mat r i x of second d e r i -v a t i v e s must have p r i n c i p a l minors a l l non-negat ive. The Hess ian mat r i x has t y p i c a l element a 2 * 3x. 3 n l H.. i , j = 1 , . . . , 6 . (6.12) 3U.3IJ. ~ 3IJ. " " i j i J .7 The l i n e a r homoqeneity makes the Hessian matr ix s i n q u l a r , and one row and column can be der i ved from the remaining elements. Th i s Hess ian mat r i x has element, sca led by the p o s i t i v e f a c t o r ir*/U.u\, w i th the t r an s l oq form - 139 -e (e - 1) + S i - J H - i,j=l,...,6 (6.13) V i + hi where e^ = X ^ U ^ /TT*, the ratio of expenditures on good i to variable profits. This is derived in the Appendix, together with the Hessian for an arbitrary variable profit function. When [U] = 1 and x^ = 1, e^ = a^, and the in (6.13) are para-meters. The scaling factor T T * / U ^ U J = exp (CQ)» is also constant, at this point. Hence convexity at the point of expansion is tested by the requirement M > 0 i=l,...,6 (6.14) where are the principal minors of the Hessian matrix {H }. Since this depends only on parameters, s t a t i s t i c a l inference can be applied in theory. Sample-wide convexity can be "tested" i f the principal minors of H are non-negative. At each sample point, the are obtained from the equations (6.13). This completes the regularity tests, summarized in Table 6.1. 6.4 Tests of Bank Technology 6.4.1 Introduction The prior set of restrictions determines the regularity of the variable profit function. The more relevant tests for policy purposes concern the existence of monetary subaggregates and whether technologies excluding financial commodities or having incomplete user cost computa-tions are valid representations of bank production. - 140 -Table 6.1 Test S t r u c t u r e , R e g u l a r i t y Cond i t i on s (with l i n e a r homogeneity r e s t r i c t i o n s de le ted) E q u a l i t y 8. . = <$. . i , j = 1 , . . . , 5 ( I n t e g r a b i l i t y ) 4. Convexity ( i n p r i ce s ) Expansion po int _> 0 Free Parameters 1. U n r e s t r i c t e d 63 2. Symmetry 6.. = 6.. 53 3. Symmetry & a i = Y i i » j=1 , . . . » 5 35 r e s t r i c t i o n s 28 4. Monoton ic i ty Expansion po int >^  0 i=1,2 a . < 0 i=3 , . . . ,5 l — ' ' Sample-wide xM.J-n* >_ 0 i=1,2 - x i U i/ir* >_ 0 i=3, . . . ,5 28 (U , X ( < ) = 1 28 Sample-wide M^ _> 0 i=1,. . . ,5 (any U,x K ) •Note: Sample-wide monoton ic i ty and convex i ty are not based on parametr ic r e s t r i c t i o n s . A l s o , one of the v a r i a b l e goods i s removed, g iven l i n e a r homogeneity. - H I -Any tests for subaggregates are subject to the problem raised in Blackorby, Primont and Russell [1977, 1978], There i t is shown that the test of weak separability in the translog is a joint one, simultaneously requiring a linear logarithmic form. The linear logarithmic subaggregate implies that the form has extremely restrictive substitution possibili-t i e s . Further, because a structure may exhibit weak separability without being linear logarithmic, tests imposing both jointly are likely to lead to rejection of the former when it is true. Woodland [1978] has proposed a partial solution, namely to express the variable profit function as 1 1 2 2 2 ir*(f (U ),f (x )) where x denotes the quantities of goods included in, and U the prices of goods excluded from the subaggregate. Then i f a 2 2 1 1 subaggregate f (x ) exists, and f (U ) is the index of the remaining goods, £nir*(U1 ,x2) = *nf 1(U 1) + £nf 2(x 2) (6.15) 1 2 3 and neither f (•) nor f (•) need be linear logarithmic. In the translog context this implies that the second order cross terms between members of groups 1 and 2 are zero. There are two main issues in implementation. F i r s t , goods in the subaggregate must appear as x 2 in the variable profit function. For 2 estimation purposes, i f these x commodities are exogenous, the multiple regression model applied to a system akin to (6.7) - (6.9) is free from simultaneous equations bias. Otherwise, a procedure of f u l l information estimation such as three stage least squares is necessary to purge the system of the endogeneity. Second, suppose there Is an alternative - 142 -aggregating structure, for example into I) and x . Then the variable 1 —1 —2 profit function ir*(f (U ), f(x )) is different from the previous case, and there is no method of determining which one represents the data. The test procedures are nevertheless based on this structure, for they have the advantage of not requiring linear logarithmic subaggregates. 6.4.2 Existence of Monetary Subaggregates 6.4.2.1 Introduction > An important issue for monetary control and the effective conduct , 0 of monetary policy is whether the money supply can be aggregated^ There V O A * * ^ * ^ is controversy on what constitutes the money supply, whether narrowly or broadly defined, but less empirical testing on whether these forms exist. 1* If no money subaggregate exists, the notion of adopting a rule at the central bank restricting the growth of some monetary definition may have no practical policy effect on either nominal or real variables. The presence of some monetary subaggregate among financial firms provides an indication as to what should be regulated by the central bank in terms of target control. Since the sample constitutes banks in the same area, administered by the Federal Reserve Bank of New York, and thus the target qroup for monetary control, the tests have important potential policy significance. This research does not examine the rationale for focusing on any one monetary subaggregate, or even whether monetary policy i s effective. Rather, i t provides information on which financial commodities can be viewed as constituting the money supply. If no monetary subaggregate i s - 143 -found to exist, it does undermine to some extent the conduct of monetary policy. The test is applied to the variable profit function of the banks, and corrects for the bias in hypothesis testing for subaggregation aris-ing in using second-order functional forms such as the translog and quad ratic. The presence and existence of a monetary subaggregate requires stringent restrictions, tending to lead to rejections of the hypothesis that a monetary subaggregate exists when the null hypothesis is true. 5 Tests are peformed on whether the monetary subaggregate contains cash only, cash and demand deposits (narrowly defined money), or cash, demand and time deposits. Incomplete data prohibit the construction of definition exactly paralleling M1-B, the target definition of the money supply since 1979. However, this target was not the focus of Federal Reserve policy during the sample period 1973-1978, when narrowly defined money was the object of central bank control. 6.4.2.2 Money Supply Definitions: Cash and Demand Deposits The f i r s t test is for the existence of a money definition includ-ing cash and demand deposits, or M1, an object of monetary control throughout the'sample period. If money under M1 is shown to exist, and be separable from the remaining financial and physical commodities enter ing bank production, then i t is appropriate to examine the conduct of monetary policy. If no M1 construct arises, the entire thrust of mone-tary policy is undermined. f The proposed aggregating structure does not require the money supply to be linear logarithmic. It develops a test in Woodland [1978]. Furthermore, the money supply can be recognized in an intuitive form. - 144 -Let the money components potentially in Ml be predetermined to the financial firm. Then i f these are and x^, cash and demand deposits, the unrestricted variable profit function is TTMU 1, X 2 , X 3 ) = max {u^x 1: xeS, U » 0, x » 0} (6.16) 1 x where a dot denotes an inner product, and (x*,U*) denotes the quantity and price of variable goods other than monetary ones. Also x* > 0 for outputs and x^< 0 for inputs. 6 Since x 2 and x^ are given, both are non-negative. The transformation function is T(x) = 0 and S is the production possibly set. If a money supply containing cash and demand deposits exists, T(x) = T*(f j(x2»x.j), x*). ^ e index is f ^ ( x 2 > x 3 ) which can correspond to narrowly defined money. By the implicit function theorem, the transformation function can be expressed in terms of one of i t s arguments. Selecting the money supply f 1 ( x 2 , x 3 ) = h^x 1) (6.17) or f 1 ( x 2 , x 3 ) -h^x 1) = T(x) = 0. Rearranging, (x 1 )/f 1 (x 2 ,x 3) = 1. Let h^ exhibit constant returns to scale. Under these restrictions (6.16) becomes - 145 -* 1 i l l 1 TT (U ,x 2,x 3) = max{U «x : h^x ) = f^x^x.^)} (6.18) K 1 = gjCU , f 1 ( x 2 , x 3 ) ) = g 1 ( U 1 , l ) f 1 ( x 2 , x 3 ) (6.19) = g*(U 1)f 1(x 2,x 3). (6.20) The equality (6.19) follows the linear homogeneity of h^ : i f f 1 ( x 2 , x 3 ) were changed to Xf^x^x.j) for some X > 0, then because of the linear homogeneity of h^, i t can be seen that the i n i t i a l l y optimal variable profits would be multiplied by X also. Note that linear homogeneity of f^ is not required in order to obtain the decomposition of if* into the expression defined by (6.20). Thus we have generalized the Woodland [1978] test for separability to the case of a nonhomogenous f^. The index g^ has the interpretation of the variable profit per unit of money. This permits a comparison of bank efficiency, through the * levels of g p Under linear homogeneity in user costs, TT^(u* ,x2 ,x3) = f^(x 2,x 3)g^(u^) normalizing on one element. If is selected, * * 1 1 iT^ = -rr^/Ug, g^ = gj^ /Ug and u = U /U^. In empirical applications, i t may be appropriate to normalize user cost or price data and variable profits ex ante. - 146 -Taking logarithms of the normalized variable profit function 1 1 fcrnr^u ,x 2,x 3) = £nf 1(x 2,x 3) + £ng1 (u ) (6.21) which is the sum of one function containing only monetary goods, Inf^ , and another containing the remaining goods. A translog specification of Jin T r^(u\ x^, x 3) yields 1 1 1 1 1 1 inir. = a' + E a. £nz. +1/2 £ E B. . £nz. £nz. (6.22) 1 0 1=1 1 1 i=1 j=1 r J 1 * where z^ , i=1,...,l denotes the mixed prices and guantities (u^, x.,, x 3, u^, u,., u^). 7 If cash and demand deposits constitute money, then (6.20) requires that the second order terms between these and the remaining goods be zero. Hence p} 2 = 0 1=1,4,5,7 (6.23) 3 1. 3=0 or eight parametric restrictions. For estimation, supply equations are added to assist in identifying the parameters. Hence 3£mr x.u. 1 I 1 • = a + E g . £nz. (6.24) *nz. TT l 1J j 1 — 1 y * * • ? * Since cash and demand deposits are exogenous in quantity, an increase in either increases variable profit. The bank does not operate in the short run in a region where this monotonicity condition f a i l s . This implies Sir/Sx^ and 3ir/3x3 are both non-negative. - 147 -The validity of the restrictions (6.23) supports the construction of a money supply of cash and demand deposits. The money supply aggregate in logarithmic form is 1 1 1 2 1 £nf.1 = £nx 2 + Znx3 + 1/2l3 2 2Unx 2) + £nx 2 Inx^ + 1 /26 3' 3(Jlnx 3) 2. The Woodland [1978] test requires the additional restrictions: a 2 + a 3 = 1, 3 2 2 + e 2 3 = 0 and f3 2 3 + e 3 3 = 0. (6 .25) but the test developed here does not require (6.25) to obtain. This permits the money supply to have a translog form, with non-unit e l a s t i c i t i e s of substitution between cash and demand deposits. The usual restrictions on the variable profit function yield separability tests requiring a Cobb-Douglas form. In (6.25), this requires the 1 1 1 additional restriction = $ 2 3 = &33 =0. A money supply can exist without being Cobb-Douglas, and whether cash and demand deposits have a unit elasticity of substitution can be tested. The conventional simple sum money supply of x 2 + x 3 involves further restrictions, of a limiting form, on the parameters. This can also be tested approximately, as a limiting case. Any test for a money supply which simultaneously requires a Cobb-Douglas structure thus tends to be biased against acceptance. The proposed test is not biased, and provides more accurate determination of whether a money supply exists. - 148 -6.4.2.3 Money Supply D e f i n i t i o n : Cash, Demand and Time Depos i t s The test fo r a monetary subaggregate M2 con ta i n i n g cash, demand depo s i t s and time depos i t s f o l l ows by ex ten s i on . The money supply i n t h i s case i s f ^ X 2 ' X 3 ' X 4 ^ * ^ analogy with the cash and demand depos i t form, the v a r i a b l e p r o f i t f unc t i on i s * 2 * 2 TT 2 (U , \?, x^, x^) = f 2 ( x 2 , x^, x^) g 2 (U ) (6.26) where U represents the v a r i a b l e user co s t s of non-monetary goods. A t r an s l o g s p e c i f i c a t i o n of the v a r i a b l e p r o f i t f unc t i on y i e l d s _ I _ I I _ lnv~ = a„ + E a. Inz. + 1/2 E E p. . Inz. inz. (6.27) 2 0 i=1 1 1 i=1 j=1 1 J 1 J where z = (u^, x^, x^, x^, u 5 , u ? ) , with u^ = U^lU^, = U^/Ug, Uj = '* U 7/Ug and i r ^ = K^/U^. The ex i s tence of a monetary subaggregate con ta i n i n g cash, demand and time depos i t s requ i re s that the second order &-j> i,j=1 , . . . ,5 terms between money and non-money terms be ze ro . The r e s t r i c t i o n s are ^12 = ^13 = ^14 = ° 1 = 1 ' 5 ' 7 ( 6 ' 2 8 ) or nine i n a l l . As before, the r e s t r i c t i o n permits t e s t i n g fo r a monetary subaggreqate without r e q u i r i n g a Cobb - Douglas form. The money supply M2 i s 4 _ 4 4 _ Jlnf, = E a. Jinx. + 1/2 E E 0 . . inx. Inx. L i=2 1 i=2 j=2 - 149 -4 _ 4 _ where E a. = 1 and E B ; . = 0 for j=2,. . . ,4 under homogeneity, 1=2 i=2 J though th i s i s not required by the t e s t . The Cobb-Douglas money form invo lves a l l & = 0, i , j =2 , . . . , 4 , and can be tes ted. The simple sum M2 convent ional ly used x., + + x, i s a l i m i t i n g testab le J 2 3 4 a case. F i n a l l y , for completeness a test of a monetary subaggregate conta in ing cash only can be performed. In t h i s case the var i ab le p r o f i t * * 0 0 funct ion i s TTQ = f p / x 2^ ^ ^ ^ where U i s the user cost vector of the remaining goods. The test involves s im i l a r r e s t r i c t i o n s on the second order terms. The tests are summarized in Table 6.2. 6.5 Econometric Issues 6.5.1 Exogeneity of P r i ces and Quant i t ies The pr ices of var iab le inputs are U,= (U^, . . . ,Ug) . User costs for labor and mater ia ls may be regarded as outside the determination of an i n d i v i d u a l bank. User costs for f i n a n c i a l goods depend on in teres t ra tes , loan loss prov is ions and regulat ions such as deposit rate c e i l i n g s , reserve requirements and deposit insurance prov i s ions . The nested system under th i s s p e c i f i c a t i o n can be estimated as a mu l t i va r i a te regression model with non-zero contemporaneous covar iances. For the var iab le p ro f i t funct ion, net suppl ies of f i n a n c i a l outputs, and demands for f i n a n c i a l inputs and labor, let there be an add i t ive error £, with d i s t r i b u t i o n N(0,E), where N (« ,« ) denotes the mu l t i va r i a te normal,, and E i s a s i x -by - s i x covariance matrix with non-zero o f f -- 150 -Table 6.2 - Test ing f o r Money Supply D e f i n i t i o n s Free Parameters 1. U n r e s t r i c t e d 28 2. Cash (5 r e s t r i c t i o n s ) 23 ^0 = f 0 U 2 ) q 0 ( U 1 ' U 3 ' V V U 7 } 3. Cash and demand depos i t s (8 r e s t r i c t i o n s ) 20 111 = f 1 ( x 2 ' X 3 ) g l ( u l ' U V u 5 ' u 7 * 4 . Cash, demand depos i t s and time depos i t s (9 r e s t r i c t i o n s ) 19 2 ^2 = f 2 ( x 2 ' X 3 ' \ ^ g 2 ( u 1 ' u 5 ' "7* - 151 -d iagona l elements. E s t imat ion of a l l nested forms can be performed by the contemporaneous covar iance or seemingly unre la ted procedure of Z e l l n e r [1962]. I t e r a t i n g on E u n t i l i t becomes a d iagona l matr ix y i e l d s g est imates with maximum l i k e l i h o o d p r o p e r t i e s . Tests for monetary subaggregates cannot be performed without changing assumptions, given that the regressors con ta in a mix of (u,x) v a r i a b l e s . There are two po s s i b l e s o l u t i o n s . The f i r s t i s to assume that each non-nested model not only corresponds to a d i f f e r e n t s p e c i f i c a -t i o n , but a l so to a d i f f e r e n t s t r u c t u r e . As one s p e c i f i c a t i o n , each set of reg res so r s may be viewed as exogenous, con ta i n i n g a mix of p r i c e s and q u a n t i t i e s (Woodland [1978]). The problem i s that s i nce the s t r u c t u r a l forms d i f f e r , comparisons between d i f f e r e n t sets of t e s t s i s d i f f i c u l t , a l though e s t imat i on i s s i m p l i f i e d . A second s o l u t i o n i s to view the exogenous v a r i a b l e s as being env i ronmenta l l y determined, and to be the same rega rd le s s of s p e c i f i c a -t i o n . The non-nested models then conta in endogenous v a r i a b l e s from x as r e g r e s s o r s , with non-zero covar iance with d i s tu rbance terms. An app rop r i a te e s t imat ion procedure i s i t e r a t i v e three stage l e a s t squares, w i th the dependent x v a r i a b l e s purged on the f i r s t round by"be ing regressed on a l l exogenous v a r i a b l e s , and then the i t e r a t i v e procedure app l i ed on the re levant covar iance mat r i x . This procedure has the advantage of ensur ing comparab i l i t y of r e s u l t s between models p o s i t i n g a l t e r n a t i v e monetary subaggregates. 6.5.2 P o o l i n g Time Se r i e s and Cross Sec t i on Data - Bank E f f e c t s The observat ions c o n s t i t u t e pooled time s e r i e s and c ros s s e c t i o n - 152 -data on e ighteen banks in the New York Federa l Reserve D i s t r i c t 1973-1978, with s i x equations for each. Let y denote the stacked l i s t of dependent v a r i a b l e s ( £ m r , X ^ U ^ / T T , X ^ U ^ / T , X ^ U ^ / T T , X ^ U ^ / T T , X ^ U ^ / T T ) . The dimension of y i s NT by u n i t y , where N i s the number of banks and T the number of years . A corresponding a d d i t i v e e r r o r i s e. Fu r t he r , X denotes the l i s t of exogenous v a r i a b l e s in the v a r i a b l e p r o f i t f u n c t i o n . Under l i n e a r homogeneity i n v a r i a b l e good p r i c e s , X conta in s the con s tan t , f i v e r e l a t i v e p r i c e s , the quan t i t y of c a p i t a l and twenty-one second order v a r i a b l e s , or 28 in a l l . A t y p i c a l observat ion i s y = X T + e _ (6.29) •'nt nt nt where T i s a 168 by un i ty stacked vector of parameters and n=1 , . . . ,N w i th t = 1 9 7 3 1 9 7 8 . I f t h i s i s rearranged as a matr ix w i th 28 parameter rows and s i x equation columns, the parameters to be est imated are r = 75 KK <3 M r IK' 0. .6 '15 5K 0 (6.30) The above form may be est imated as a m u l t i p l e reg re s s i on model i f a l l X v a r i a b l e s are exogenous, or by a f u l l i n fo rmat ion method i f some endo-genous v a r i a b l e s are regres sor s . However, i f there are sy s temat ic bank e f f e c t s , the est imates of T are b i a sed . - 153 -Unbiased estimation of r with pooled time series and cross section dependent variable mean, over time, of the nth bank. An equivalent method of estimating this model is to introduce a bank dummy variable matrix Z with parameter 9. This model permits the examination of systematic bank effects in 9. Also, by st a t i s t i c a l inference on 8, i t may be possible to reduce the number of required dummy variables. Mundlak [1978] terms this model 'within' estimation of r , and is unbiased even i f there is intercorrelation between X and Z. Both models are used and compared in estimation, to examine whether bank effects arise. If 9 = 0, then the estimation can proceed without bank effects. 6.6 Concluding Remarks This concludes the discussion of specification, hypothesis testing and estimation. A few remarks may be made on alternative research in specification of bank technology. Mullineaux [1978] also uses the FCA data to estimate a bank profit function. Only the bank profit function, specified as translog is estimated, with no supply functions. The large number of parameters cannot easily be identified with only the profit function, and a multicollinearity problem may arise. Bell and Murphy [1968] use a Cobb-Oouglas specification to estimate bank technology, with a l l the concomitant implications of constant shares in compensation and unit e l a s t i c i t i e s of substitution. data requires the insertion of bank effects. 10 A typical observation becomes y nt - 154 -The advantage of the s p e c i f i c a t i o n used i s that the supply func-t i o n s p rov ide i d e n t i f i c a t i o n for the v a r i a b l e p r o f i t f u n c t i o n . No r e s t r i c t i o n i s placed on s u b s t i t u t i o n p o s s i b i l i t i e s between p h y s i c a l or f i n a n c i a l goods. The ex i s tence of monetary suhaqqregates can be t e s ted a l s o without a p r i o r i r e s t r i c t i o n s . - 155 -Appendix-Chapter 6  Derivation of Hessian for Variable Profit Function This note derives the Hessian matrix for an a r b i t r a r y v a r i a b l e p r o f i t f u n c t i o n . The r e s u l t i s then s p e c i a l i z e d to the t r a n s l o g form. A s i m i l a r d e r i v a t i o n of the Hessian for the t r a n s l o g v a r i a b l e p r o f i t func-t i o n i s contained i n K o h l i [1975, p.29]. The v a r i a b l e p r o f i t f u n c t i o n has form T T ( U , X ) where TT i s v a r i a b l e p r o f i t s d i v i d e d by the user cost of m a t e r i a l s and u = (u^, u^, u^, u^, u,_) i s the r e l a t i v e user cost, of v a r i a b l e i n p u t s . C a p i t a l i s measured by x^. The convention here i s u^> 0, i=1,...,5 and x^ > 0 for outputs and x.< 0 f o r inp u t s , i=1,..,5, with TT > 0. Now and 3TT - 5 — = x. 3u. 1 1 3u.3u. 3u. 1 J J i=1,...,5 (6.A.1) i,j=1,...,5 (6.A.2) the l a t t e r being a t y p i c a l Hessian element. So i n (6.13) i n the t e x t , e i ~ x ^ ^ l t * t n e e x P e n d i t u r e share, i=1,...,5. This i m p l i e s e^ = XMJTI, for the normalizing f a c t o r occurs i n both numerator and denominator. Now ~„ x.u. 3JtniT 1 1 • 1 c \ i\ - T - T — = = e. 1=1,...,5 (6.A.3) 3£nu. I T 1 ' 1 and - 156 -x . = TT 32.mr u. 3£nu. 1 1 i='l , . . . ,5 (6.A.4) implying 3x. , l -1 •x = U . 3u. l J 3TT 3£mr 3e. 3u. 3u. 3£nu. J i + TT -r - X 3u. J i 3u. J = u. -1 3e. 3u. l I x. e. + ir - 5 — - x. - 5 — "j l 3u . I 3u. J J u. x.e. 3e. x. 3u. J i , i i i TT 3 U . Tf 3U . J J u.u. 3e. l e .e. + u. -~— 1 J J 3 u . u . x. 3u . 3 i i . TT 3u . i , j=1,...,5. (6.A.5) This i s the qeneral form of the Hessian, and s i n c e n/u.u. > 0 i J -the s i g n i s determined by the bracketed term. For the t r a n s l o g , 3e. 3.. i _ _ i J 3u . u . J J (6.A.6) usinq the equations i n the t e x t . Off the p r i n c i p a l d i a g o n a l , i * j and 3u./3u. = 0, so the Hessian element becomes i J 3x. 1 TT 3u. u.u. i j i j J 1 J [e.e. + 3..] i,j="1 ,..-,5, (6.A.7) On the p r i n c i p a l d i a g o n a l , 3u^/3u.-= 1, so - 157 -3x [ e. + 0. . - e. J 3u. " 2 i " i i i l u. i = - 2 - ^ - 1 ) + B U ] u. I (6.A.8) This y i e l d s the Hessian mat r i x , p r opo r t i ona l to H = e 1 ( V 1 ) + P11 e 1 6 2 + *12 e 1 e 2 + e i 2 e 1 e 5 + 3 15 e 2 ( V 1 ) + 6 2 2 - ' - - 6 2 e 5 + 3 25 6 1 e 5 + 3 15 e 0 e c + 8 - c . . . . e c(e,--1) + 8,-c 2 5 25 3 3 33 (6.A.9) and i f the p r i n c i p a l minors of t h i s matr ix are non-negat ive, the f unc t i on i s convex in output and input user cost s for a l l sample p o i n t s . Convex i ty at the po int of expansion r e l i e s on the r e s u l t that when u^=1, i=1, . . . ,5 and x^ = 1, e^ = a., i=1,...,5 and a l l elements of H are rep laced a c c o r d i n g l y . - 158 -Notes The d e r i v a t i v e of the v a r i a b l e p r o f i t f unc t i on y i e l d s 3 T T / 3 U = x where u is- the vector of normalized user co s t s , and IT i s normal ized v a r i a b l e p r o f i t . Monoton ic i ty requ i re s that x be p o s i t i v e for outputs and negat ive for i npu t s . The not ion of i n t e g r a b i l i t y has i t s h i s t o r i c a l o r i g i n s i n A n t o n e l l i [1886], Further i s sues on i n t e g r a b i l i t y are explored by Hurwicz [1971], and a tes t on aggregate consumer expenditure data for the Un i ted S tates performed in Ch r i s ten sen , Oorgenson and Lau [1975]. See a l so B lackorby , Primont and R u s s e l l [1978]. 3 T h i s r e s u l t i s der ived i n Woodland [1978, 387]. ^The i s sues as to what the appropr ia te target of monetary p o l i c y i s , and what forms of subaggregates are candidates are w e l l summarized i n S i ve sk i nd and Hurley [1980] and Berkman [1980]. 5 B l a c k o r b y , Primont and R u s s e l l [1977] show that i f the f u n c t i o n f o r f i rm technology i s t r a n s l o g , any subaggregate must s a t i s f y the c o n d i t i o n s of a Cobb-Douglas, r e q u i r i n g un i t e l a s t i c i t i e s of s u b s t i t u t i o n between a l l elements of money i n the current con tex t . The problem i s somewhat f i nes sed i f the form i s used as an approx imat ion. 6 F o r these purposes, i t should be noted that c a p i t a l i s regarded as v a r i a b l e i n t e s t i n g for monetary subaggregates. I f c a p i t a l i s f i x e d , then i t enter s the f i x ed subaggregate being t e s t e d . As an example, i n s tead of an M1 form con ta in i ng cash and demand d e p o s i t s , there i s a form with cash, demand depos i t s and c a p i t a l . S ince these three are i n quan t i t y form, the t e s t of M1 subsequently w i l l r equ i r e a Cobb-Douglas form. Here U^ i s the r e l a t i v e user cost of c a p i t a l . Without no rma l i z a t i on i t i s U , and u = U /U . 7 7 7 6 Q The f u l l system a l so conta ins a demand f unc t i on f o r raw m a t e r i a l s . The d e l e t i o n of t h i s demand f unc t i on in the no rma l i z a t i on f o r l i n e a r homogeneity of the v a r i a b l e p r o f i t f unc t i on makes the covar iance mat r i x nons ingu la r . 9 See Kmenta and G i l b e r t [1968]. 1 0 T h e d i s cu s s i on i s conta ined in Maddala [1971] and Mundlak [1978]. - 159 -CHAPTER 7  EMPIRICAL RESULTS 7.1 Introduction The e m p i r i c a l r e s u l t s for the v a r i a b l e p r o f i t f unc t i on f o r the e ighteen banks i n 1973-1978 are examined. To focus the p o l i c y d i s c u s s i on s fo r monetary c o n t r o l , i t i s d e s i r a b l e to ob ta in es t imates of the respons iveness of the supply of loans and demand d e p o s i t s , the output s , w i th respect to own user c o s t s . Analogous ly, the cu rva tu re of the input demand func t i on s for cash, time depo s i t s , labor and m a t e r i a l s can be examined. Apart from the hypotheses on r e g u l a r i t y of technology and e x i s t ence of monetary and other subaggregates, there i s the e s t ima t i on of s u b s t i t u t a b i l i t y and t rans fo rmat ion between goods for a f i n a n c i a l f i r m . S u b s t i t u t a b i l i t y examines s h i f t s i n r e l a t i v e demands for an input p a i r as the r e l a t i v e p r i c e r a t i o of that p a i r changes. Trans format ion measures the convers ion of inputs to outputs, or of a l l o c a t i n g resources between a p a i r of ou tput s . For the f i n a n c i a l f i r m , t h i s i n c l ude s the technology by which time depos i t balances are converted to l oans , or the u t i l i z a t i o n of cash ba lances, and the convers ion of these to revenue producing i tems. Es t imates of the e l a s t i c i t i e s of t rans fo rmat ion and the own and c ro s s p r i c e e l a s t i c i t i e s of supply and demand are r equ i r ed . For output s , own p r i c e e l a s t i c i t i e s of supply are p o s i t i v e , with compensated s upp l i e s upward s l o p i n g . For i npu t s , own p r i c e e l a s t i c i t i e s of demand are negat i ve , with demand curves downward s l o p i n g . These es t imates have - 160 -i m p l i c a t i o n s for monetary p o l i c y . I f loan supp l i e s are shown to be i n e l a s t i c with respect to i n t e r e s t rates a f f e c t i n g the loan user c o s t , the conduct of monetary p o l i c y may be undermined. Even i f a monetary subaggregate can be con s t ruc ted , i t may be i n s e n s i t i v e to i n t e r e s t r a t e s . Th is leads to i m p l i c a t i o n s on whether i n t e r e s t rates should be c o n t r o l l e d d i r e c t l y , or money g u a n t i t i e s d i r e c t l y , in the a d m i n i s t r a t i o n of monetary p o l i c y . In s e c t i o n 2, the e l a s t i c i t i e s of t r an s fo rmat ion and the p r i c e e l a s t i c i t i e s of supply and demand are d e r i v e d . For an a r b i t r a r y n e o c l a s s i c a l product ion technology, these are dependent upon data p o i n t s . In the t r an s l o g con tex t , these v a r i a b l e e l a s t i c i t i e s are c o n s t r u c t e d . At a no rma l i za t i on point where the arguments of T T ( U , X ^ ) are u n i t y , these e l a s t i c i t i e s are pa ramet r i c , and s t a t i s t i c a l i n f e rence can be a p p l i e d . Sec t i on 3 repor t s on the r e g u l a r i t y t e s t s on the technology, f o r s a t i s f a c t i o n of i n t e g r a b i l i t y or symmetry and e q u a l i t y , monoton i c i t y , and c o n v e x i t y . Tests on whether bank e f f e c t s are present are performed. These t e s t s are performed i n s e r i e s , and impose r e s t r i c t i o n s both on the number of parameters and the space i n which the parameters can i i e . Sec t i on 4 t e s t s for the ex i s tence of a money supply aggregate. In s e c t i o n 5 the est imates on the e l a s t i c i t e s of t r an s fo rmat ion and supply and demand are repor ted, for the most r e s t r i c t i v e subaggregate accepted. Loans and demand depos i t s have upward s l op ing supply sched-u l e s . Cash, time depos i t s , labor and m a t e r i a l s have downward s l op i n g demand schedu les . The adding up r e s t r i c t i o n s permit- the es t imates fo r - 161 -m a t e r i a l s to be cons t ructed once the remaining e l a s t i c i t i e s are known. The e l a s t i c i t y of p r o f i t s with respect to p h y s i c a l c a p i t a l can be obta ined as 3£mr(u,x )/3£nx , as w e l l as the ex post ra te of re turn on K K c a p i t a l . In s e c t i on 6 some i m p l i c a t i o n s of the r e s u l t s for the conduct of monetary p o l i c y are d i s cu s sed . Included are the e f f e c t s of changes i n i n t e r e s t ra tes through Federa l Reserve a c t i v i t y , as w e l l as changes i n reserve reguirements. The theory develops a cost of a reserve requirement as part of the user cost of each depo s i t . Changes i n reserve requirements can be examined fo r e f f e c t s on loans and other f i n a n c i a l goods. Sec t i on 7 presents some conc lud ing remarks on the e m p i r i c a l r e s u l t s . The r e s u l t s i n d i c a t e that i t i s p o s s i b l e to cons t ruc t an e s t imab le and t e s t a b l e model of a f i n a n c i a l f i r m . Such a model appears c e n t r a l to any complete examination of monetary p o l i c y . 7.2. E l a s t i c i t i e s of Transformation, Demand and Supply Of important p o l i c y re levance are the e l a s t i c i t i e s of t r a n s f o rma t i on . These may be used to de r i ve p r i c e e l a s t i c i t i e s of supply f o r outputs and demand fo r i npu t s . Consequently, the response of f i n a n c i a l f i rm product ion with respect to user cos t s can be ob ta i ned . S ince the user co s t s depend on i n t e r e s t r a te s as w e l l as regu la ted v a r i a b l e s such as depos i t insurance rates and reserve regui rements, the e f f e c t of monetary p o l i c y on the banking system can be d e r i v e d . As def ined i n (4 .10) , the e l a s t i c i t y of t ran s fo rmat ion between goods i and j , i , j = 1 , . . . , 6 i s n.. = TTTT. ./TT.TT ., where v.. i s 3 2 T T / 3 U . 3 U . - 162 -and i s 3 T T / 3 U ^ . V a r i a b l e p r o f i t s and user cos t s are measured r e l a t i v e to the user cost of m a t e r i a l s . From the d u a l i t y r e s u l t s , 3TT x. = i 3u and x . >_ 0 i f i i s an output x. < 0 i f i i s an input (7.1) 1=1,...,5 with the f i v e v a r i a b l e s being i n order loans, demand d e p o s i t s , cash, t ime depos i t s and l abo r . V a r i a b l e p r o f i t s TT and user cos t s u are both measured r e l a t i v e to m a t e r i a l p r i c e s . Further i f e. = X . U . / T T i i i 3 2 * 3u^3uj u .u . i J 3e. e . e . + u u .x. J i 3u. j J 3u j TT 3U , f o r i =1 , . . . , 5 . S u b s t i t u t i n g (7.1) and (7 .2 ) , the t r an s fo rmat i on e l a s t i c i t y i s (7.2) 1 e .e . i J 3e. e . e . + u u.x. 3u." J i i i j J 3u, TT 3U , (7.3) u. 3e. 1 + — i 1 3u. TT 1 e-.e. 3u. u.x. 3u. 1 J J 1 J J i » j = 1»•••»5 • For the t r a n s l o g , 3e./3u. = 3. . /u . with 6.. beinq the second order i J • i j J i j parameter between i and j . S ince 3u./3u. = 1 for i = j , and otherwise i s zero n..= 1 + —= 2 e. 1 + 6 i e j i , j = 1 , . . . , 5 . (7.4) - 163 -These own t rans fo rmat ion e l a s t i c i t i e s are non-negat ive and vary with each data po i n t . At the point of no rma l i z a t i on where [u] = 1, then e i = a i ' i = 1 »•••>'>, and the e l a s t i c i t i e s are independent of the d a t a . The e l a s t i c i t i e s f o r the s i x t h v a r i a b l e good, m a t e r i a l s , can be 6 6 con s t ruc ted given that E e. = 1 and E n..e. = 0 as der i ved i n j=1 J j=1 1 J J (4.10) - ( 4 .12 ) . The e l a s t i c i t i e s of supply and demand fo r r e s p e c t i v e outputs and inputs are i= j (7.4) i , j = 1 , . . . , 5 and aga in , these are parametr ic where [u]=1, with e^ = a^, i = 1 , . . . , 5 . With e^ >_ 0 for outputs , u i ^ i s non-negat ive for ou tput s , w i th an upward s l o p i n g compensated supply cu rve . Inputs have e. _< 0, so u ) „ i s n o n - p o s i t i v e , with demand curves for inputs downward s l o p i n g . For 6 m a t e r i a l s , the e l a s t i c i t i e s of demand are obtained from E w.. = 0 . These e l a s t i c i t i e s permit the c a l c u l a t i o n of guan t i t y responses to changes in user c o s t s . The e f f e c t of monetary p o l i c y measures such as changes i n reserve requirements, depos i t insurance p r o v i s i o n s or i n t e r e s t rates themselves can be ana lyzed. w.. = n. .e . = e. + l e, e. I e^ - 1 - 164 -7.3 R e g u l a r i t y Tests The f i r s t r e g u l a r i t y t e s t s are for symmetry and e q u a l i t y . In the case of symmetry, t h i s requ i res the second order terms i n the supply and, demand func t i on s to be equa l . E q u a l i t y requ i re s that the parameters i n these func t i on s be the same as t h e i r analogues i n the v a r i a b l e p r o f i t f u n c t i o n . A l l t e s t s are performed on two a l t e r n a t i v e models, r e s p e c t i v e l y w i t h bank e f f e c t s excluded and i n c l uded . With bank e f f e c t s i n c l uded , dummy v a r i a b l e s are u t i l i z e d by bank in each egua t i on . These are removed i n the model without bank e f f e c t s , so i t i s po s s i b l e to t e s t f o r such phenomena. An equ iva lent bank e f f e c t s model i s to t ransform the data as d e v i a t i o n s from the sample mean, by bank, f o r dependent and independent v a r i a b l e s . I f bank dummy v a r i a b l e s are i n c l uded , w i th e ighteen banks and s i x equat ions , even the removal of one bank to avoid s i n g u l a r i t y i n vo l v e s the a d d i t i o n of 108 parameters. On e s t ima t i on of the u n r e s t r i c t e d model w i th these e f f e c t s , the banks were shown to be grouped i n t o f i v e . Us ing the o r i g i n a l number codes supp l ied by the New York Federa l Reserve Bank wi th the data, the aroups in the dummy s p e c i f i c a t i o n used are, with bank 29 used as a normal izer (7.6) z i = 1 for bank 6 Z2 = 1 for banks 3 or 15 z 3 = 1 for banks 1,2,4,21,25 or27 zH - 1 banks 16 or 28 z 5 = 1 fo r banks 14,19,22,or 23. The dummies are zero fo r cases complementary to those s p e c i f i e d . - 165 -App ly ing the l i n e a r homogeneity in p r i c e s r e s t r i c t i o n , and us ing the m a t e r i a l s user cost as a numeraire, the e s t imat i ng equat ions a re , f o r the no bank e f f e c t s case 5 5 5 £mT = a . + Z a . £nu. + a , £nx.. + - r - E E g . . £nu. £nu. 0 1 = 1 i i K K 2 1 = 1 . = ] xj i j 5 1 2 + E 0. £nu. £nx + T 0 (£nx ) (7.7) j=1 J K £ KK K and x i u i i — = Y i + . E 1 6 i j * n u j + 6 i K t n x K 1=1,...,5. (7.8) V a r i a b l e p r o f i t s r e l a t i v e to m a t e r i a l p r i c e s are TT = T T * / U . and u = U / U . , 6 6 where TT* are the non-normalized v a r i a b l e p r o f i t s and user c o s t s . The bank e f f e c t s model i nc ludes the f i v e dummy v a r i a b l e s i n each equat ion a d d i t i o n a l l y . Data on the exogenous v a r i a b l e s are entered as d e v i a t i o n s from t h e i r geometric means. Tests f o r the presence of bank e f f e c t s , symmetry and e q u a l i t y are repor ted i n Table 7.1. Panel A r epo r t s the logar i thm of the l i k e l i h o o d f u n c t i o n w i th bank e f f e c t s i n c l u d e d . Panel B i n d i c a t e s the l oga r i thm of the l i k e l i h o o d f unc t i on without bank e f f e c t s , and the t e s t s of bank e f f e c t s are i n Panel C. In a l l cases, the hypothes i s of no bank e f f e c t s i s r e j e c t e d . Thus the dummy v a r i a b l e s are re ta ined throughout. 2 The t e s t s t a t i s t i c s used are a s ympto t i c a l l y d i s t r i b u t e d as x • Berndt and Savin [1977] have shown that there are three a l t e r n a t i v e 2 forms of t e s t s t a t i s t i c d i s t r i b u t e d a s ympto t i c a l l y as x • In descending order of magnitude, these are the Wald, l i k e l i h o o d r a t i o and Lagrange m u l t i p l i e r fo rms. 3 A t e s t which i s not accepted under the Lagrange - 166 -Table 7.1 Test S t a t i s t i c s , Symmetry and E q u a l i t y of Va r i ab l e P r o f i t Funct ion £nl_ ( logar i thm of l i k e l i h o o d funct ion) Degrees of freedom (DF) Test S t a t i s t i c (X 2/DF) C r i t i c a l Value (0.01) A Bank e f f e c t s inc luded 1. U n r e s t r i c t e d 750.93 2. Symmetry 725.83 10 5.02 2.32 3. Symmetry and Equality 648.09 35 5.88 1.70 B Bank e f f e c t s excluded 1. Unrestricted 651.43 2. Symmetry 626.21 10 5.04 2.32 3. Symmetry and Equality 555.43 35 5.49 1.70 C . Test of Bank Effects, by Model 1. Unrestricted - 30 6.63 1.79 2. Symmetry - 30 6.64 1.79 3. Symmetry and Equality 30 6.18 1.79 - 167 -multiplier form is not accepted a f o r t i o r i under the two alternatives. Hence the results are reported for this form. The hypothesis of symmetry and equality is rejected, but is then imposed. The non-acceptance of symmetry and equality may arise from a number of sources, apart from the rejection of producer demand theory.This renders i t d i f f i c u l t to view the particular test as one confirming demand theory. First, multicollinearity exists in the variable profit function by i t s e l f , rendering i t d i f f i c u l t to identify the parameters, and increasing their standard errors. It may be easier to accept this hypothesis If share equations are eliminated, as in Mullineaux [1978], but the cost is imprecise parameter estimation. Second, a l i t e r a l interpretation of symmetry and equality with additive errors in the demand functions implies a complex and heteroskedastic disturbance for the variable profit function. The variable profit function parameters, with symmetry imposed, are indicated in Table 7.2. The bias in parameter estimates arising when bank effects are excluded is demonstrated. At the geometric means of the sample, Is the elasticity of variable profits with respect to capital. Without bank effects this is 0.840, but i t changes to 0.879 with bank effects. The return on capital is 3ir/3x^ = < X^ 1 I/ X^- At the geometric; mean, for a given */x^ the no bank effects model leads to an upward bias in the realized return on capital. I The remaining a elements are e l a s t i c i t i e s of variable profits with respect to user costs of variable goods. Loans and demand deposits are outputs, as indicated lhlthe classification tests, and increases in loan - 168 -Table 7.2 Parameter Estimates, Variable Profit Function (Asymptotic standard errors in parentheses) Parameter Bank effects included Bank effects excluded Intercept a l a 2 A 3 ak A 5 "K P l l 013 014 015 B1K 022 023 024 625 g2K 033 034 035 3 ^ *4K P55 BKK 14.638 1.280 0.515 -0.073 -0.201 -0.416 0.840 0.070 -0.284 -0.006 0.153 0.054 -0.074 0.291 0.020 -0.002 0.053 -0.081 -0.035 -0.002 -0.010 0.006 -0.140 -0.005 0.000 -0.075 0.141 0.409) 0.073) 0.061) 0.013) 0.032) 0.070) 0.235) 0.061) 0.033) 0.015) 0.023) 0.037) 0.044) 0.055) 0.036) 0.004) 0.036) 0.037) 0.033) 0.004) 0.010) 0.008) 0.010) 0.013) 0.019) 0.039) 0.040) 0.013 (0.058) 14.474 (0.155) 1.251 (0.028) 0.601 (0.023) -0.081 (0.005) -0.175 (0.012) -0.492 (0.026) 0.879 (0.106) -0.076 (0.081) -0.068 (0.018) -0.191 (0.036) 0.188 (0.027) 0.097 (0.047) -0.077 (0.020) 0.197 (0.059) 0.041 (0.039) -0.001 (0.004) 0.006 (0.004) 0.009 (0.017) -0.021 (0.044) -0.001 (0.004) 0.004 (0.013) -0.010 (0.004) -0.146 (0.010) -0.022 (0.015) 0.012 (0.008) -0.072 (0.042) 0.059 (0.018) -0.027 (0.037) Note: a elements are f i r s t order, and 3 elements second order parameters, under symmetry. Subscripts are: 1 loans, 2 demand deposits, 3 cash, 4 time deposits, 5 labor, K capital. Given linear homogeneity, data are normalized by the user cost of materials. Intercept refers to the variable profit function constant term a^. - 169 -returns and demand deposit returns increase profits. At the geometric sample mean, a one percent increase in loan user costs with bank effect included increases profits by 1.28 percent, and a similar increase for demand deposits raises profit by 0.515 percent. Goods 3,4 and 5 are respectively cash, time deposits and labor. These are inputs under the classification rule, and increases in the user costs of each reduces profits. The e l a s t i c i t i e s are -0.073, -0.201 and -0.416 respectively. Regarding monotonicity, the results on the ou parameters, 1=1,..., confirm monotonicity at the geometric mean. Monotonicity requires 3TT/9U£ > 0 for an output and 3T T/8U^ < 0 for an input. Now 6 i = X i U i ^ = a j l n l T / 8 £ n u i 1=1,...,5 (7.9) so 3T T/3 u, = e.Tr/u.. (7.10) i l l Given that u^ > 0 by definition and TT > 0 by inspection for a l l data points, sign (3T T/3U^) = sign (e.), i=1,...,5. For a l l the sample points, e^ is s t r i c t l y positive for loans and demand deposits, and 6 negative for labor, time deposits and cash. The constraint I e.= 1 is i=1 used to calculate the relative expenditure for materials, and this i s negative for a l l observations. Table 7.3 reports these relative expenditures. For every observation, monotonicity applies. This indi-cates that the financial firm technology exhibits profit increases when the user costs of loans and demand deposits increase. Profits decrease - 170 -Table 7.3 R e l a t i v e Expend i tures , Outputs and Inputs (Monoton ic i ty Test , Bank E f f e c t s Included) Mean Standard Deviation Minimum Maximum Loans 1.280 0.232 0.888 1.790 Cash -0.073 0.037 -0.190 -0.032 Demand Deposits 0.515 0.160 0.272 1.096 Time Deposits -0.201 0.101 -0.411 -0.006 Labor -0.416 0.142 -0.912 -0.221 Materials -0.105 0.036 -0.194 -0.042 Relative expenditure is x.u./ir, calculated at each observation. - 171 -when the user costs of cash, time deposits, labor and materials increase. As for convexity, the Hessian matrix evaluated for the geometric mean bank is reported in Table 7.4. The matrix is singular for the six by six case, given linear homogeneity of the variable profit function. Accordingly, the row and column corresponding to materials are dropped. Along the principal diagonal, a l l elements are positive. To determine positive semi-definiteness of the matrix, the principal minors are calculated, starting from the f i r s t row and column. The principal minors are 0.42912, 0.03249 , 0.00813 , 0.00009 and 0.00011.1* The results from the principal minors indicate that the variable profit function is convex, evaluated at the geometric mean. Evaluating the Hessian at every data point, similar results are obtained, indicating that the function has similar properties for a l l observations. This completes the regularity tests for symmetry and equality, monotonicity and convexity, together with the examination of bank effects. The variable profit function obeys the restrictions of mono-tonicity and convexity at a l l data points, normalized around the geomet-. . 5 n c mean. 7.^ Tests of Monetary Aggregation The test results focus on the M1 and M2 forms. A cash only money supply has few practical monetary policy implications. Furthermore, there is no aggregation problem in this 1 one good case. Hence we turn to other money aggregates. - 172 -Table 7.4 Convexity Test - Hessian Matrix of Variable Profit Function (H..) Loans Cash Demand Deposits Time Deposits Labor Loans 0.4291 -0.0988 0.3755 -0.1047 -0.4787 Cash -0.0988 0.0985 -0.0724 0.0125 0.0199 Demand Deposits 0.3755 -0.0724 0.0417 -0.1057 -0.1612 Time Deposits -0.1047 0.0125 -0.1057 0.1013 0.0785 Labor -0.4787 0.0199 -0.1612 0.0785 0.5140 Note: Hessian matrix element i s , from (7.2) H 3^Tf TT i j 3u i3u^ UM. 3e^ u j x i ** ui e.e. + u. - 5 — - — — - - 5 — 1 J j 3u, TT 3u j For translog, Ze.JZu^ = and at [u] = 1, = a., i=1,...,5. U j so H 3 TT i j 3u.3u. J 1 J a . a . + 0. . 1 J i j a i + hi ~ a i i = J Table elements are reported without the scaling factor T T / U ^ U ^ . The sixth row correponds to materials, and is dropped given the linear homogeneity. - 173 -The M1 forms containing cash and demand deposits are indicated in Table 7.5. Variable profit for this form, n is the return to cash and demand deposits. The dependent variables in the return to cash and return to demand deposit equations are respectively u^x-,/^ and U3X3/^1T1 " Since these sum to unity, the cash equation is deleted. The unrestricted model, with symmetry imposed is reported in the 2 f i r s t column. The test statistic is x /8, and is 18.43 against a c r i t i c a l value at 1 percent of 2.51. For this and a l l tests, the statis t i c s are reported as the computed x~ divided by the number of degrees of freedom. This obtains for both the c r i t i c a l value and test s t a t i s t i c . The flexible functional form M1 supply is not accepted. The Cobb-Douglas form involves the additional restrictions that Inx^ and fcnx^ do not enter the demand deposit equation. The test s t a t i s t i c for a Cobb-Douglas, compared with the unrestricted model is 19.17. The 2 c r i t i c a l value of x /11 at one percent is 2.32. Comparing the Cobb-Douglas with the translog, the statistics are 22.01 against 4.61 for x^/2 and one percent significance. The results support monotonicity, or positive returns to increasing the quantity of money. For demand deposits, 3£nTr^/Sfcnx^ at the geometric sample mean is 0.875 for the unrestricted model. Were a M1 money supply validated, the compensation shares would be approximately seven-eights demand deposits, and one-eighth cash. For the money supply M2, the results are indicated in Table 7.6. Table 7.5 Money Supply Aggregates M1, Parameter Estimates (asymptotic standard errors in parentheses) Variables Unrestricted Flexible form (translog) Cobb-Douglas Loans Intercept 2.041 (0.215) 2.245 (0.137) 2.252 (0.137) (UiXi/Tf! ) £nui 1.137 (0.305) 0.934 (0.303) 0.790 (0.303) £nx 2 -0.129 (0.135) £nx 3 -0.032 (0.006) £nui+ 0.008 (0.078) 0.067 (0.076) 0.140 (0.076) £nu 5 -0.232 (0.079) -0.238 (0.078) -0.208 (0.078) £nu7 -0.783 (0.177) -0.705 (0.176) -0.688 (0.176) Demand Deposits Intercept 0.875 (0.003) 0.891 (0.003) 0.898 (0.003) (U3 x 3/*l) £nuj -0.032 (0.006) £nx 2 -0.076 (0.003) -0.064 (0.002) £nx 3 0.067 (0.003) , 0.064 (0.002) Jlnuit -0.006 (0.002) £nu 5 -0.001 (0.003) £nu7 0.021 (0.003) Time Deposits Intercept -0.383 (0.055) -0.332 (0.035) -0.334 (0.035) ( - U i ^ / l ^ ) fcnuj 0.008 (0.078) 0.067 (0.076) 0.140 (0.076) £nx 2 -0.035 (0.034) £nx 3 -0.006 (0.002) £ n ^ -0.151 (0.025) -0.138 (0.024) -0.159 (0.024) £nu 5 0.029 (0.024) 0.028 (0.023) 0.010 (0.033) £nu7 0.119 (0.042) 0.039 (0.041) 0.012 (0.041) Labor Intercept -0.843 (0.056) -0.875 (0.035) -0.876 (0.035) ( - 115X5/1^ ) £nui -0.232 (0.079) -0.238 (0.078) -0.208 (0.078) £nx 2 0.026 (0.035) £nx 3 -0.001 (0.003) £nui+ 0.029 (0.024) 0.028 (0.023) -0.159 (0.070) £nu 5 0.039 (0.034) 0.033 (0.033) 0.047 (0.033) £nu7 0.153 (0.042) 0.140 (0.042) 0.138 (0.042) Capital Intercept -1.325 (0.138) -1.645 (0.088) -1.647 (0.088) £nui -0.783 (0.177) -0.705 (0.176) -0.688 (0.176) £nx 2 0.234 (0.087) £nx 3 0.021 (0.003) *nuit 0.119 (0.042) 0.039 (0.041) 0.012 (0.041) £nu 5 6.153 (0.042) 0.140 (0.042) 0.138 (0.042) £nu7 0.410 (0.121) 0.479 (0.121) 0.509 (0.121) AnL 613.02 539.19 517.18 Note: The dependent variable is noted in parentheses in the left column. User costs and quantities are measured positively in the data. Table 7.6 Money Supply Aggregates M2, Parameter Estimates (asymptotic standard errors in parentheses) Variables Unrestricted Flexible form (translog) Cobb-Douglas ( U 1 X 1 / T T 2 ) (ui tx 4/n 2) ( - U 5 X 5 / T r 2 ) ( - U 7 X 7 / T T 2 ) Loans Intercept £nuj £nx 2 £nx 3 £nu 5 inuy Demand Deposits Intercept ( U 3 X 3 / T T 2 ) £ n u ! & n x 2 £ n x 3 £ n x i + £ n u 5 & n u 7 Time Depos i t s I n t e r cep t Irnii £nx 2 * n x 3 Anx^ Jlnu 5 Jlnu 7 Labor I n te r cep t Anuj £nx 2 £nx 3 Inx.^ Jlnu 5 £nu 7 C a p i t a l I n te r cep t Jlnu^ Jlnx 2 Anx 3 Anus Jlnu 7 1.425 1.133 -0.129 -0.425 0.427 -0.028 (0.086) (0.092) (0.054) (0.025) (0.027) (0.038) -0.250 (0.069) 0.648 -0.425 -0.084 0.207 -0.181 -0.029 0.106 0.256 0.427 0.025 -0.181 0.211 0.035 (0.021) (0.025) (0.013) (0.014) (0.015) (0.014) (0.017) (0.022) (0.027) (0.014) (0.015) (0.016) (0.015) -0.095 (0.018) -0.591 (0.032) -0.028 (0.038) 0.057 (0.021) -0.029 (0.014) 0.035 (0.015) 0.056 (0.028) 0.012 (0.025) -0.966 (0.090) -0.250 (0.069) 0.200 (0.057) 0.106 (0.017) -0.095 (0.018) 0.012 (0.025) 0.009 (0.075) 1.641 (0.054) 0.793 (0.083) -0.164 (0.035) -0.558 (0.066) 0.718 (0.013) -0.018 (0.003) 0.032 (0.004) -0.014 (0.004) 0.183 (0.014) -0.016 (0.002) -0.014 (0.004) 0.030 (0.005) -0.662 (0.020) -0.164 (0.035) 0.052 (0.025) 0.100 (0.023) -1.236 (0.057) -0.558 (0.066) 0.100 (0.023) 0.422 (0.063) 1.642 (0.057) 0.792 (0.083) -0.171 (0.035) -0.538 (0.066) 0.693 (0.020) 0.220 (0.022) -0.663 (0.023) -0.171 (0.035) 0.068 (0.025) 0.085 (0.023) -1.236 (0.067) -0.538 (0.066) 0.085 (0.023) 0.416 (0.063) 619.87 Mote: £nL 784.79 691.43 For M2, time depos i t s are inc luded i n the money supp ly . An grease i n the quan t i t y * increases v a r i a b l e p r o f i t s , so the i n t e r c e p t c o e f f i c i e n t i s p o s i t i v e . - 176 -The translog flexible form is not accepted, having a test s t a t i s t i c of 20.74 (2.41) with x /9 at a 1 percent significance level in parentheses. The Cobb-Douglas compared with the unrestricted model has a test s t a t i s t i c of 21.99 compared with 2.04 for x^/15 and one percent significance. Finally, the Cobb-Douglas compared with the translog has 2 test s t a t i s t i c 23.85. The hypothesis is not accepted, since x /6 at the one percent level is 2.80. Both monetary aggregates M1 and M2 are not accepted s t a t i s t i c a l l y . However, the Cobb-Douglas form is always rejected in favor of the flexible money supply. The results confirm the bias in testing separability noted by Blackorby, Primont and Russell [1977]. Suppose money supply forms are imposed. For the translog form, in column 2 of Table 7 .5, the cash parameters can be recovered by the 1 linear homogeneity restrictions = 1 - 0.891 = 0.109. As estimated in 1 1 the demand deposit equation B.^ = -0.064 and B^ = 0.064. The money supply index, where x^ = x3/*2 1 S — — ? g^trans) = x ? exp(0.891 £nx 3 + 0.064(fcnx3) /2) and under the Cobb-Douglas structure, i t is g^CD) = x 2exp(0.898 fcnx^) . The geometric mean quantities of cash in excess reserves and demand deposits are respectively, in millions of one dollar units, 6 and 110. . - 177 -The sample mean observat ions in 1978, measured in d e v i a t i o n form are Inx-, = 0.42 and £nx^ = 0.92. On a base of un i t y at the geometric mean fo r the index and the cash quan t i t y g^(trans) = 2.433653 and g.^(C0) = 2.384525. The commonly used s imple sum i s g^sum) = x 2 + x 3 and i n index form, the 1978 observat ion i s 2.458222. The e r r o r from us ing a s imple sum monetary form i s about 1 percent, and over 2 percent fo r the Cobb-Douglas. The former ove r s ta te s monetary growth because of the pe r f e c t s u b s t i t u t a b i l i t y assumption and the l a t t e r unders tates i t . Whether an overstatement of money supply of 1 percent i s l a r ge or sma l l depends on p o l i c y weights . In an environment where money supply t a r g e t s are being used, a c tua l growth..oJaserved to be above a g iven upper bound may not prove to be so. Monetary growth as measured may be o v e r s t a t e d . For the money supply M2, the analogous Ind ices a re , us ing the est imates i n the second column of Table 7.6, with x^ = x^/x^ or the r a t i o of time depos i t quan t i t y to cash g , ( t r an s ) = x,exp(0.718 Jinx, + 0.183 Jinx, + 0.032(£nx- > ) 2 /2 2 2 3 4 3 -0.014inx £nx^ + 0 .030(£nx^) 2 /2) and the Cobb-Douglas and s imple sum forms are g 2 (CD) = x 2 exp(0.693 Jinx + 0.220 £nx^) and - 178 -g2(sum) = x-, + + x^. The mean time depos i t quan t i t y , i n m i l l i o n s i s 112.9, and the 1978 geometr ic sample mean i s 0.83. On a bas i s of un i t y at the geometr ic mean fo r cash and the i n d i c e s , ( t rans ) = 2.357688, g-,(CD) = 2.355375 and g2(sum) = 2.376887. Aga in, the s imple sum y i e l d s an upward b i a s of about 1 percent . In an era of i n c rea s i ng q u a n t i t i e s , s e l e c t i n g the l a s t sample year y i e l d s the l a r g e s t d i f f e r e n c e s from the geometr ic mean. The obta ined r e s u l t s are s i m i l a r to the M1 case. In terms of s e l e c t i n g between M1 and M2 as the appropr i a te money supply, the r e s u l t s are i n c o n c l u s i v e . In both cases the t e s t of a monetary index i s r e j e c t e d . Using the p rob -va lue , or p r o b a b i l i t y that the n u l l hypothes i s cannot be r e j e c t e d , the r e s u l t s lean s l i g h t l y i n favor of M1, but the d i f f e r e n c e i s s m a l l . The r e s u l t s suggest that i t i s p o s s i b l e to develop a t e s t a b l e model on the money supply, and i t s c o n s t i t u e n t components. 7.5 Estimation of Transformation, Supply and Demand E l a s t i c i t i e s The e l a s t i c i t i e s of t rans fo rmat ion are reported i n Table 7.7. Those fo r m a t e r i a l s are obta ined r e s i d u a l l y , us ing the c o n s t r a i n t s that the r e l a t i v e expendi tures sum to one, and that the e l a s t i c i t i e s weighted by r e l a t i v e expenditures sum to z e r o . -For the geometric mean data po i n t , the e l a s t i c i t i e s are de f i ned 1 + e i i / c t i 2 " 1 / a i 1 = j i , J = 1 ,..., 6 (7.11) 1 + B i j ^ a i a j i * j - 179 -Table 7.7 Estimates of Elast i c i t i e s of Transformation and Relative Expenditures (at geometric mean of sample) Loans Cash Demand Deposits Time Deposits Labor Materials Loans 0.262 1.060 0.570 0.407 0.899 0.907 Cash 1.060 18.557 1.932 0.854 0.656 5.268 Demand Deposits 0.570 1.932 0.157 1.021 0.753 1.439 Time Deposits 0.407 0.854 1.021 2.510 0.939 0.847 Labor 0.899 0.656 0.753 0.939 2.972 0.626 Materials 0.907 5.268 1.439 0.847 0.626 10.314 Relative Expenditures <«,) 1.280 -0.073 0.515 -0.201 -0.416 -0.105 Note: El a s t i c i t i e s of transformation are 1 + 3 i i / a i " 1 / a i i = j i,j=l,...,6 ^ 1 + i 3 l j / o 1 o j „ i * j and relative expenditures are X ^ U ^ /TT = i=l,...,6, with > 0 for an output, and a < 0 for an input. - 180 -w i th m a t e r i a l s beinq the s i x t h good. A l l the est imates are s i g n i f i -c a n t l y d i f f e r e n t from zero at the 5 percent l e v e l . This de te rm ina t i on i s made by performing the s u b s t i t u t i o n B n = a] ( l u - D + ctj i=j i , j = 1 , . . . , 6 (7.12) 3.. = c . a . ( n i r 1 ) i*i and r e - e s t i m a t i n q the v a r i a b l e p r o f i t f u n c t i o n . Th i s h i gh l y non - l i n ea r system i s est imated us ing the Newton method. The e l a s t i c i t i e s of t rans fo rmat ion are reported on the upper panel of Table 7.7. Along the p r i n c i p a l d i a gona l , a l l elements are s t r i c t l y p o s i t i v e , s a t i s f y i n g the requirement that these be non-negat ive . The o f f - d i a g o n a l terms i n d i c a t e the degree of s u b s t i t u t a b i l i t y and comple-menta r i t y between inputs and output s . In the lowe»* pane l are the r e l a t i v e expend i tu res . I t i s noted that whether two goods are s u b s t i t u t e s or complements cannot be determined s o l e l y by the s ign of n.^, s i nce both outputs and i npu t s are i n the c o n f i g u r a t i o n . For cost f unc t i on e s t i m a t i o n , w i th output exogenous, a negat ive o f f - d i a g o n a l element i n the s u b s t i t u t i o n mat r i x imp l i e s complementar ity. The e l a s t i c i t i e s of supply and demand are repor ted i n Table 7.8. These are 0). . a . + B../a. - 1 i=,J i , j = 1 , . . . , 6 . 1 1 1 1 (7.13) a . + 0 . . / a . i * j i i j J On the p r i n c i p a l d iagonal are the own e l a s t i c i t i e s of supply and - 181 -Table 7.8 Est imates of Own and Cross P r i c e E l a s t i c i t i e s of Supply and Demand to., (at geometric mean of sample) Loans Cash Demand Depos i t s Time Depos i ts Labor M a t e r i a l s Loans 0.3351 1.3571 0.7296 0.5212 1.1509 1.1609 Cash -0.0772 -1.3519 -0.1407 -0.0622 -0.0478 = ^0.3838 Demand Depos i t s 0.2933 0.9942 0.0810 0.5253 0.3875 0.7404 Time Depos i t s -0.0818 -0.1715 -0.2051 -0.5044 -0.1887 -0.1703 Labor -0.3738 -0.2727 -0.3131 -0.3906 -1.2360 -0.2603 M a t e r i a l s -0.0957 -0.5552 -0.1516 -0.0893 -0.0660 -1 .0871 Mote: to.. = n . .e . where n. . i s the t ran s fo rmat ion e l a s t i c i t y and e. r e l a t i v e expend i tu re , i , j =1 , . . . , 6 - 182 -demand. Since loans and demand deposits are outputs, the own e l a s t i c i -ties are positive. In the case of loans, a 1 percent increase in the user cost of loans increases the loan supply by 0.3351 percent, implying a relatively inelastic supply. For demand deposits, the supply elasticity is 0.0810 also revealing an inelastic supply. To determine significance of the point estimates, which are parametric only at the geometric mean of the sample, asymptotic standard errors are required. These are obtained by the substitution 6 i i = a i ( a ) i i " ! ) " a i i = j i . J - l , . . . , 6 (7.14) B = a.(co. . - a.) i * j and re-estimation. The non-linear system, again estimated by the Newton method, indicates that a l l diagonal elements are significantly different from unity at the 5 percent level. Demand for cash by banks is relatively elastic. The own e l a s t i c i t y is -1.3519 with respect to its user cost, essentially the interest fore-gone by holding cash. For time deposits, the e l a s t i c i t y is -0.5044, again significantly different from unity. For physical inputs, the technology i s relatively more flexible. The demand for both labor and raw materials is elastic, with the labor demand el a s t i c i t y -1.2360, and that for materials -1.0871. Off the principal diagonal, i t is possible to classify the various pairs of goods. Where both are inputs demanded by the bank, a positive cross price e l a s t i c i t y indicates the goods are substitutes. A negative cross price e l a s t i c i t y indicates complements. - 183 -It is possible to classify pairs of goods as substitutes or complements, whether inputs or outputs. There are three combinations, being two outputs, two inputs, and one input and one output. Consider f i r s t the two output case. If output j is a substitute for output i , 3x^/3Uj < 0. The supply of output i decreases as the price of substitute output j increases. Since = 3TT/3 U ^ , 3x^/3u^ < 0 2 implies the Hessian element 3 T T / 3 U ^ 3 U J < 0 i f i and j are substitutes. The reverse condition obtains for complements. Now consider the two input case. If input j is a substitute for input i , 3x^/3u. > 0. That is the demand for input i increases as the price of substitute input j increases, and hence i t s demand f a l l s . If x^ is an input = -Sir/Su^, then 3xi/3u^ > 0 implies the Hessian 2 element 3 ir/Su^u^ < 0 i f inputs i and j are substitutes. Again, the reverse condition holds for complements. The third case obtains for one input and one output. If good j is an output and good i an input, 3x^/3u^ > 0 i f these are complements. An increase is the price of output e l i c i t s an increase in quantity supplied, and in the quantity demanded of an input which is complementary. Symmetrically, i f the input price u increases, i t s - 184 -quantity declines, and i f x^ . is a complement, x. must decrease. Since 2 3x^/9uj = 3 TT/3U^3U_., the Hessian element is positive i f goods i and j are complements and negative i f they are substitutes. This indicates a general classification rule for substitutes and complements. Goods i and j are substitutes i f and only i f 2 2 3 n/3u^3uj < 0 and complements i f and only i f 3 T T/3U^3 U J ^ > 0. The procedure can be applied to any pair of goods, and not only two inputs, as in the cost function approach. The procedure generalizes the definition of substitutes and complements to the profit function. The class i f i c a t i o n for the bank, data is indicated in Table 7.9 using the Hessian matrix of the variable profit function, Table 7.4. The cross price elasticity is 3x^/3u^ • u^ /x^ , or the Hessian element times u_./x^ . If x^ is an input then the sign of the cross price e l a s t i c i t y is opposite to that of the Hessian since inputs are measured negatively. If x^ is an output then the cross price e l a s t i c i t y has the same sign as that in the Hessian matrix. So i t is also possible to use Table 7.8 to classify pairs. On the output side, i f the cross price elasticity between any two outputs is positive, they are complements. An increase in the return to loans raises its supply, and also the supply of demand deposits. This implies that the bank produces joint services in demand deposits and - 185 -Table 7.9 C l a s s i f i c a t i o n of Pairs, Substitutes and Complements Two inputs Complements Substitutes Cash - Labor Cash - Time Deposits Cash - Materials Time Deposits - Labor Time Deposits - Materials Labor - Materials Two Outputs Complements Substitutes Loans - Demand Deposits One Input, One Output Complements Substitutes Loans - Cash Loans - Time Depsots Loans - Labor Loans - Materials Demand Deposits - Cash Demand Deposits - Time Deposits Demand Deposits'- Labor Demand Deposits - Materials - 186 -loans. The bank cannot extend loans without a deposit base, and the demand deposits services are produced simultaneously with loans. In Table 7.9 is indicated the direction of quantity response of an input or output when the user cost of another changes. This is obtained by reading down each column of Table 7.8. For example, -0.0772 is the price e l a s t i c i t y of supply of loans when the user cost of cash increases. An increase in the user cost of cash reduces the supply of loans. This permits an examination of the response in pairs containing one input and one output. A l l pairs indicate substitutabilty between input and outputs. In the case of loans, supply is decreasing in the user cost of a l l inputs. A l l effects are relatively inelastic, in that they are less than unity. The largest magnitude is with respect to labor costs, at -0.3738. The remaining responses are reported in Table 7.9. Estimates on the demand for money also indicates low e l a s t i c i t i e s of substitution between financial goods. Barnett [1981, Appendix E] obtains many ela s t i c i t i e s close to zero. Of 23 estimates presented for substitution between passbook savings, small time and negotiable deposits at various institutions, only two exceed unity. The results are reported with the exception of the two cases just described, substitutability between financial assets has remained very low. Earlier published studies of substitutability between monetary assets have a l l indicated very low substitutability between monetary assets (Barnett [1981], p. 218). The comments pertain to the demand side, and the construction of aggregate money demand. 187 -The cross ' p r i c e e l a s t i c i t i e s of supply, i n the case of loans and demand depos i t s in the f i r s t and t h i r d columns, and demand, for cash, t ime depo s i t s , labor and m a t e r i a l s , are gene ra l l y l e s s than u n i t y , again suggest ing a r e l a t i v e l y i n f l e x i b l e technology on the part of the banks. A l l of the cross p r i ce e l a s t i c i t i e s are l e s s than un i t y except for t h ree . These are the demands for l abor and ma te r i a l s and cash when the user cos t of loans changes. As the user cost of loans i n c rea se s , more loans are s upp l i ed , and a d d i t i o n a l demands fo r cash and labor to s e r v i c e these loans r e s u l t s . R e l a t i v e l y l a rge changes in the p r i c e v a r i a b l e s under l y i ng user co s t s , in i n t e r e s t r a t e s , depos i t insurance charges, wage ra te s and m a t e r i a l p r i c e s , are requ i red to induce s u b s t a n t i a l s h i f t s i n the supply of loans and demand depo s i t s , and input demands by banks. Th i s has i m p l i c a t i o n s f o r whether monetary q u a n t i t i e s or i n t e r e s t r a te s should be the object of c e n t r a l bank c o n t r o l i n monetary p o l i c y . 7.6 Rate of Return on Capital The. f ina l item i n the e s t imat ion i s the determinat ion of the r a te of r e tu rn on c a p i t a l ex post . In p r o f i t f unc t i on e s t imat i on without 7 demand or supply equat ions, t h i s has proved d i f f i c u l t to i d e n t i f y . The ra te of r e tu rn on c a p i t a l i s 3 T T ( U , X )/3x and fo r a p o s i t i v e ra te of r e t u r n , and short run ope ra t i on , some qua s i - r en t s must be covered. Th i s r equ i r e s 3TT (u,x K>/3x^ > 0. A l s o , 31nTr (u,x K )/31nx K = (c)-a(u,x^)/C)X^)X^/T! > 0 under the same c o n d i t i o n s , provided qua s i - r en t s n are p o s i t i v e . For the v a r i a b l e p r o f i t f unc t i on as s p e c i f i e d K i=1 and 3TT _ _ 9£,nTf TT__ IT 3xj^ " U K " '3Anx K x~ = ^ \ + . \ B i K £ n U i + 0 K K £ N X K 1=1 (7.16) wi th 3TT/3X^ the ex post shadow user cost of c a p i t a l . I t i s thus measured analogously to other user c o s t s . This i s the ex post r e tu rn i f f i t t e d values are used for TT and 3£nir/3Jtnx , and est imates f o r a and 0 i K , 1=1 , . . . ,5 and B ^ . At the geometric mean of the sample, 3TT/3X = a ir/x^, = u . Hence ct^ = U ^ X ^ / T T , the value of c a p i t a l s e r v i ce s d i v i ded by p r o f i t s . Under constant returns to s ca le and compet i t i ve markets for outputs and i npu t s , product exhaust ion obta in s 'and c a p i t a l s e r v i c e expend i tures are equal to v a r i a b l e p r o f i t s . Here u^x^ = ff'and = 1. A te s t f o r = 1 and B j ^ = 0, i=1,. . . ,5 wi th B ^ = 0 i s a s u f f i c i e n t c o n d i t i o n f o r constant returns to s c a l e . The l i k e l i h o o d r a t i o t e s t r e j e c t s t h i s 2 2 hypothes i s at the 0.01 l e v e l , with a x te s t s t a t i s t i c for x /7 of 8.75. Hence the c a p i t a l parameters accepted by the data are those of Table 7.2 w i th a = 0.840, i n d i c a t i n g that c o m p e t i t i v e l y p r i ced c a p i t a l K s e r v i c e s do not exhaust a l l p r o f i t s made by banks. L o c a t i o n a l r e n t , manager ia l p r o d u c t i v i t y not measured i n labor i npu t , and uncompet i t i ve market phenomena are other po s s i b l e e xp l ana t i on s . The return u i s measured analogously to the user c o s t s . The re tu rn i s thus the premium - 189 -earned on c a p i t a l above that earned on low r i s k investments. I f I L . < 0 then the bank does not engage in p roduc t i on . The extent of u^ > 0 i s a measure of the a d d i t i o n a l re turn to c a p i t a l in banking. The measure u^ i s the user cost of c a p i t a l in p h y s i c a l and f i n a n c i a l forms. This i s measured in the same un i t s as the other user c o s t s , namely i n d i scounted form. The mean v a r i a b l e p r o f i t s a t t a i ned are $6,098 m i l l i o n . The va lue o f p h y s i c a l and f i n a n c i a l c a p i t a l i s $22,698 m i l l i o n f o r the mean bank. The r a t i o TT/X , or average v a r i a b l e p r o f i t to c a p i t a l , i s 0.268. M u l t i p l y i n g by a = 0.84 the ex post r e a l i z e d re turn on c a p i t a l i s 0.225. This imp l i e s that the ra te of re tu rn on c a p i t a l i s 22.5 percent before t a x . The marg ina l ra te of corporate income tax paid by the banks, i s 0.48. So T T ( 1 - T ) / X k = 0.268*0.52 or 0.139. The a f t e r tax ra te of r e tu rn on c a p i t a l i s 11.6 percent . Th is re tu rn covers d e p r e c i a t i o n , oppo r tun i t y co s t s and the c a p i t a l i z e d l o c a t i o n a l , manager ia l and compet i t i v e or uncompet i t ive aspects of bank behav ior . 7.7. Policy Implications; Monetary Policy and Bank Behavior 7.7.1 I n t r oduc t i on The e m p i r i c a l r e s u l t s suggest that bank technology i s c h a r a c t e r i z e d by an i n e l a s t i c supply f o r outputs , and r e l a t i v e l y e l a s t i c demand for i n p u t s . Both loans and demand depos i t s have supply e l a s t i c i t i e s l e s s than 0.5 at the geometric mean of the da ta . This has i m p l i c a t i o n s fo r monetary p o l i c y , for the o f f e r i n g of loans i s r e l a t i v e l y r i g i d w i th respect to changes i n user cost components such as i n t e r e s t r a t e s . - 190 -On the input s i de , the bank i s a net demander of cash, time d e p o s i t s , l abor and m a t e r i a l s . From Table 7.8 the r e spec t i v e e l a s t i c i -t i e s of demand f o r a bank having sample geometric mean c h a r a c t e r i s t i c s are -1.3519, -0.5044, -1.2360 and -1.0871. Three of these are g rea te r than u n i t y . However, fo r time depo s i t s , the demand i s r e l a t i v e l y i n e l a s t i c . In the f i n a n c i a l sector of bank ope ra t i on s , a p i c t u r e of a r i g i d technology a r i s e s . While banks are r e l a t i v e l y respons ive to p r i c e s i n h i r i n g p roces s ing and managerial employees, or i n purchas ing a d v e r t i s i n g copy or o f f i c e s upp l i e s , they are l e s s respons ive to i n t e r e s t r a te s or o ther monetary p o l i c y r e gu l a t i o n s . To examine the behavior of banks regard ing monetary p o l i c y , some p o l i c y experiments are performed. The f i r s t , cor respond ing to the subsequent de regu la t i on of depos i t i n t e r e s t r a te s i n 1980, permits an increase i n the maximum i n t e r e s t r a te payable on time depo s i t s of one ha l f of one percent . The second e l i m i n a t e s the reserve requirements on demand depo s i t s . The t h i r d examines the s t r u c t u r e ofchanges i n FDIC premiums. I t i s assumed that there i s no change i n coverage. 7 .7 .2 . I n t e r e s t Rate C e i l i n g Deregu lat ion The user cost of time depos i t s i s U, = -1 + (1 + r TD + b TD + Rk TD - s T l J/(1+R) (7.17) where r TD i s the i n t e r e s t ra te paid on time depo s i t s , b TD the depos i t insurance premium, R the discount r a t e , k. TD the reserve requirement and s e r v i c e charge revenue. In 1978, the mean time depos i t user cost i s 1.1565 percent . 1 9 1 -S ince 3uy D/8 r-^ = 1/0+R), an increase of 0.5 percent in time depos i t r a te s r a i s e s user cos t s by 0.5/O+R) percent . The mean i n t e r e s t r a te paid on such depos i t s in 1978 i s 5.037 percent . An inc rease of 0.5 percent r a i s e s the average i n t e r e s t rate by 9.9 percent . Th is i s approx imately the same as the e f f e c t on the user co s t , because the d i scount f a c t o r i s c l o se to u n i t y . Barro and Santomero [1972] have shown that the c e i l i n g rate c o n s t r a i n t i s b i nd i ng , and Santomero and S i e g e l [1981] have examined the aggregate e f f e c t s of t h i s . The compara-t i v e s t a t i c f o r the ac tua l depos it c e i l i n g de regu l a t i on imp l i e s an approximate 10 percent increase i n user c o s t s . From Table 7.8, the own e l a s t i c i t y of demand for time depos i t s i s Q -0 .07 . Th i s imp l i e s a 7 percent dec l i ne i n the quan t i t y of time d e p o s i t s . Bank p r o f i t s are a f f ec ted by 3£mr/3£nu^ = at the sample mean. From Table 7.2 t h i s i s - .20 , so the e f f e c t i s to lower bank p r o f i t s by 2.0 percent , by o b l i g i n g the bank to pay a h igher ra te to d e p o s i t o r s . An argument against depos i t r a te c e i l i n g removal i s that banks pass on the lower i n t e r e s t rates as reduced costs to borrowers. Apart from the e f f i c i e n c y and equ i ty aspects of t h i s t r a n s f e r , i t i s p o s s i b l e to examine the degree to which t h i s a l l eged cross s u b s i d i z a t i o n takes p l a c e . The cross p r i c e e l a s t i c i t y of loan supply w i th respect to time depos i t user cos t s i s -0.08, so a 10 percent increase reduces loan q u a n t i t i e s by 0.8 percent. The e l a s t i c i t y i t s e l f i s c l o se to zero n u m e r i c a l l y , but u l t i m a t e l y a p o l i c y d e c i s i o n i s requ i red on whether a r educ t i on i n loan volume of 0.8 percent i s l a r ge or s m a l l . 9 - 192 -On depos i t sw i t ch i n g , the evidence i s a l so of s l ugg i sh response. As i n t e r e s t rates r i s e on time depo s i t s , holders s h i f t from demand to time d e p o s i t s . Th is has the e f f e c t of i nc rea s ing the average cost of depos i t s to the bank. The cross p r i c e e l a s t i c i t y of demand depos i t supply with respect to the user cost of time depos i t s i s - 0 .21 , the d e c l i n e in the d o l l a r quan t i t y of demand depos i t s i s 2.1 percent . In c onc l u s i o n , depos i t r a te c e i l i n g de regu la t i on has smal l numeri-c a l e f f e c t s on the compos i t ion of loans and depo s i t s . Hence the conse-quences of removing these d i s t o r t i o n s are not s u b s t a n t i a l . 7 .7.3. Reserve Requirement Costs Reserve requirements enter the user cos t s of depo s i t s e x p l i c i t l y . These requirements act as taxes on the f i n a n c i a l f i r m . The second p o l i c y experiment i nvo l ve s abo l i s h i n g the reserve requirement on demand d e p o s i t s . As reserve reguirements i nc rea se , banks face h igher user c o s t s of d e p o s i t s . The user cost of demand depos i t s i s U 2 = -1 + (1 + r D n + b Q D + R k n o - s D D )/(1+R) (7.18) analogous ly to (7 .17) . Here r n p i s p o s i t i v e only i n 1978, where NOW accounts are inc luded as of November. The depos i t insurance premium i s bpp, and the reserve requirement cost Rk^p. Se rv i ce charges and p e n a l t i e s are s ^ . I f reserve requirements were e l i m i n a t e d , then Rk^p = 0. As an oppos i t e po l a r case, the I r v i n g F i she r [1935] "100 percent money" p o l i c y i m p l i e s k ^ = 1, and Rkpp = R. In 1978 the mean user cost of demand depos i t s i s -4.07 percent . The negat ive user cost imp l i e s that - 193 -demand depos i t s y i e l d net revenue to the banks, or are outputs . The reserve requirement e f f e c t Rk^p i s 0.475 percent, on average. Now Su^/Skpp = R/(1+R), the e f f e c t on demand depos it user co s t s of changing reserve requirements. I f k ^ = 0, the e f f e c t on i s to e l i m i n a t e the Rkpp/M+R) term or 0.0456 p e r c e n t . 1 0 This reduces user co s t s f o r demand depos i t s to -4.53 percent . The reserve requirement e l i m i n a t i o n would reduce user cos t s by 11.3 percent for the mean bank. The own p r i c e e l a s t i c i t y of supply fo r demand depos i t s i s 0.08, so an i nc rease i n net revenue per d o l l a r se rv i ced i n such an account per year i nc reases depos i t s by 0.9 percent . The banks are more w i l l i n g to supply demand depos i t s i f the taxes imposed by the reserve requirement are e l i m i n a t e d . The e f f e c t i s s m a l l , because of the low own p r i c e e l a s t i c i t y of supply . The e f f e c t on p r o f i t s i s ^mr/a^nu^ = at the qeometr ic mean of the sample, where if and u^ are v a r i a b l e p r o f i t s and the user cost of demand depos i t s r e s p e c t i v e l y normal ized by the p r i c e of m a t e r i a l s . From Table 7.2 t h i s i s 0.84, or an 11 percent increase in net revenue per un i t depos i t i nc reases v a r i a b l e p r o f i t s by 9.2 percent . In terms of r e a l l o c a t i o n i n loans and phy s i c a l i npu t s , the c ross e f f e c t s are l a r ge s t f o r cash. As the demand depos i t revenue i n c r e a s e s , banks i nc rea se employment of a l l four v a r i a b l e i nput s , and expand loans a l s o . Cash ho ld ings inc rease by over 12 percent, and employment of l abor i nc reases by 0.39*0.11, or by 4.3 percent. The r e s u l t s i n d i c a t e - 194 -that the reserve requirement imposes costs on bank ope ra t i on s , and reduces output and employment for those in the banking s e c t o r . Th i s conc lu s i on r e s t s on the view of reserve requirements as pure taxes . While normative conc lu s ions depend on the weights p o l i c y makers a s c r i be to employment and bank e f f i c i e n c y , and u l t i m a t e l y on the bene-f i t s of the r e g u l a t i o n s , i t i s po s s i b l e to compare the two p o l i c y measures. The i n t e r e s t ra te de regu la t i on in the f i r s t s i m u l a t i o n , permits i nc reases of 0.5 percent per year. The cost of the reserve requirement on demand depos i t s i s 0.475 percent per year , an almost i d e n t i c a l f i g u r e . Yet a de regu l a t i on on demand depo s i t s , the l a t t e r case, i nc reases bank revenues more s u b s t a n t i a l l y than i n t e r e s t r a te de regu l a t i on on time depo s i t s , and has g reate r e f f e c t s on output and employment i n the banks. 7.7.4. Depos it Insurance - FDIC Regu la t ion The f i n a l comparative s t a t i c i s on changes i n the FDIC premium. The comparative s t a t i c s of the premium are examined. C a p i t a l i s f i x e d and exogenous dur ing the pe r i od . I t may be po s s i b l e to model c a p i t a l adequacy, or r egu l a t i on s on shareho lder s ' e q u i t y . In the e x i s t i n g s t r u c t u r e , changes i n c a p i t a l , have vary ing e f f e c t s dependent on whether assets or l i a b i l i t i e s are a l t e r e d as a conseguence. Another i s sue i s the coverage of the FDIC premium, or th re sho ld depos i t l e v e l up to which the depos i to r i s e l i g i b l e for reimbursement. Th i s increased dur ing the pe r i od , implying a g reater insurance re tu rn to the bank per d o l l a r of premium p a i d . A d d i t i o n a l depos i t s may be ob ta i ned . S ince i n d i v i d u a l depos i t data are not a v a i l a b l e , the coverage - 195 -e f f e c t cannot be adjusted f o r , but i s recogn ized. Re lated to t h i s i s the c a p i t a l adequacy p r o v i s i o n s , on regu la ted sha reho lde r s ' e qu i t y . There may be u l t i m a t e l y a r egu l a to r y t r adeo f f between the FDIC premium and the degree of deb t -equ i t y r e g u l a t i o n . A complete a n a l y s i s would inc lude a v a r i e t y of r equ la to r y t r a d e o f f s . Q u a n t i f i a b l e costs of depos i t insurance r e g u l a t i o n are r e a d i l y a v a i l -ab le only f o r the premium paid to FDIC. I nd i r e c t r e g u l a t i o n , in so lvency s u p e r v i s i o n , asset and l i a b i l i t y coverage, and i n s p e c t i o n may a l so o b t a i n , as Buser, Chen and Kane [1981] have pointed out . Fu r t he r , r i s k poo l ing and c ross s u b s i d i z a t i o n may make the premium lower than that which would have obta ined had a p r i v a t e agency been the i n s u r e r . I t remains the case tha t FDIC coverage i s mandatory fo r the banks i n the sample. The r e g u l a t i o n s over the sample per iod 1973-1978 prov ide that a premium of 1/12 of one percent of depo s i t s be l e v i e d . Th i s i s rebated to an e f f e c t i v e premium of 1/30 of one percent approx imate ly . I f no rebate i s made, the e f f e c t i v e premium inc reases by a m u l t i p l e of 30/12, or 2 .5. The e f f e c t of e l i m i n a t i n g t h i s rebate i s examined. For demand depo s i t s , the average FDIC premium ra te as c a l c u l a t e d on the average d o l l a r Is 0.0392 percent i n 1 978 . 1 0 App ly ing t h i s f a c t o r , the premium rate becomes 0.098 percent . The FDIC premium i s a l ready a n e g l i g i b l e component of the user cost of demand d e p o s i t s . Using the sample mean values i n Table (5.13) i n percent r D D = 0.0006 bDD = 0 ' 0 3 9 2 R k D D = 0.4750 s D 0 = 0.7167 - 196 -w i th the s e r v i c e charge and penalty rate of 0.7167 percent y i e l d i n g s u f f i c i e n t to exceed the other components. Now ^ . , / 3 b ^ = l/(1+R), and the change i n FDIC premium i s 0.059 percent . Fu r the r , 0.059/O+R) i s 0.056 percent , the change i n the user cost of demand d e p o s i t s . From the mean demand depos i t user cost of -4.07 percent, the FDIC rebate a b o l i -t i o n reduces the net revenue per un i t of demand depos i t s to 4.01 percent , or 1.5 percent . Th i s e f f e c t of 1.5 percent compares with the 9 percent e f f e c t of e l i m i n a t i n g the reserve requirement, so the impact i s p r o p o r t i o n a t e l y s m a l l e r . Hence the e l i m i n a t i o n of the premium rebate has a sma l l e f f e c t on ou tpu t . Demand depos i t s increase by 0.6 of 1 percent , and loans by 0.4 of one percent . These are the d i r e c t e s t imate s . I f the depo s i t o r s pe r ce i ve h igher premium rates as an i n d i c a t i o n of s a fe r banks, depo s i t s may i nc rea se f u r t h e r . 7.8 Concluding Remarks The r e s u l t s i n d i c a t e that a user cost f o rmu la t i on of loans and depo s i t s can be app l i ed to data on the banking system. A r b i t r a r y c l a s s i f i c a t i o n of inputs and outputs can be dispensed w i t h , fo r the procedure determines t h i s . The e s t imat i on conf i rms a wel l -behaved p roduc t i on technology, e x h i b i t i n g convex i ty and monoton i c i t y . A wide range of p o l i c i e s can be ana lyzed, because the user c o s t s i n c l u d e reserve requirements, depos i t insurance and i n t e r e s t r a t e s . The bank technology on the supply of loans and demand depos i t s has been shown t o be i n f l e x i b l e , w i th low e l a s t i c i t i e s of supply . The a n a l y s i s - 197 -of money demand has been ex tens i ve , but les s a t t e n t i o n has been paid to the process by which money i s s upp l i ed . The r e s u l t s i n d i c a t e that such an a n a l y s i s i s p o s s i b l e . - 198 -NOTES 1lhis is result (6.A.5) in the Appendix to Chapter 6 and is derived there. For the general case, with an arbitrary variable profit function 1 + O K . = n . .e . = e. i j i J ] J u. 3e. 9u. ' J 1 TT 1 e .e . 3u. u.x. 3u. 1 j J 1 J J For the own price e l a s t i c i t i e s of supply (outputs) and demand (inputs), 3u./3u. = 1, and i=j hence U i 8 e i U i i = n i i e i = e i 1^ ~ 1 = e± + 3Jtnei/3£nui - 1 i=1,...,5 where Slne./SlnUj is the elasticity of the relative expenditure with respect to i t s own user cost. For the cross price e l a s t i c i t i e s , 3u^/3u^ = 0 and i * j " i i = n i j e j - = e j 1 + e i e j 3 u j = + 3£ne^/3)lnuj i,j=1 5 where 31ne./31nu^ is the cross relative expenditure elasticity for good i with respect to good j . In a l l cases, e^ >^ 0 for an output and e. < 0 for an input, i=1,...,5. The Lagrange multiplier form involves imposing the restrictions as constraints on the likelihood function. See Berndt and Savin [1977] for an explicit derivation. ^The convexity is also tested at each data point in the sample, following the appendix to Chapter 6. It obtains for a l l observations. 5To determine the sensitivity of results to the point of normali-zation, the entire model was re-estimated at the data point correspond-ing to a l l 1973 observations on bank 1. The results did not differ substantially. To examine the global properties of the translog, renormalization at every every sample point would be necessary. - 199 -D The MQ money supply i s a degenerate case, s ince an aggregate c on t a i n i n g one good can be obtained by the i m p l i c i t f unc t i on theorem. Fu r the r , a l l cons idered money aggregates conta in at l ea s t cash. 7 The e l a s t i c i t y used i n t h i s and in the remaining s i m u l t a t i o n s i s that ob ta i n i n g at the sample mean. For use with data in 1978, t h i s i s not s t r i c t l y app rop r i a te , as another e l a s t i c i t y matr ix i s requ i red f o r the 1978 da ta . However, the matr i ces are s i m i l a r in s t r u c t u r e . Q As the depos i t base f a l l s , the capac i t y to make f u r t h e r loans may a l s o be a f f e c t e d . g The d i scount ra te R, used as the minimum i n t e r e s t ra te paid by any sample bank on time depo s i t s , i s 4.03 percent . 1 0 The average FDIC premium r a t e i nc ludes i n the denominator accounts with po r t i on s over the insurance l i m i t . - 200 -CHAPTER 8 IMPERFECT COMPETITION AND THE FINANCIAL FIRM 8.1 Introduction The objective is to develop a model of financial firms which can be estimated empirically. Typically, estimation of firm technologies assumes that the firm is a price taker in output and input markets. Financial firms such as banks, whether in loans or deposits markets, or in the markets for physical labor or materials, are assumed to exert no noncompetitive presence. It is assumed they face perfectly elastic supply schedules in input markets and perfect elastic demand schedules in output markets. Making such price taking assumptions testable In both output and input markets has implications for regulatory policy. The effect of monetary policy may differ i f price taking is imposed on a structure where this is not the case. Section 2 develops the institutional context of imperfect competition in the banking industry. It is shown that imperfect competition can exist at both regional and national levels in the product markets relevant for financial firms. In Section 3 a model is developed which allows s t a t i s t i c a l testing of competitive behavior in both input and output markets. An implementable specification is developed in section 4, and empirical results are in section 5. Section 6 analyzes the implications for monetary policy. The data used are 1973-1978 observations on eighteen banks in the New York Federal Reserve District. The banks supply loans and demand - 201 -deposits to customers with inputs labor, time deposits and cash. Price taking behavior is accepted as a hypothesis, only in the labor market. The analysis of the effects of monetary policy must take account of this. 8.2 Noncompetitive Banking Behavior: The Context The fundamental case for a policy of stimulating competition in the financial system must rest on ensuring that credit is allocated to i t s most valuable uses at the minimum average cost. Competition also ensures that a broad range of financial instruments is made available to asset holders, offering the most favorable combinations of risk, liquidity and expected yie l d . 1 Financial firms produce several outputs. The products include services, such as demand deposits and different kinds of loans. Each product constitutes a separate market in which the financial firm operates. In these product markets, the firm, such as a bank, faces competition in varying degrees both from other banks and from non-bank financial institutions. Banks have to compete with one another and other firms for their inputs, typically savings deposits, labor, materials and capital. Financial firms also operate in different geographic markets. In a survey conducted by the Federal Reserve System i t was found that the bank market for large business loans is national while that for small business loans is local. There appear to be at least two institutional reasons that contribute potentially to imperfect competition in the financial sector. The f i r s t is the regulatory structure. Laws and regulations - 202 -d e a l i n g with cond i t i on s of en t ry , branching, and ho ld ing company expansion have not always acted to maximize compet i t ion among f i n a n c i a l f i r m s . In many r u r a l markets in the United S tates there i s only one bank. A l so r egu l a t i on s r e s t r i c t i n g unsound compet i t i on , such as the p r o h i b i t i o n of i n t e r e s t payments on demand depo s i t s , may r e s u l t i n inc reased market power f o r i n d i v i d u a l banks. Second, there may be economies of s ca l e i n f i n a n c i a l i n t e r m e d i a t i o n . P r i c e s , i n t e r e s t r a t e s and user cos t s are t y p i c a l l y u n c e r t a i n , as are regu la to ry changes by the Fede ra l Reserve System and the FDIC. I f l a r g e r i n s t i t u t i o n s are ab le to hedge more s u c c e s s f u l l y aga inst these u n c e r t a i n t i e s , then monopo l i s t i c tendenc ies can a r i s e . As examples, forward con t r a c t s and f u tu re s markets may requ i re l a r ge minimum cont rac t purchases, and average brokerage and l e g a l fees may d e c l i n e with the amount of funds i n v o l v e d . F i n a n c i a l i n s t i t u t i o n s d i s c r i m i n a t e on p r i c e s . D i f f e r e n t p r i c e s are charged to d i f f e r e n t customers. Th is may be i n d i c a t i v e of i m p e r f e c t l y compet i t i ve behav io r . The t r a d i t i o n a l approach to measuring monopo l i s t i c power i n an i ndu s t r y i s to use concent ra t i on r a t i o s . These are subject to s e r i o u s m i s i n t e r p r e t a t i o n un less supplemented with other f a c t u a l m a t e r i a l . The major danger of t h e i r use i n the banking i ndus t r y i s i n d e f i n i n g the app rop r i a t e market, both product and geographic. Concent ra t ion r a t i o s i n banking are u s u a l l y measured in terms of depos i t s f o r three separate geographic markets, n a t i o n a l , s t a te and met ropo l i t an a rea . Concent ra t ion i n the na t i ona l market i s r e l a t i v e l y low compared w i th many other American i n d u s t r i e s . S tates pe rm i t t i n g s ta tewide branching are more heav i l y concentrated than s t a t e s with u n i t bank ing, - 203 -a lthough the increase i n the number of branch o f f i c e s has been s u b s t a n t i a l l y g reate r i n s t a t e s with branch banking. At the l o c a l market l e v e l concent ra t i on appears h igh , and becomes higher the sma l l e r the met ropo l i t an a rea. S ta tes with branch banking have un i fo rmly h igher r a t i o s than those l ocated with un i t banking. Ra t io s f o r areas having l i m i t e d branch banking f a l l i n between the other two. In the average l o c a l banking market i n 1977 there were the equ iva lent of only 2.3 banks on a s i ze -we igh ted ba s i s , imply ing the average He r f i ndah l index was 0 . 4 4 . 4 Whi le a high degree of concent ra t i on i s i n i m i c a l to a c t i v e p r i c e c o m p e t i t i o n , i t does not n e c e s s a r i l y imply a l ack of such c o m p e t i t i o n . K l e i n [1971] argues that although government s e c u r i t i e s can be sa id to be i n p e r f e c t l y e l a s t i c supply to the i n d i v i d u a l bank, t h i s i s not the case f o r p r i v a t e s e c u r i t i e s or loans . C e t e r i s pa r i bu s , i f a bank wishes to inc rease i t s loan/asset r a t i o i t must accept a r educ t i on i n the marg ina l r e tu rn on l o a n s . 5 Hence these loans are i n i m p e r f e c t l y e l a s t i c supply to the i n d i v i d u a l bank, imply ing some form of impe r f e c t c o m p e t i t i o n . Elsewhere K l e i n [1972] argues that f a i l u r e to recogn i ze t h i s d i s t i n c t i o n c o n s t i t u t e s a major weakness i n t r a d i t i o n a l p o r t f o l i o t h e o r e t i c models and i s r epons ib l e fo r the almost nonex i s tent use of such models i n app l i ed banking re sea rch . Sealey [1980] argues that depos i t markets are not p e r f e c t l y c o m p e t i t i v e , p a r t i c u l a r l y where i n te rmed ia r i e s set ra tes and face random depos i t l e v e l s . I t i s f u r t h e r argued that because pe r fec t compet i t i on i s u s u a l l y assumed in depos i t markets, l i q u i d i t y con s i de ra t i on s are i gno red . In e s t ima t i n g a p r o f i t f u n c t i o n , Mul l ineaux [1978] ob ta i n s r e s u l t s which do not conform to a p r i o r i expec ta t i on s . He t e n t a t i v e l y - 204 -i n t e r p r e t s these r e s u l t s as evidence of monopoly power f o r banks i n h i s sample. I f i t i s assumed that pe r fec t compet i t ion e x i s t s when monopoly power i s p resent , est imates of s u b s t i t u t i o n and t rans fo rmat ion p o s s i b i l i t i e s between outputs and inputs may be b i a sed . I t i s important to know the e l a s t i c i t y of demand f a c i ng the f i n a n c i a l f i rm f o r i t s products i n order to obta in the f i n a l change i n output when there i s a change i n i t s p r i c e . S i m i l a r l y , e l a s t i c i t i e s of supply f o r i nput s are necessary. Th is i s e s p e c i a l l y t rue s ince many monetary p o l i c y changes a f f e c t the components of user co s t s or p r i c e s , f o r the products of the f i n a n c i a l f i r m . Monetary p o l i c y r e s u l t s d i f f e r depending on whether pe r f e c t compet i t i on i s assumed or not . I t i s d e s i r a b l e to be able to t e s t s t a t i s t i c a l l y f o r c ompe t i t i v e behavior of f i n a n c i a l f i r m s . Appelbaum [1979] has developed a t e s t u t i l i z i n g d u a l i t y theory which can be extended to s e ve r a l m o n o p o l i s t i c a l l y supp l i ed o u t p u t s . 6 However, t h i s method i s based on the cost f u n c t i o n and hence must assume input markets are c o m p e t i t i v e . For f i n a n c i a l f i r m s , both input and output markets may be noncompet i t i ve . A model i s developed which a l lows s t a t i s t i c a l t e s t i n g of compet i t i ve behavior in both input and output markets. 8.3 Imperfect Competition and the Financial Firm The f i n a n c i a l f i r m i s a m u l t i p l e output, m u l t i p l e input e n t i t y . The -d imens iona l vector z denotes q u a n t i t i e s of output s , and the N^-d imens iona l vec to r x denotes q u a n t i t i e s of v a r i a b l e i n p u t s . P h y s i c a l c a p i t a l i n equipment, s t r u c t u r e s and i nvento ry , x^ i s f i x e d i n the - 205 -d e c i s i o n making pe r i od . The product ion p o s s i b i l i t y set y i e l d s the t r an s f o rmat i on func t i on between outputs and inputs T(z ,x ,x^) = 0. By the i m p l i c i t f unc t i on theorem, the t rans fo rmat ion f unc t i on can be expressed i n terms of one of the arguments. S e l e c t i n g the f i r s t i npu t , we have the product ion f u n c t i o n , x 1 = F ( z , x 2 , . . . , x K ) (8.1) 7 where both outputs and inputs are measured p o s i t i v e l y (z > 0, x > 0 ) . Monoton ic i t y of the f unc t i on imp l i e s 3F/9z^ > 0, i=1 , . . . and 9F/9x^ < 0, i=2, . . . ,N^. For the v a r i a b l e goods there are user c o s t s , or p r i c e s per u n i t of s e r v i c e . The user cos t s f o r outputs are negat i ve , and we denote output p r i c e s by v = ( v ^ , . . . , v ^ ) = ( -u^ , . . . - u ^ ) where u^ are the user co s t s of ou tpu t s , t y p i c a l l y of loan and depos i t s e r v i c e s . Inputs have p o s i t i v e user c o s t s . We denote input p r i c e s f o r f i n a n c i a l and p h y s i c a l goods by w= ^ . . . . w ^ ) = ( u N i + 1 > _ f " N I + N 2 > -Demand f o r the s e r v i c e s of the f i n a n c i a l f i r m i s i n d i c a t e d by the inverse, demand f unc t i on v i = D i ( z i ) 1=1 N 1 (8.2) where 9D^(z^) / 3z^ _< 0. Demands by consumers for f i n a n c i a l s e r v i c e s are downward s l o p i n g . This s p e c i f i c a t i o n accomodates non-compet i t i ve behavior of f i n a n c i a l f i r m s . I f ^ ( Z j ) i s cons tant , independent of z . , then the f i n a n c i a l f i rm i s a p r i c e taker i n the i t h output market. Fu r t he r , the D , ( z f ) s p e c i f i c a t i o n can account f o r quan t i t y r e l a t e d - 206 -p r i c i n g , such as lower loan i n t e r e s t ra tes on l a r g e r loan s i z e s . 3 Supply of inputs to the f i n a n c i a l f i rm i s determined by analogous i n ve r se supply f unc t i on s . These are w. = S. (x.) j=1 , . . . , N , . (8.3) J J J J > > 2 Thi s permits t e s t i n g for p r i c e tak ing i n input markets. Under complete p r i c e t a k i n g , S. (x.) i s a cons tant , and the observed w. i s J J J independent of quant i t y s upp l i ed . The requirement of minimum depos i t ba lances , with d i f f e r e n t i n t e r e s t ra tes paid above and below the t h r e s ho l d l e v e l , e xemp l i f i e s non-pr i ce t ak i ng behavior f o r f i n a n c i a l goods. For p h y s i c a l goods, quan t i t y d i s count s on purchases and overt ime wage ra te s are a l so examples. The f i n a n c i a l f i rm i s assumed to choose the i nput -output combinat ion which maximizes p r o f i t dur ing the p roduct ion p e r i o d . 1 0 V a r i a b l e p r o f i t fo r the f i n a n c i a l f i rm i s t o t a l revenue l e s s t o t a l v a r i a b l e cost or z»D(z) - x*S(x) w i th the dot denot ing an inner product . V a r i a b l e p r o f i t s are maximized subject to the p roduct ion f u n c t i o n c o n s t r a i n t , or TT = max {v.»z - w x : x^ = F ( z , x , . . . , x )} (8.4) z,x z > 0 x > 0, x > 0 . S u b s t i t u t i n g (8.2) and (8.3) i n t o (8.4), v a r i a b l e p r o f i t s of the f i n a n c i a l f i rm are TT = max{D(z)*z - S (x) *x:x^ = F(z,\^ , . . . ,x^)}. (8.5) z,x Now l e t ~x denote the vector of v a r i a b l e inputs i n the product ion - 207 -f u n c t i o n , x = x . , , . . . , x^ . The corresponding supply f unc t i on s are S = S _ ( x_ ) , . . . , S.. (x.. ). The product ion f unc t i on can then be expressed 2 2 N 2 N 2 x.^  = F ( z , x", x ^ ) . S u b s t i t u t i n g for x^ TT = max{D(z)*z - S^  ( F ( z , x , x^ ) ) F ( z , x , x^ ) - S ( x ) «x } . (8.6) z ,x The term S^(F(z ,x ,x^) ) F ( z , x , x^ ) i s the v a r i a b l e cost a s soc i a ted with the f i r s t i npu t , x^ . V a r i a b l e cost fo r other inputs i s represented by S ( x ) » x . The f i r s t order c ond i t i on s f o r p r o f i t max imizat ion are obta ined by d i f f e r e n t i a t i n g the v a r i a b l e p r o f i t s w i th respect to the cho ice v a r i a b l e s of the model, namely output and input q u a n t i t i e s . These are set equal to zero s imu l taneous l y . The f i r s t order c o n d i t i o n s with respect to output q u a n t i t i e s a re , 3 IT 9 D i n - . 3 S1 3F c 3F n 977 = 2 i 317 + ° i " ^."'V 3x7 3zT ' S1 317 = 0 1 i 1 i 1 3 D i . 3F 3 S< = Z i Tl\ + . D i " 17^ S1 + F< Z»*»*|C> 3 x j ] = 0 i=1 , . . . ,N 1 . (8.7) F i r s t order c ond i t i on s with respect to input q u a n t i t i e s a re , i l - _ x ! ! l . S - F (z x" x ) - ^ i — - s IE - 0 3x.j ' j 3x j S j ^ z ' * > \ > 3 x ^ ^ 3 x ^ - u 3 S i 3F - 3 S1 •*) 3 X 1 " S i " f . [ S 1 + F ( *'*» X K> 3 ^ ] = ° j=2 , . . . ,N 2 . (8.8) - 208 -By rearranging (8.7) and (8.8) and recalling the inverse demand functions for outputs, v = ^ i ^ z i ^ ^ o r *=^"'" * * ' ^ l a n c* t' i e ^ n v e r s e supply functions for inputs = S .(x^) for 1=1,...,^ the following results are obtained, 3 D < 3 F - dSl V i = " Z i 3i7 + JT^l + F ( Z ' X ' V ^ 1-1.....N, (8.9) 3S 3 F _ 3S1 W j = " X j 9 ^ 7 " 9^. [ S1 + F ( Z ' X ' X K ) 3 X 7 1 J=2»---'N2 j 3 1 (8.10) 3S The term in square brackets is equal to w^+ x^ 1_ which is the shadow 3 x l price of F(z,x,x^) = x^  . Equation (8.9) states that the firm produces output z^ u n t i l the observed output price v^ is equal to the marginal 3F product of output z^, , expressed in value terms less the imperfect competition term z^3D^/3z^. Now 3F/3z^ > 0 for an output, and i f price taking obtains in the ith output market, as well as for the f i r s t input, v^ = (3F/3z^) w .^ If the financial firm is not a price taker, and faces a downard sloping demand, SD^/Sz^ < 0, so -z^ SD^/Sz^ > 0. This implies the output price exceeds the marginal cost. For an input, monotonicity requires 3F/3x^ < 0, so in (8.10) - 3F/3xj > 0. If the financial firm faces a perfectly elastic input supply, 3SJ/3XJ = 0, and i f the f i r s t input has a similar condition, Wj • (3F/3Xj) w^ . The factor payment is equal to the marginal product. In a case where SS^/Sx^ > 0, - X J 3 S J / 3 X J is negative, so the factor payment exceeds the marginal product. Multiplying both sides of (8.9) by z±/xl - 209 -2 v . z . - z . 3D. c 3S 1 1 1 1 1 3£nF r c nt — \ 1 i = " 5— + T » — IS. + F ( z , x , x . J - 5 — J x.j x^ 3z. 3£nz. 1 ' K 3x^ i =1 , . . .N 1 (8.11) and m u l t i p l y i n g both s ides of (8.10) by xj/*-] w.x. - x . 2 3S. ~, ,- 3S. — = — I T 1 " l i ^ 1 L S 1 + F ( Z , 7 , X „ ) ^ - 1 ] x^ x^ ax. j K 3x^ j = 2 , . . . ,N 2 . (8.12) Equat ion (8.11) s t a t e s that the output e l a s t i c i t y i s l e s s than the r e l a t i v e expend i ture share v.z.fx. i f 3D./3z. < 0 or i f non p r i c e t a k i n g r 1 1 I 1 1 a r i s e s . For the input markets, -3£nF/3£nXj, the input e l a s t i c i t y i s p o s i t i v e , hence monopsony power a r i s e s i f the r e l a t i v e expend i ture i s l e s s than the input e l a s t i c i t y . Th is occurs i f 3S./3x. i s J 3 p o s i t i v e . I f the f i r s t input market has been s e l e c t ed to be one where p e r f e c t compet i t i on ob ta i n s , then 3S^/3x^ i s z e r o . 1 1 The p r i c e s v^ and w^ are measured r e l a t i v e to x^ , the f i r s t i npu t . Hence w^  i s equal to 3S u n i t y . Then S. + F ( z , x , x 1 / ) 1 = 1. Equations (8.11) and (8.12) become 3 x 1 2 — v . z . - z . 3D. 3£n F(z,x,x..) 1 1 1 1 ' K + x.j x^ 3z^ 3£nz^ 1 i = 1 , . . . N . (8.13) - 210 -w.x. - x . 3S. 3Jln F(z,x,x..) J J _ J J * x. 3x . 1 • J 3£nx . J j=2,. . .N. (8.14) r e s p e c t i v e l y . Suppose that inverse demand funct ions fo r outputs z^ can be adequately approximated by the f o l l ow ing f unc t i on s : D(z.) = a. + b.Jlnz. l l i i 1 = 1 ,...N 1 (8.15) over the re levant z^ range. Inverse supply func t i on s are approximated over the re levant x^ range by the f unc t i on s , S(x.) = c . + d . Jinx. J J J J J=2,...,N. (8.16) where the vec to r s a^,b^, i=1,.. . ,N^ and c ^ , d j , j =2 , . . . ,N_, are parameters. I f b^ < 0 then the demand f unc t i on i s downward s l op i ng f o r output i and i f d . > 0 fo r input j the supply i s upward s l o p i n g . J S u b s t i t u t i o n of (8.15) and (8.16) i n t o (8.13) and (8.14) y i e l d s v i z i z i b i 3 £ N F V Z » X » X K ^ 3£nz. l 1=1,...,ii. (8.17) w.x. - x . d 4 3£n F ( z , x , x K ) J J J J 3Jlnx. J j=2, . . . ,N. (8.18) "1 1 Given the observable p r i c e and guant i ty v a r i a b l e s f ac i ng the f i r m , v,w,x and z , the system of equations (8.17) and (8.18) can be j o i n t l y est imated once we assume a d i f f e r e n t i a b l e f u n c t i o n a l form for the product ion f u n c t i o n F ( z , x , x ). Note that i f b. = 0 in (8.17) the producer i s - 211 -behaving c o m p e t i t i v e l y , s e l l i n g output such that the output e l a s t i c i t y equals the r e l a t i v e expenditure share. I f b^< 0 then the f i rm i s not a p r i c e taker in output market i and faces a downard s l o p i n g demand curve. I f d j = 0 i n (8.18) the producer i s again behaving c o m p e t i t i v e l y . But i f d. > 0 then he i s behaving l i k e a monopsonist i n input market j . F i n a l l y , Zlnz^/Zln v^= v^/bj i s the p r i c e e l a s t i c i t y of demand fo r output z. . I f the abso lute value of v./b. < 1 then the f i r m l i i operates i n the i n e l a s t i c reg ion of the demand curve. For supp ly , 3£nx./3£nw. = w./d. and i f t h i s i s l e s s than one then the f i rm i s J J J J behaving as a c l a s s i c a l monopsonist. 8.* Specification The s t r u c t u r e i s app l i ed to the bank technology, c on t a i n i n g as v a r i a b l e goods loans , demand depo s i t s , cash, time depo s i t s , l abor and m a t e r i a l s . User cos t s per un i t of s e r v i ce are cons t ruc ted f o r these s i x , but there i s no p r i o r determinat ion that the user cost i s i nde -pendent of the l e v e l of the quan t i t y of s e r v i c e . For the data on 18 banks i n the New York Federa l Reserve D i s t r i c t , 1973-1978, loans and demand depos i t s are c l a s s i f i e d as output s , being net revenue earners for the banks, wh i le time depo s i t s , cash, l a b o r , m a t e r i a l s and c a p i t a l are i npu t s . Output z = (z^,z^) r e s p e c t i v e l y r e f e r r i n g to loans and demand depo s i t s . Inputs are x = ( x ^ , x ^ , x ^ ,x^) r e s p e c t i v e l y r e f e r r i n g to raw m a t e r i a l s , cash, time d e p o s i t s , l abor and c a p i t a l . - 212 -The product ion f unc t i on i s x = F ( z 1 ,x^,x^,x^ ,x^) between i npu t s and outputs , w i th raw m a t e r i a l s used as the dependent v a r i a b l e . A t r an s l o g s p e c i f i c a t i o n for F y i e l d s 2 5 2 2 JlnF = ct„ + E a . £n z . + E y. Jinx. + 1 /2 E E B. .Jlnz. inz. 0 i i i l i j l j i=1 i=2 i=1 j=1 (8.20) 5 5 2 5 + 1/2 E E 6. .Jinx. Jinx. + 1/2 E E 9 . . Jlnz . Jinx . i=2 j=2 1 J 1 J i=1 j=2 1 J 1 J and the e l a s t i c i t y of the aggregate F wi th respect to each good y i e l d s 3 * n F = ct. + E 6 . . i n z . + E 6..Jinx. 1=1,2 (8.21) dlnzi i j = 1 i j j j _ 2 i j j f o r the output s , and 2 5 4T^- = Y. + E 9..J lnz. + E 6..Jinx. 1=2,... ,4 (8.22) 3 *nx i i j = 1 i j J j = 2 i j J p f o r i n p u t s . S ince c a p i t a l i s f i x e d , no e l a s t i c i t y i s taken wi th respect to t h i s f a c t o r . The e l a s t i c i t i e s need only be s ub s t i t u t ed i n t o the p r i c e de te rminat i on equat ions f o r i nput s and outputs to y i e l d v - z b z 2 5 - ^ - i = — — + a . + E B..Jlnz. + E 9. .£nx. i=1,2 (8.23) x 1 x1 1 j=1 l ^ J j=2 1 J J where the v^, output user co s t s , are measured r e l a t i v e to the p r i c e of m a t e r i a l s . The dependent v a r i a b l e i s the r a t i o of output revenue to expend i ture on m a t e r i a l s and s u p p l i e s . The independent v a r i a b l e s are the r a t i o of output to m a t e r i a l s q u a n t i t y , a constant and the logar i thms of other q u a n t i t i e s . For i n p u t s , the analogous f unc t i on s are - 213 -w.x. d.x. 2 5 - i - ^ = — + Y . + E 9..£nz. + Z 6 . . inx . i=2, . . . ,4 (8.24) X1 X1 1 j=1 1 J J j=2 i J J with the dependent v a r i a b l e being the r a t i o of input expendi tures on good i to those on m a t e r i a l s . I f b.= 0 f o r an output market, the f i rm s e l l s output i n a p e r f e c t l y compet i t i ve market. Whatever output l e v e l i s produced can be so ld at a g iven user cost v^. For b^ = 0, an u n l i m i t e d quan t i t y of loans can be absorbed by f i n a n c i a l markets at p r e v a i l i n g i n t e r e s t r a te s and other components of user c o s t s . I f b^ < 0 then the demand f a c i ng the f i n a n c i a l f i rm i s downward s l o p i n g . A change i n quan t i t y supp l ied i nc reases p r o f i t s by l e s s than the user c o s t . Input markets can be examined ana logous ly . I f d^ = 0 the f i rm faces a p e r f e c t l y e l a s t i c supply, and an u n l i m i t e d quan t i t y of input can be purchased at w.. I f d j * 0 then the supply f a c i n g the f i n a n c i a l f i rm i s not p e r f e c t l y e l a s t i c . I t i s upward s l op i n g f o r dL > 0. The data are as be fore , c on ta i n i n g pooled time s e r i e s and c ro s s s e c t i o n observat ions on e ighteen banks i n the New York Federa l Reserve D i s t r i c t 1973-1978. There are two output equat ions and three input demand equat ions , or f i v e i n t o t a l . The dependent v a r i a b l e of r e l a t i v e expend i tu res i s y = (v^z^/x^, \^z^lx^, w^x^/x^ w^x^/x^, w^x^/x^). The independent v a r i a b l e s i n the system are = ( 1 , Anz^ , fcnz^, Inx^ , Jinx.,, £ n x 3 , £nx^, £nx 5 ) and = ( z ^ x ^ ^ / x , , , x^/*^, x ? / x 1 , X ^ / x ^ . The f i r s t b lock of v a r i a b l e s enter s a l l e s t imat i ng equat ions , wh i l e on ly one - 214 -variable from the second block enters each equation. If X = (X^,X.,), then *nt = X n t F + ent n=1,...,18 (8.25) t=1973,...,1978 and there are NT observations. There are eight variables in X^  and five in X 2. Hence Y is 13 by 5, or a 68 by unity column vector. Rearranging this as a matrix with 13 rows and 5 columns, the parameters to be estimated are B l l • » 6 1 5 b l 0 0 0 0 a 2 B 1 2 . 9 2 5 0 b 2 0 0 0 T 2 9 2 1 • •• 6 2 5 0 0 d 2 0 0 ^3 8 3 1 6 3 5 0 0 0 ° 3 0 e " t l • •• 6U5 0 0 0 0 df Restrictions can be applied to this T matrix. In addition, there may be systematic bank effects, arising from the pooled data. Unbiased estimates of T are obtained by 'within' estimation (Mundlak [1978]). In practice, this is achieved by a system whose typical element is y .- y = (X . - X ) r + e e Where the J r 7nt 'n' nt n* nt n« dot notation indicates the sample mean for each bank. Alternatively, bank dummy variables can be introduced as with parameter 0. The latter permits s t a t i s t i c a l testing on bank effects. If 0=0 there are no bank effects. - 215 -8.5 E m p i r i c a l Re su l t s 8.5.1 Hypothes is Tes t ing on Compet i t ive Behavior P r i o r to examining imperfect compet i t ion in the input and output markets f o r banks, some r e g u l a r i t y cond i t i on s are v e r i f i e d . Test s of bank e f f e c t s with f i v e dummy v a r i a b l e groups are performed. With f i v e dummy v a r i a b l e s , there are 25 degrees of freedom f o r the t e s t . In the u n r e s t r i c t e d case, x 175 i s 3.71. The hypothes i s i s not accepted, s ince the c r i t i c a l value i s 1.79 at a 1 percent s i g n i f i c a n c e l e v e l . Subsequent t e s t s are app l i ed to a model w i th bank e f f e c t s , and symmetry imposed. I f bank e f f e c t s are excluded when they should be i n c l u d e d , the e s t imates of r are b i a sed . Parameter es t imates with and without bank e f f e c t s are i n d i c a t e d i n Table 8.1. The columns l a b e l l e d 'bank e f f e c t s unadjus ted ' exclude them. The r e s u l t s i n d i c a t e tha t the markets f o r outputs and i npu t s suggest some non-pr i ce t ak i ng behavior by banks. I n c l ud i ng bank e f f e c t s the b^ c o e f f i c i e n t of z.j/x.j i s -8.97 and i s s i g n i f i c a n t l y d i f f e r e n t from z e r o . The v a r i a b l e y^ /x^  i s entered p o s i t i v e l y i n est imat ion-, so the r e s u l t of b^ < 0 i n d i c a t e s a downward s l op i ng demand curve f o r l oans . Ana logous l y , the demand by customers fo r demand depos i t s i s downward s l o p i n g , w i th c o e f f i c i e n t b^ of -3.06. For the inputs of cash, t ime depo s i t s and l abo r , the c o e f f i c i e n t s of x^/x^, 1=2,...,4 are a l l p o s i t i v e , suggest ing upward s l op ing supply cu rve s . In the case of l abo r the c o e f f i c i e n t i s not s i g n i f i c a n t l y d i f f e r e n t from ze ro . - 216 -Table 8.1 Parameter Es t imates , Bank Supply and Demand Funct ions (asymptot ic standard e r r o r s i n parenthes i s ) Loans ( - v i z i / x x ) Bank E f f e c t s Adjusted Bank E f f e c t s Unadjusted Demand Depos i ts ( - V 2 Z 2 / X ! ) Bank E f f e c t s Adjusted Bank E f f e c t s Unadjusted I n t e r c e p t Inzi £nz2 in\2 inx3 inx^ inx5 z i / x i -3.62 (1.10) -5.52 (4.19) 4.74 (0.68) -1.03 (0.27) 1.45 (2.40) 0.68 (0.51) -0.51 (0.70) -8.97 (0.79) - 1.63(0.86) - 5.84(4.27) 4.27(1.57) - 0.92(0.28) 1.72(2.47) 1.08(0.54) - 0.63(0.75) -10.54(0.81) I n te r cep t * n z ! inz 2 inx 2 inx3 inxi+ * n x 5 Z2/x i - 2 .28 (0.51) 4.74 (1.59) -4.12 (0.79) 0.31 (0.13) -1.69 (0.91) 0.95 (0.28) 0.36 (0.34) -3.06 (0.32) -2.66 (0.33) 4.27 (1.57) -4.64 (0.72) 0.38 (0.13) -1.91 (0.92) 1.67 (0.26) 0.50 (0.35) -3.28 (0.29) Cash (w 2X2/x ! ) Bank E f f e c t s Adjusted Bank E f f e c t s Unadjusted Time Depos i t s ( w 3 x 3 / x ! ) Bank E f f e c t s Adjusted Bank E f f e c t s Unadjusted I n t e r c e p t £nzi Jlnz 2 Jinx 2 * n x 3 Jlnx^ inx5 X 2 / X ! 0.30 (0.07) -1.03 (0.27) 0.31 (0.13) 0.24 (0.05) 0.55 (0.16) -0.20 (0.05) 0.13 (0.06) 0.44 (0.04) 0.29(0.05) - 0.92(0.28) 0.38(0.13) 0.27(0.05) 0.55(0.17) - 0.34(0.05) 0.10(0.06) 0.48(0.04) I n te r cep t inz 1 inz 2 £nx 2 * n x 3 Jlnx^ Jinx 5 * 3 / * l 1.06 (0.42) 1.45 (2.40) -1.69 (0.91) 0.55 (0.16) 0.35 (1.42) -0.44 (0.24) 0.37 (0.29) 1.10 (0.29) 0.66 (0.29) 1.72 (2.47) -1.91 (0.92) 0.55 (0.17) 0.24 (1.45) -0.67 (0.24) 0.32 (0.29) 1.03 (0.27) Labor Bank Bank (W4XI+/X1) E f f e c t s E f f e c t s Adjusted Unadjusted I n t e r c e p t 3.63 (0.31) 4.34(0.16) inz\ 0.68 (0.51) 1.08(0.54) inz 2 0.95 (0.28) 1.67(0.26) Jinx 2 -0.20 (0.05) - 0.34(0.05) * n x 3 -0.44 (0.24) - 0.67(0.24) Jlnxi, -1.08 (0.36) - 1.24(0.35) inxs -1 .05 (0.24) - 0.92(0.25) X l + / X l 0.37 (0.29) 0.51(0.13) Note: Output q u a n t i t i e s are: z i loans , z 2 demand d e p o s i t s . Input q u a n t i t i e s are x i ma te r i a l s and s u p p l i e s , X2 cash, x 3 t ime d e p o s i t s , xit l abo r , X5 c a p i t a l . - 217 -Tests for imperfectly competitive behavior are performed sequen-t i a l l y and separately on each market and are reported in Table 8.2. For loans, the logarithm of the likelihood function is -375.23. The logarithm of the likelihood function under the bank effects model is -349.12, so the resulting x 2 s t a t i s t i c is 52.22 with one degree of freedom. The hypothesis of price taking behavior is not accepted. The test sta t i s t i c s are reported in Table 8.3. There is one parameter restriction in each case. For the labor market, the x 2 test st a t i s t i c is 7.22 against a c r i t i c a l value of x 2 of 7.88, so the hypothesis of price taking behavior in the labor market is not rejected. It cannot be rejected that banks face perfectly elastic supplies of labor. Finally, the test of competitive behavior in a l l markets yields the results of Table 8.4. This hypothesis is not accepted. The conclusion is that banks face competitive labor markets, but that such behavior does not necessarily obtain in other markets. 8.5.2 Output Demand and Input Supply E l a s t i c i t i e s The set of results most directly applicable to the banks is the bank effects adjusted group for d^ = 0, or competitive labour markets in Table 8.2. On the consumer demand for loans, the price elasticity is v^/b^. Sample stati s t i c s on the user costs of variable goods are reported in Table 8.5. In estimation the data are measured as deviations from geometric sample means. This includes the variables z./x^, i=1,2 and x^/x^, x^ =2,...,4, whose coefficients measure deviation from price taking behavior. These data are entered, using loans as an example, as C I o Table 8.2 Parameter Estimates, Tests of Competitive Price Taking in Separate Markets (asymptotic standard errors in parentheses and bank effects adjusted) bi = 0 only b2 = 0 only d2 = 0 only d 3 = 0 only di+ = 0 only Loans Intercept -13.26(0.71) - 3.60(1.10) -2.85 (1.10) -4.83 (1 .05) -3.79 (1.10) Jtnzi -14.95(4.11) - 2.58(4.19) 0.14 (4.15) -9.68 (4.05) -5.31 (4.19) £nz2 - 1.13(0.27) - 0.82(0.27) -1.26 (0.28) -1.05 (0.27) -1 .08 (0.27) £nx 2 9.10(1.54) 4.17(1.59) 3.21 (1.58) 6.45 (1.52) 5.00 (1.59) £nx 3 6.22(2.36) - 0.65(2.39) -1 .75 (2.38) 3.63 (2.33) 1.59 (2.40) Jlnx^ 1.93(0.50) 0.44(0.51) 0.11 (0.50) 0.93 (0.50) 0.03 (0.47) £nx 5 - 1.74(0.69) - 0.71(0.70) -0.75 (0.70) -0.47 (0.70) -0.61 (0.70) 0 - 8.82(0.79) -9.77 (0.78) -7.78 (0.72) -8.94 (0.79) Cash Intercept 0.31(0.07) 0.78(0.06) 0.52 (0.07) 0.32 (0.07) 0.30 (0.07) fcnzi - 1.13(0.27) - 0.82(0.27) -1 .26 (0.27) -1.05 (0.27) -1 .08 (0.27) £nz 2 0.25(0.05) 0.71(0.03) 0.46 (0.04) 0.26 (0.05) 0.24 (0.05) £nx 2 0.33(0.13) - 0.07(0.13) 0.23 (0.13) 0.30 (0.13) 0.31 (0.13) £nx 3 0.57(0.16) 0.25(0.16) 0.60 (0.16) 0.56 (0.16) 0.57 (0.16) Anx^ - 0.17(0.05) - 0.22(0.05) -0.19 (0.05) -0.20 (0.05) -0.17 (0.05) *nx5 0.16(0.06) 0.18(0.06) 0.18 (0.06) 0.13 (0.06) 0.14 (0.06) X 2 / X ! 0.44(0.04) 0 0.24 (0.03) 0.43 (0.03) 0.44 (0.04) Demand Deposits Intercept - 1.91(0.51) - 4.80(0.47) -5.43 (0.39) -1.78 (0.49) -2.34 (0.51) Jtnz! 9.10(1.54) 4.17(1.59) 3.21 (1.58) 6.45 (1.52) 5.00 (1.59) £nz 2 0.33(0.13) - 0.07(0.13) 0.23 (0.13) 0.30 (0.13) 0.31 (0.13) £nx 2 - 5.44(0.78) - 4.64(0.79) -4.84 (0.79) -4.38 (0.79) -4.07 (0.79) £nx 3 - 3.96(0.89) - 0.77(0.91) 0.12 (0.89) -2.92 (0.86) -1 .72 (0.91) Anxit 0.54(0.28) 1.43(0.28) 1.44 (0.28) 0.79 (0.28) 0.65 (0.27) £nx 5 - 0.07(0.34) 0.31(0.34) 0.28 (0.34) 0.29 (0.34) 0.30 (0.34) z 2 / x i - 3.45(0.32) - 0.65(0.26) 0 -3.54 (0.29) -3.05 (0.32) Time Deposits Intercept 2.43(0.40) 1.46(0.42) 0.01 (0.41) 2.22 (0.29) 1.21 (0.42) £nzi 6.22(2.36) - 0.65(2.39) -1.75 (2.38) 3.63 (2.33) 1.59 (2.40) £nz2 0.57(0.16) 0.25(0.16) 0.60 (0.16) 0.56 (0.16) 0.57 (0.16) £nx 2 - 3.96(0.89) - 0.77(0.91) 0.12 (0.89) -2.92 (0.86) -1.72 (0.91) £nx 3 - 1.52(1.41) 1.68(1.42) 1.50 (1.42) -0.33 (1.41) 0.38 (1 .42) Anxit - 0.87(0.23) - 0.45(0.24) -0.24 (0.24) -0.70 (0.23) -0.55 (0.23) £nx 5 0.14(0.29) 0.55(0.29) 0.43 (0.29) 0.36 (0.29) 0.34 (0.29) X 3 / X i - 0.21(0.26) 0.72(0.29) 2.18 (0.26) 0 0.97 (0.29) Labor Intercept 3.77(0.31) 3.70(0.31) 3.78 (0.31) 3.72 (0.31) 4.21 (0.26) inzi 1.93(0.50) 0.44(0.51) 0.11 (0.50) 0.93 (0.50) 0.03 (0.47) lr\Z2 - 0.17(0.05) - 0.22(0.05) -0.19 (0.05) -0.20 (0.05) -0.17 (0.05) ^nx2 0.54(0.28) 1.43(0.28) 1.44 (0.28) 0.79 (0.28) 0.65 (0.27) *nx3 - 0.87(0.23) - 0.45(0.24) -0.24 (0.24) -0.70 (0.23) -0.55 (0.23) Irxx^ - 1.10(0.36) - 1.21(0.36) -1.10 (0.36) -0.93 (0.36) -0.14 (0.22) £nx 5 - 1.35(0.24) - 1.07(0.24) -1.06 (0.24) -1.01 (0.24) -0.78 (0.22) XI+/X! 0.39(0.12) 0.45(0.12) 0.40 (0.12) 0.35 (0.12) 0 AnL -375.23 -393.96 -374.17 -354.36 -352.73 Note: Dependent variables are identical to those indicated in parentheses in Table 8.1 - Sa-l a b l e 8.3 Test S t a t i s t i c s , Competit ive Behavior in Output and Input Markets (X 2/DF) S i n g l e Input or Output Markets Test S t a t i s t i c C r i t i c a l Value (0 .005) , DF Loans 52.22 7.88,1 Demand Depos i t s 89.68 7.88,1 Cash 50.10 7.88,1 Time Depos i t s 10.48 7.88,1 Labor 7.22 7.88,1 A l l Markets 26.23 2.57,5 - 220 -Table 8.4 Parameter Es t imates , Tests of Compet i t i ve Rank Behav ior , A l l Markets (asymptot ic standard e r r o r s i n parentheses and bank e f f e c t s adjusted) Loans Demand Depos i t s I n te rcept £n z 2 £nx 2 £ n x 3 Jlnxit £nx 5 z i / * l z 2 / x i -13.32 (0.71) - 9.49 (4.01) - 1.13 (0.26) 8.14 (1.50) 3.07 (2.31) 0.82 (0.45) - 2.16 (0.69) 0 -5.56 (0.39) 8.14 (1.50) 0.01 (0.13) -6.17 (0.77) -2.31 (0.84) 0.85 (0.26) -0.21 (0.34) 0 Cash Time Depos i t s I n te r cep t £nzj, £ n z 2 &nx 2 £nx 3 £nx 5 X2/X1 X3/x i 0.79 (0.06) -1.13 (0.26) 0.71 (0.03) 0.01 (0.13) 0.37 (0.16) -0.16 (0.05) 0.22 (0.06) 0 2.28 (0.29) 3.07 (2.31) 0.37 (0.16) -2.31 (0.84) 0.12 (1.40) -0.88 (0.22) 0.26 (0.29) 0 Labor . I n te rcept £nzi £ n z 2 £ n x 2 £nx 3 £nxi+ £ n x 5 X L J / X ! 4.51 (0.26) 0.82 (0.45) -0.16 (0.05) 0.85 (0.26) -0.88 (0.22) -0.25 (0.22) -1.12 (0.22) 0 £nL -414.70 - 221 -( z^fz )/(x^fx ) where z^ and x^ are the r e s p e c t i v e l y geometric sample means fo r loans and m a t e r i a l s . The dependent v a r i a b l e remains expend i ture on a g iven good d i v i ded by that on m a t e r i a l s , or v . z ./x^ f o r output s . In a c t u a l e s t i m a t i o n , the p r i c e and guant i t y of output i _ __ * _ _ » are r e s p e c t i v e l y (v^z^/x^) = v^ and (z^/x^) • (x.Jz^) = z ^ . The demand and supply e l a s t i c i t i e s are c a l c u l a t e d at the geometr ic mean i n Table 8.5. Both loans and demand depos i t s have p r i c e e l a s t i c i t i e s of demand i n excess of u n i t y . The e l a s t i c i t y of loan demand w i th respect to own user cost i s -1 .72. Consumers are even more p r i c e s e n s i t i v e i n responding to demand depos i t user c o s t s . The p r i c e e l a s t i c i t y of demand i s - 2 .25 . I n t e re s t payments on checking accounts , such as NOW accounts, e l i c i t a l a rge response i n depos i t i n c r ea se s . On the supply s i d e , i n conformity wi th the hypothes is t e s t i n g , the l abor market i s c o m p e t i t i v e . P e r f e c t l y compet i t i ve labor markets imply that the e l a s t i c i t y of supply i s i n f i n i t e . The e l a s t i c i t i e s f o r cash arid t ime d e p o s i t s , both supp l ied by customers, are a l so g rea te r than u n i t y . Consumers thus appear to be r e l a t i v e l y i n t e r e s t r a t e s e n s i t i v e , f o r example, i n time d e p o s i t s . 8.6 P o l i c y I m p l i c a t i o n s 8.6.1 Costs of Noncompetit ive Behavior A l l the demand e l a s t i c i t i e s f o r output and supply e l a s t i c i t i e s f o r i nput s are g reate r than u n i t y . Although the te s t of p r i c e t a k i n g behavior i n a l l markets i s not accepted, the r e l a t i v e l y e l a s t i c - 222 -Table 8 . 5 Price Elasticities of Demand for Outputs and Supply for Inputs (eighteen New York/New Jersey banks 1 9 7 3 - 1 9 7 8 ) User Cost Scaling User Cost Price (Unsealed) Factor Index Elasticity of (1) (2) (3) =(D*(2) Demand(Supply) Loans v l 0.0376 409.94 A 15.41 . * . vi/bi -1.72 Demand 0.0451 z 2/xi 151.87 * v 2 6.85 * v 2/b 2 -2.25 Deposits v 2 Cash w2 0.0520 x 2/ X l 16.38 * w2 0.85 * , w2 /d 2 1.93 Time 0.0082 x 3/ X l 237.94 * w3 1.95 * w3/d3 2.01 Deposits w3 Labor 1.1872 X1+/X! 4.86 * w4 5.77 * Wi^d^ 00 The estimates of b±, i=l,2 and d.. , j=2,...,4 are from Table 8.2 with bank effects adjusted. A l l data are at geometric sample means. Demand el a s t i c i t i e s are negative, supply el a s t i c i t i e s positive. - 223 -e s t imates may suggest the costs of imposing pe r fec t compet i t i on are low. Cons ider ing the loan market, the est imated equat ion with bank e f f e c t s adjusted i s - v 1 z 1 / x 1 = -3.79 - 5 . 3 U n z ] -1 .08£nz 2 +5.0(Hnx 2 + 1 .59fcnx -0.03£nx^ - 0 . 6 U n x 5 - 8 . 9 4 z 1 / x 1 (8.27) the negat ive s ign on v^ a r i s i n g because user cos t s of loans are expressed nega t i v e l y , as net revenues. I f pe r f ec t compet i t i on i s imposed on a l l markets, the loan equation i s , again with bank e f f e c t s adjusted - v l z 1 / x 1 = -13.32 -9.49Jlnz 1 - 1 . 13£nz 2 +8.14£nx 2 +3.07£nx 3 -0.82£nx^ -2 .16£nx 5 (8.28) The mean 1975 obse rva t i on , w i th data measured as d e v i a t i o n s from the geometr ic mean i s f o r the e n t i r e sample £ n z 1 0.035 £nz 2 0.017 irxx^ 0.198 Inx^ 0.052 * n x 2 0.038 £ n x 3 0.117 z 1 / x 1 1.017 so - v 1 z 1 / x 1 = -12.74 i n (8 .27) . With z 1 / x 1 = 1.017, the v 1 index i s -12.53, under non-pr ice t ak i ng behav io r . I f pe r fec t compet i t i on i s imposed, from (8.28) the same value i s -15.04, or a user cost index of -14.79. User cost s of output are negat i ve . Here, i n the compet i t i ve case, -v.j = 14.79, or v^ = -14.79. Smal ler negat ive values imply h igher r e t u r n s , which obta in i n the impe r f ec t l y compet i t i ve model. The net re tu rn from loans i s understated by about 15 percent . The r e s u l t s conf i rm that imperfect compet i t i on r e s u l t s in higher p r i c e s . The a c tua l d i f f e r e n t i a l i s 15.2 percent . This imp l i e s that i f p e r f e c t compet i t i on i s imposed and e s t imated , and t h i s does not o b t a i n , - 224 -loan revenues for a g iven loan l e v e l are understated by 15.2 percent . F u r t h e r , the loan demand i s not i n s e n s i t i v e to i n t e r e s t rates and other user cost components. The response i s performed for the same l e v e l of l oans , depos i t s and other q u a n t i t i e s , but i n p r a c t i c e the output q u a n t i t i e s would t y p i c a l l y be lower under imperfect c ompe t i t i o n . For p o l i c y purposes, est imates based on imposed p r i c e tak ing may lead to e r r o r s . I f other components of loan user cos t s are cons tant , i t imp l i e s that loan i n t e r e s t rates are higher than under compet i t i ve assumptions. 8.6.2 Monetary P o l i c y The second i ssue examined i s the i m p l i c a t i o n of these r e s u l t s f o r the conduct of monetary p o l i c y . As an example, cons ider a Fede ra l Reserve a c t i on to change the quan t i t y of money as r e f l e c t e d i n x.,, cash . Suppose there i s a ten percent reduc t i on in cash or excess re se rve q u a n t i t y . In the loans equation (8.27) with a c o e f f i c i e n t of 5.00, the dependent v a r i a b l e changes by +0.19. In the pe r f e c t compet i t i on imposed model the c o e f f i c i e n t i s 8.14, so the e f f e c t of monetary p o l i c y i s s u b s t a n t i a l l y g r ea te r . Regarding time depo s i t s , the c o e f f i c i e n t of x^ i n logar i thms i s 1.59 i n the non p r i c e tak ing equat ion, and 3.07 in the p r i c e tak ing equa t i on . The c o e f f i c i e n t on demand depos i t s i s -5.31 in the non p r i c e t a k i n g model, and -9.49 i n the p r i c e tak ing model. In a l l cases the conc lu s i on s are s i m i l a r . Regardless of the type of monetary good con s i de red , monetary p o l i c y e f f e c t s on the loan market are over s ta ted i f p e r f e c t l y compet i t i ve markets are i n c o r r e c t l y assumed. The p red i c ted amount of loan response, given user co s t s , i s only about 60 percent of - 225 -the magnitude p red i c ted i f time depos i t balances change. On the input s i de , the demand by hanks for time depo s i t s , where p r i c e t a k i n g i s not imposed i s w 3 w 3 / x 1 = 1.21 + 1.59Jlnz 1 + 0.57J>nz2 - 0.72Jlnx 2 + 0 .38£nx 3 - 0.55Jlnx^ + 0 .34£nx 5 - 0 . 97x 3 /x 1 (8.29) and the corresponding eguation with p r i c e tak ing imposed i n a l l markets i s w 3 w 3 / x 1 = 2.28 + 3.07£nz 1 + 0 .37£nz 2 - 2 . 3 U n x 2 + 0.12Jlnx 3 - O.SSJlnx^ - 0 .26£nx 5 (8.30) Aga in , there are d i f f e r e n c e s i n response to monetary p o l i c y . An i nc rease i n cash of one percent from x 2 reduces time depos i t s by 2.31 percent i n the model w i th p r i c e t ak ing imposed. The non p r i c e t ak i ng model i n vo l ve s a response of 1.72 percent, or about 30 percent s m a l l e r . 8.7 Conc lud ing Remarks The r e s u l t s i n d i c a t e that i t i s p o s s i b l e to develop and t e s t a model of non p r i c e t ak ing in banking. The r e s u l t s i n d i c a t e that c o m p e t i t i v e p r i c e tak ing i s not r e j ec ted only i n the labor market. The parameter es t imates obtained by imposing p r i c e tak ing when i t i s not the case are s i m i l a r i n some cases, but d i s s i m i l a r i n o the r s . The ana l y s i s of monetary p o l i c y u l t i m a t e l y r equ i re s a complete model of the microeconomics of f i n a n c i a l f i r m s . I f these f i rms are not p e r f e c t compet i to r s , t h i s must be recognized in the model b u i l d i n g . - 226 -NOTES ^ e e Bond and Shearer [1972, p. 315]. 2 S e e Luckett [1976, p. 72-92] . 3 There are two a l t e r n a t i v e procedures fo r measuring c o n c e n t r a t i o n s . The market snare held by a s p e c i f i c number of f i rms and the H e r f i n d a h l index which i s the sum of the squares of the shares. Hence, three banks of equal s i z e would have a H e r f i n d a h l index va lue of ( 1 /3 ) 2 + ( 1/3 ) 2 + (1/3) = 3/9 = 0.33. During the sample per iod the A n t i t r u s t D i v i s i o n of the Department of J u s t i c e used the former measure and a sw i tch to the l a t t e r measure was made in 1982. '•See Mingo [1977]. 5 K l e i n [1971, p. 207]. 6 L a u [1974, p. 193-194, 1978] and Diewert [1971, 1982] a l s o have i n d i c a t e d how d u a l i t y theory can be u t i l i z e d even i f there i s m o n o p o l i s t i c behavior on the part of producers. Two drawbacks to Lau ' s method are that ( i ) i t cannot be te s ted whether the producer i s i n f a c t behaving c o m p e t i t i v e l y on the output market and ( i i ) the est imated equat ions can not be used to p r e d i c t output quan t i t y or s e l l i n g p r i c e s e p a r a t e l y . D i ewe r t ' s approach r equ i r e s the assumption of a convex technology and a l o c a l knowledge of the demand and supply curves tha t the f i r m i s e x p l o i t i n g so that appropr i a te shadow p r i c e s can be c a l c u l a t e d . See Diewert [1982, pp. 584-590] f o r more i n f o r m a t i o n . See Ch r i s ten sen , Jorgenson and Lau [1973], where l abo r input i s used as the dependent v a r i a b l e i n an analogous s p e c i f i c a t i o n . 8 Assuming D^  i s d i f f e r e n t i a b l e at z^ > 0. Demand by consumers can a l s o depend on f a c t o r s such as consumer income, persona l c h a r a c t e r i s t i c s and p r i c e s of other goods. These have the e f f e c t of s h i f t i n g the r e c i p r o c a l demand f u n c t i o n . Hence the D^ can be sca led by s h i f t e f f e c t s to account fo r these f a c t o r s . See Diewert [1982] , p. 585. q P r i c e - t a k i n g behavior on output markets has been te s ted by Appelbaum [1979] f o r the U.S. petroleum indus t r y and Appelbaum and K o h l i [1979] f o r Canadian aggregate output. l 0 T h e assumption of p r o f i t maximizing behavior u n d e r l i e s the models of Pesek [1970], Towey [1974], Adar, Agmon and Org le r [1975], Greenbaum,. A l i , and Mer r i s [1977], Sealey and L i nd l e y [1977], Mingo and Wolkowitz [1977] and Mul l ineaux [1978]. 1 1 I n e s t i m a t i o n , although i s parametr ic i t may s t i l l be not 1 p o s s i b l e to i d e n t i f y t h i s , and a no rma l i z a t i on i s r e q u i r e d . An a l t e r n a t i v e way of i n t e r p r e t i n g the s p e c i f i c a t i o n used i s to view the remain ing imper fect compet i t ion e f f e c t s as o c cu r r i n g r e l a t i v e to the f i r s t input market. - 227 -CHAPTER 9 CONCLUDING REMARKS Th i s research has i n ve s t i g a t ed the short run product ion technology and the e f f e c t s of r e gu l a t i on on f i n a n c i a l f i r m s . Regu la -t i o n s cons idered inc lude reserve reguirements, i n t e r e s t r a te c e i l i n g s , and depos i t i n surance. User co s t s per un i t of s e r v i ce have been der i ved fo r a l l goods. For f i n a n c i a l s e r v i c e s , these i nc lude the e f f e c t s of reserve r e q u i r e -ments, c a p i t a l ga ins or l o s se s , depos i t insurance, i n t e r e s t r a t e s , and s e r v i c e charges . Items generat ing more expendi ture than revenue fo r the f i r m have p o s i t i v e user co s t s , and are def ined to be i npu t s . Those wi th negat ive user co s t s are def ined as output s . Though i t i s not important which f i n a n c i a l goods are inputs and which are outputs to the f i r m , i t i s important that p r i c e s (or user cos t s ) be assigned to each good. The user c o s t s f o r f i n a n c i a l and n o n f i n a n c i a l goods are arguments of the p r o f i t f u n c t i o n . Comparative s t a t i c s on p r o f i t s , s upp l i e s of output and demands f o r input are der ived f o r i n t e r e s t ra tes and monetary r e g u l a t i o n s . A s p e c i f i c a t i o n has been der ived f o r the v a r i a b l e p r o f i t f u n c t i o n , and the t e s t i n g of r e g u l a r i t y c o n d i t i o n s such as monoton ic i t y and c o n v e x i t y . A t e s t f o r the ex i s tence of a producer based money supp ly , as a subset of f i n a n c i a l goods has been deve loped. The t e s t imposes no p r i o r r e s t r i c t i o n on the form of the money supply . Symmetry i s imposed on the e s t imat i ng system. Given t h i s , both monoton i c i t y and convex i ty hold f o r the geometric mean and at a l l data p o i n t s . - 228 -The mat r i x of e l a s t i c i t i e s of t rans fo rmat ion i s w e l l behaved. A l l p r i n c i p a l d iagona l elements are p o s i t i v e . The e l a s t i c i t i e s of supp ly , f o r loans and demand depo s i t s , are both l e s s than u n i t y . On the demand s i d e , e l a s t i c i t i e s for cash, l abo r , and m a t e r i a l s exceed u n i t y , but are r e l a t i v e l y c l o se to u n i t y , whi le that for time depos i t s i s l e s s than one. Th is suggests an i n f l e x i b l e technology for f i n a n c i a l i nput s and output s , wh i l e the technology i s r e l a t i v e l y more f l e x i b l e f o r p h y s i c a l i n p u t s . R e l a t i v e l y l a r ge changes i n the p r i c e v a r i a b l e s under l y i ng user c o s t s , i n i n t e r e s t r a t e s , depos i t insurance charges, wage ra te s and m a t e r i a l p r i c e s , are requ i red to induce s u b s t a n t i a l s h i f t s i n the supply of loans and demand depo s i t s , and input demands by banks. This has i m p l i c a t i o n s f o r whether monetary q u a n t i t i e s or i n t e r e s t r a te s should be the ob jec t of c e n t r a l bank c o n t r o l i n monetary p o l i c y . Test s on the ex i s tence of a producer based monetary subaggregate are performed. The c o n d i t i o n f o r s e p a r a b i l i t y i s that the r e l a t i v e user cos t f o r any p a i r of f i n a n c i a l commodities w i t h i n the subaggregate i s independent of the q u a n t i t i t y of any commodity out s ide i t . Tests are performed on whether the monetary subaggregate conta in s cash on l y , cash and demand d e p o s i t s , or cash, demand depos i t s and time d e p o s i t s . The proposed aggregating s t r u c t u r e does not r equ i r e the money supply to be e i t h e r l i n e a r homogenous or l i n e a r l o g a r i t h m i c . A l l of the money subaggregates are not accepted s t a t i s t i c a l l y . However, the i f l e x i b l e money supply i s always p r e f e r ab l e to the Cobb-Douglas ( l i n e a r l o g a r i t h m i c ) aggregate. The r e s u l t s suggest that the b i a s i n t e s t i n g - 229 -f o r s e p a r a b i l i t y noted by B lackerby, Primont and R u s s e l l [1977] may be s u b s t a n t i a l . Some comparative s t a t i c s on changes i n r e gu l a t i on s are performed us ing the est imated technology. S p e c i f i c a l l y , i n t e r e s t ra te c e i l i n g s , depos i t insurance and reserve requirements are changed. The theory i s extended to account for market impe r fec t i on s f a c i n g f i n a n c i a l f i r m s . The demand fo r output i s permitted not to be p e r f e c t l y e l a s t i c , and s i m i l a r f l e x i b i l i t y i s permitted on the supply of i n p u t s . P rev ious models do not permit non p r i c e t ak ing i n output and input markets . A l s o , the e l a s t i c i t i e s are a l l e s t imated, and do not r equ i r e a p r i o r i i n f o r m a t i o n . The model developed commences from the p roduct ion f u n c t i o n , and i s not s t r i c t l y comparable to the v a r i a b l e p r o f i t f u n c t i o n model. Th i s i s because a t r an s l o g s p e c i f i c a t i o n i s used, and the form i s not s e l f - d u a l . Tes t s are developed separa te l y f o r p r i c e t ak i ng i n l oans , cash, demand d e p o s i t s , time depos i t s and l a b o r . In the e m p i r i c a l r e s u l t s f o r the e ighteen New York and New 3ersey banks 1973-1978, p r i c e t a k i n g i s accepted i n the labor market, but not accepted i n the remaining four markets . However, a l l the p r i c e e l a s t i c i t i e s exceed u n i t y . Th i s i n t roduces the i s sue of the cost of imposing p r i c e t ak ing when i t i s not the case. P r i c e t ak i ng i s imposed i n a l l markets, and the est imates compared w i th those when p r i c e tak ing i s not imposed. Monetary p o l i c y responses are c a l c u l a t e d f o r ho ld ings of cash, demand depo s i t s , and time d e p o s i t s . In some cases, the d i f f e r e n c e i n r e s u l t s i s s m a l l , wh i le i n o thers the e r r o r can be as l a rge as 20 percent . - 230 -BIBLIOGRAPHY Adar, Z., T. Agmon, and Y.E. Org ler [1975], "Output Mix and Jo i n tne s s i n P roduct ion i n the Banking F i r m , " Jou rna l of Money C r e d i t and Banking, 7, 235-243. A l h a d e f f , D.A. [1954], Monopoly and Compet i t ion i n Banking, Be rke ley , C a l i f o r n i a : U n i v e r s i t y of C a l i f o r n i a P re s s . A i gner , D .J . [1973], "On E s t imat i on of an Econometric Model of Short-Run Bank Behav i o r " , Journa l of Econometr ics, 1, 201-228. A n t o n e l l i , G.B. [1886], "On the Mathematical Theory of P o l i t i c a l Economy", t r a n s l a t e d by J . S . Chipman and A.P. Kirman i n P r e f e r ence s ,  U t i l i t y and Demand, J . S . Chipman, L. Hurwicz, M. R i c h t e r and H. Sonnenschein, eds . , New York: Harcourt Brace Jovanov i t ch . Appelbaum, E. [1979], " Te s t i n g P r i c e Taking Behav io r " , Jou rna l of  Econometr ics , 9, 283-294. Appelbaum, E. and U.J.R. K o h l i [1979], "Canada-United S tates Trade: Test f o r the Small-Open Economy Hypothes i s " , Canadian Jou rna l of Economics, 12, 1-14. B a r n e t t , W.A. [1978] , "The User Cost of Money", Economics L e t t e r s , 1, 145-149. Ba r ne t t , W.A. [1980], "Economic Monetary Aggregates: An A p p l i c a t i o n of Index Number and Aggregat ion Theory", Annals of App l i ed Econometr ics (supplement to the J ou rna l o f Econometr ic s ) , 14, 11-48. B a r n e t t , W.A. [1981] , Consumer Demand and Labor Supply: Goods, Monetary  A s se t s , and Time, Amsterdam: No r th -Ho l l and . Ba r r o , R.3 and A.M. Santomero [1972], "Household Money Hold ings and the Demand Depos i t R a t e " , J o u r n a l o f Money, C r ed i t and Banking, 25, 397-413. Becker , W.E. [1975] , "Determinants of the United States Currency-Demand Depos i t R a t i o " , Jou rna l o f F inance, 30, 57-74. B e l l , F.W. and N.B. Murphy [1968], "Cost s i n Commercial Bank ing: A Q u a n t i t i a t i v e Ana l y s i s of Bank Behavior and I t s R e l a t i o n to Bank R e g u l a t i o n s " , Research Report No. 41, Boston: Federa l Reserve Bank of Boston. Benston, G . J . [1964] , "Economies of Sca le and Marg ina l Cost i n Banking Ope r a t i on s " , N a t i o n a l Banking Review, 2, 507-549. Benston, G . J . [1965], "Branch Banking and Economies of S c a l e " , The  Jou rna l o f F i nance , 20, 312-31. - 231 -Berkman, N. [1980] "The New Monetary Aggregates: A C r i t i c a l Approach, " J ou rna l of Money, C r e d i t and Banking, V o l . 12, No. 2, part 1, 135-154. Berndt , E.R. and L.R. Chr i s tensen [1974] " Te s t i n g fo r the Ex i s t ence of a Cons i s tent Aggregate Index of Labor I nput s " , American Economic Review, 64, 391-404. Berndt, E.R. and N.E. Savin [1977], " C o n f l i c t Among C r i t e r i a f o r Te s t i n g Hypotheses i n the M u l t i v a r i a b l e L inea r Regress ion Model " , Econometr ica, 45, 1263-1278. Berndt, E.R. and T.H. McCurdy [1980] "On Test ing Theor ies of F i n a n c i a l Intermediary P o r t f o l i o S e l e c t i o n , " Review of Economic S t ud i e s , 47,861-873. B lacko rby , C , D. Primont and R.R. R u s s e l l [1977], "On Tes t ing Separa-b i l i t y R e s t r i c t i o n s With F l e x i b l e Func t i ona l Forms," Jou rna l of  Econometr ic s , 6, 195-209. B lacko rby , C , D. Primont and R.R. R u s s e l l [1978], D u a l i t y , S e p a r a b i l i t y  and F u n c t i o n a l S t r u c t u r e , New York: North Ho l l and . Board of Governors of the Federa l Reserve System, Federa l Reserve  B u l l e t i n , Washington, D.C., v o l s . 62,65,67, 1976-1981. Bond, N.E. arid R.A. Shearer f [1972], The Economics of The Canadian  F i n a n c i a l System: Theory, P o l i c y and I n s t i t u t i o n s , Scarborough, O n t a r i o : P r e n t i c e - H a l l . Brigham, E.F. and R.R. P e t t i t [1970], " E f f e c t s of S t r uc tu re on Pe r fo rm-ance i n the Savings and Loan I n d u s t r y " , In Study o f the Savings and  Loan I ndus t r y , Federa l Home Loan Bank Board, Washington: U.S. Govern-ment P r i n t i n g O f f i c e , 971-1209. Bryan, W.R. [1972] "The Determinants o f Bank P r o f i t s " , Research Paper N o . 8, N e w York: American Bankers A s s o c i a t i o n . Buser, S.A., A.H. Chen and E . J . Kane [1981], " F ede ra l Depos it In surance, Regulatory P o l i c y , and Optimal Bank C a p i t a l " , Journa l of F i nance , 35, 51-60. C a r l e t o n , W.T. and W.R. Bryan [1971], "Depos i t Expansion and Fede ra l Reserve - Banking System I n t e r a c t i o n : A Micro Un i t S i m u l a t i o n " , American Economic Review, 61, 901-915. Caves, D.,L. Ch r i s tensen and J . Swanson [1980], " P r o d u c t i v i t y i n U.S. Ra i l r o ad s 1951-1974", B e l l J ou rna l of Economics, 11, 166-181. Ch r i s t en sen , L.R. and D.W. Jorgenson, [1969], "The Measurement of U.S. Rea l C a p i t a l Input , 1929-1967" Review o f Income and Wealth, 15,293-320. - 232 -Ch r i s t en sen , L.R. and D.W. 3orgenson [1970], "U.S. Real Product and Real Fac to r Input, 1929-1967", Review of Income and Wealth, 16, 19-50. Ch r i s t en sen , L.R., D.W. Jorgenson, and L . J . Lau [1973], "T ranscendenta l Loga r i thmic Product ion F r o n t i e r s " , Review of Economics and S t a t i s t i c s , 55, 28-45. Ch r i s t en sen , L.R., D.W. 3orgenson and L . J . Lau [1975], "T ranscendenta l Loga r i thmic U t i l i t y F unc t i on s " , American Economic Review, 65, 367-383. Cowing, T.G. and A.G. Holtman [1980] "The E s t imat ion of H o s p i t a l Technolog ies Using a Short Run Mu l t i p roduc t Cost Func t i on " d i s c u s s i o n paper 80-1, S tate U n i v e r s i t y of New York, Binghamton. Debreu, G. [1959], Theory o f Value - an Ax iomat ic Ana l y s i s o f Economic  E q u i l i b r i u m , New York: John Wiley and Sons. D iewert , W.E. [1971], "Cho ice on Labor Markets and the Theory of the A l l o c a t i o n of Time", Research Branch, Department of Manpower and Immigrat ion, Ottawa. D iewert , W.E. [1973], " F u n c t i o n a l Forms f o r P r o f i t and Trans format ion F u n c t i o n s " , Journa l of Economic Theory, 6, 284-316. D iewer t , W.E. [1974a], " A p p l i c a t i o n s of D u a l i t y Theory", i n F r o n t i e r s of  Q u a n t i t a t i v e Economics, Volume I I , M. I n t r i l i g a t o r and D. Kendr i ck , ed s . , New York: North Ho l l a nd . D iewer t , W.E. [1974b], " I n te r tempora l Consumer Theory and the Demand f o r Du rab l e s " , Econometr ica, 42, 497-516. D iewert , W.E. [1976], "Exact and S u p e r l a t i v e Index Numbers", J o u r n a l of  Econometr ics , 4, 115-145. D iewer t , W.E. [1977], "Mathematics f o r Economis t s " , mimeographed, Un i ve r -s i t y of B r i t i s h Columbia, Vancouver. D iewer t , W.E. [1980], "Aggregat ion Problems i n the Measurement of C a p i t a l " i n The Measurement of C a p i t a l , D. Usher, e d . , Chicago: U n i v e r s i t y of Chicago P re s s . D iewert , W.E. [1982], " D u a l i t y Approaches to Microeconomic Theory" , i n Handbook o f Mathematical Economics, v o l . I I , K . J . Arrow and M.D. I n t r i l i g a t o r , eds. , New York: North H o l l a n d . Donovan, D.J. [1978], "Mode l l i n g the Demand fo r L i q u i d As set s : An A p p l i c a t i o n to Canada", I n t e r n a t i o n a l Monetary Fund S t a f f Papers 25, 676-704. Dugger, R.H. [1975], "The Non-Homothet ic i ty of Commercial Bank P roduc t i on F u n c t i o n s " , Board of Governors of the Federa l Reserve System working Paper, Washington, March. - 2^3 -E p s t e i n , L.G. [1977], Essays i n the Economics of U n c e r t a i n t y , Ph.D. t h e s i s , U n i v e r s i t y of B r i t i s h Columbia, Department of Economics. Fede ra l Deposit Insurance Co rpo ra t i on , 1977 Annual Report [1978], Washington, D.C.: U.S. Government P r i n t i n g O f f i c e . Fede ra l Resere Bank Board [1978], Func t i ona l Cost Ana l y s i s - 1977 Average  Banks, Federa l Reserve Board of Governors, Washington, D.C. Fede ra l Reserve Bank of Boston, [1980], "Depos i to ry I n s t i t u t i o n s Deregu-l a t i o n and Monetary Con t ro l Act of 1980", Boston: Federa l Reserve Bank of Boston. F i s h e r , I. [1930], The Theory of I n t e r e s t , New York: Macmi l l an . F i s h e r , I. [1935], 100% Money, New York: Ade lph ia P r e s s . Goldschmidt, A. [1981], "Economies of Sca le and O r gan i z a t i ona l E f f i c i e n c y i n Banking: A Cost - Surface I n v e s t i g a t i o n " , D i s cu s s i on Paper 81-01-1, Simon Fraser U n i v e r s i t y , School of Business A d m i n i s t r a t i o n and Economics. Gramley, L.E. [1962], A Study of Sca le Economies i n Banking, Kansas C i t y : Federa l Reserve Bank of Kansas C i t y . G r e b l e r , L. and E.F. Brigham [1963], Savings and Mortgage Markets i n  C a l i f o r n i a , Pasadena: C a l i f o r n i a Savings and Loan League. Greenbaum, S.I. [1967], "A Study of Bank C o s t s " , Na t i ona l Banking Review, 4, 415-34. Greenbaum, S. I., M.M. A l i and R.C. Me r r i s [1976] , "Monetary P o l i c y and Banking P r o f i t s " , Journa l o f F inance , 31, 89-101. Gu r l e y , 3.G. and E.S. Shaw [1960], Money i n a Theory of F inance, Washing-t o n , D . C : The Brookings I n s t i t u t i o n . H a l l , R.E. [1973] "The S p e c i f i c a t i o n of Technology w i th Severa l K inds of Output " , Jou rna l of P o l i t i c a l Economy, 81 , 878-892. Ha r t , O.D. and D.M. J a f f e [1974], "On the A p p l i c a t i o n of P o r t f o l i o Theory to Depos i tory F i n a n c i a l I n t e r m e d i a r i e s " , Review of Economic S t ud i e s , 4 1 , 129-47. Haslem, J .G . [1968], "A S t a t i s t i c a l Ana l y s i s of the R e l a t i v e P r o f i t a b i -l i t y of Banks", Jou rna l of F inance, 23, 167-176. H i c k s , J .R . [1946], Value and C a p i t a l , 2nd ed . Oxford: Clarendon P r e s s . H o r v i t z , P.M. [1963] "Economies of Sca le i n Banking" i n P r i v a t e F i n a n c i a l  I n s t i t u t i o n s , P.M. H o r v i t z , e d . , Englewood C l i f f s , New Je r sey : P r e n t i c e - H a l l , 1-54. - 234 -H o t e l l i n g , H. [1932], "Edgeworth ' s Taxat ion Parodox and the Nature of Demand and Supply Func t i on s : Jou rna l of P o l i t i c a l Economy, 40, 577-616. H u l t e n , C R . and F . C Wykoff [1980] "Economic Dep rec i a t i on and the Taxat ion of S t ruc tu re s i n U.S. Manufactur ing I n d u s t r i e s : An E m p i r i c a l A n a l y s i s , " i n The Measurement of C a p i t a l , D. Usher, e d . , New York: N a t i o n a l Bureau of Economic Research. Hurwicz, L. [1971], "On the Problem of I n t e r g r a b i l i t y of Demand Func-t i o n s " , in P re fe rences , U t i l i t y and Demand, 3. Chipman, L. Hurwicz, M. R i c h t e r and H. Sonnenschein, eds . , New York: Harcourt Brace Oovanovi tch. Hyman, O.N. [1972], "A Behav io ra l Model f o r F i n a n c i a l I n t e rmed i a t i on " Economic and Business B u l l e t i n , 24, 9-17. Jorgenson, D.W. and Z. G r i l i c h e s [1967], "The Exp lana t i on of P r o d u c t i v i t y Change", Review of Economic S tud i e s , 34, 249-83. Kane, E.3. [1980] , " A c c e l e r a t i n g I n f l a t i o n and the D i s t r i b u t i o n of Savings I n c e n t i v e s " , Cambridge, Mass.: Na t i ona l Bureau of Economic Research, Working Paper No. 412, A p r i l . Kane, E . J . [1981] , " Impact,of Regu la t ion on Economic Behav io r : A c c e l e r a -t i n g I n f l a t i o n , Techno log i ca l Innovat ion and the Decreas ing E f f e c t i v e -ness of Banking Regu l a t i o n , " Jou rna l of F inance , 36, 355-367. Kane, E . J . and E.G. M a l k i e l [1965], "Bank P o r t f o l i o A l l o c a t i o n , Depos it V a r i a b i l i t y , and the A v a i l a b i l i t y D o c t r i n e " , Qua r t e r l y J o u r n a l of  Economics, 79, 113-134. Kaufman, G. [1966] , "Bank Market S t ruc tu re and Performance: The Evidence from Iowa", Southern Economic J o u r n a l , 32, 429-439. K l e i n , M.A. [1971], "A Theory of the Banking F i r m " , J ou rna l o f Money  C r e d i t and Banking, 3, 205-218. Kmenta, J . and R.F. G i l b e r t [1968], " Smal l Sample P r o p e r t i e s of A l t e r n a -t i v e E s t imator s of Seemingly Unre lated Reg re s s i on s " , J ou rna l of the  American S t a t i s t i c a l A s s o c i a t i o n , 63, 1180-1200. K o h l i , U.J.R. [1975] , "Canadian Technology and Der ived Import Demand and Export Supply Func t i on s " , Research P r o j e c t s Group, S t r a t e g i c P lann ing and Research, Department of Manpower and Immigrat ion, Canada. Lau , L . J . [1978], " A p p l i c a t i o n s of P r o f i t Func t i on s " i n M. Fuss and D. . McFadden ( e d s . ) , P roduct ion Economics: A Dual Approach to Theory and  A p p l i c a t i o n s , Amsterdam: North Ho l l and . - 235 -Lau, L . 3 . , and P.A. Yotopoulos [1971], "A Test f o r R e l a t i v e Economic E f f i c i e n c y and A p p l i c a t i o n to Indian A g r i c u l t u r e " , American Economic  Review, 61, 94-109. Laurent , R.O. [1981], "Reserve Reguirements, Deposit Insurance and Monetary C o n t r o l " Jou rna l of Money, C r e d i t , and Banking, 13, 314-324. Longbrake, W.A. [1974], " D i f f e r e n t i a l E f f e c t s of S i n g l e - P l a n t , M u l t i -p l a n t , and M u l t i - F i r m O rgan i za t i ona l Forms on Cost E f f i c i e n c y in Commercial Bank ing " , Working Paper 74-7 Rev i sed, Federa l Depos i t Insurance Co rpo ra t i on , Washington. Longbrake, W.E. and H.D. M e r r i l l , [1974], "Demand fo r Commercial Bank P roduc t i on Workers and Adm in i s t r a t o r s : Demand Deposit O p e r a t i o n s " , Working Paper No. 74-2, Federa l Depos it Insurance Co rpo r a t i on , Washington. L u c k e t t , D.G. [1976], Money and Banking, New York, M c G r a w - H i l l . , McFadden, D. [1978], " E s t ima t i on Techniques f o r the E l a s t i c i t y of S u b s t i -t u t i o n and Other Product ion Parameters " , i n M. Fuss and D. McFadden, eds . , P roduc t i on Economics: A Dual Approach to Theory and A p p l i c a - t i o n s , Amsterdam: North Ho l l a nd . Mackara, W.F. [1975], "What Do Banks Produce?" Monthly Review, Federa l Reserve Bank of A t l a n t a , 60, 70-74. Maddala, G.S. [1971] , "The Use of Var iance Components Models i n P o o l i n g Cross Sec t i on and Time Se r i e s Da ta " , Econometr ica 39, 341-358. Mason, M. [1979] , "Model ing Mutual Funds and Commercial Banks: A Comparative A n a l y s i s " , Jou rna l of Banking and F inance, 3, 347-53. Me l ton , W.C. [1978], "The Market f o r Large Negot i ab le CDs", F e d e r a l  Reserve Bank of New York Qua r te r l y Review, 2, 22-32. Merton, R.C. [1978], "On the Cost of Deposit Insurance When There Are S u r v e i l l a n c e Co s t s " , Jou rna l of Bus iness , 51, 439-52. Mingo, J . J . [1977], "Regu la t i on of F i n a n c i a l I n s t i t u t i o n s : An Overv iew" , The Costs and B e n e f i t s of P u b l i c Regu la t ion o f Consumer F i n a n c i a l  S e r v i c e s , F i n a l Report, Arnold A. Heggestad, P r i n c i p a l I n v e s t i g a t o r , Cambridge, Massachusetts, Abt A s s o c i a t e s . Mingo, J . and B. Wolkowitz [1977], "The E f f e c t s of Regu la t ion on Bank Balance Sheet D e c i s i o n s " , Jou rna l of F inance, 32, 1605-1616. Mu l l i neaux , D.J . [1978], "Economies of Sca le and O r g a n i z a t i o n a l E f f i -c i ency i n Banking: A P r o f i t - F u n c t i o n Approach", Jou rna l o f F i nance , 33, 259-280. - 236 -Murray, 3.D. and R.M. White, [1980], "Economies of Sca le and Depos i t Taking F i n a n c i a l I n s t i t u t i o n s i n Canada", J ou rna l o f Money, C r e d i t and  Bank ing, 12, 58-70. Musgrave, D.C. [1976] " F i xed R e s i d e n t i a l and Non -Res iden t i a l Bus iness C a p i t a l i n the United S tates 1925-1975" Survey of Current Bus ines s , U.S. Department of Commerce. Bureau of Economic A n a l y s i s , 46-52. Mundlak, Y. [1978], "On the Poo l i ng of Time Se r ie s and Cross Sec t i on Da t a " , Econometr ica, 46, 69-86. Panzar, 3.C. and R.D. W i l l i g [1977], "Economies of Sca le i n Mu l t i ou tpu t P r o d u c t i o n " , Quar te r l y Jou rna l of Economics,91, 481-493. P a r k i n , J .M. [1970], "D iscount House P o r t f o l i o and Debt S e l e c t i o n " , Review of Economic S tud i e s , 37, 469-497. Pesek, B.P. [1970], "Banks ' Supply Funct ion and the E q u i l i b r i u m Quant i t y of Money", Canadian Journa l of Economics, 3, 357-383. Powers, J .A . [1969], "Branch Versus Un i t Banking: Bank Output and Cost Economies", Southern Economic J o u r n a l , 36, 153-64. P y l e , D.H. [1971], "On the Theory of F i n a n c i a l I n t e r m e d i a t i o n " , J o u r n a l  o f F i nance , 26, 734-747. Reports o f Cond i t i on and Income by S tate Member Banks of the Fede ra l  Reserve System That Have only Domestic O f f i c e s That Have Less Than  $100 M i l l i o n i n To ta l Assets [1978], Board of Governors of the Fede ra l Reserve System, FR2103, and FR2104, rev i sed December 1978. Samuelson, P.A. [1947], Foundations of Economic A n a l y s i s , Cambridge, Massachusetts: Harvard U n i v e r s i t y P res s . Samuelson, P.A. [1953-1954], " P r i c e s of Facto r s and Goods i n Genera l E q u i l i b r i u m " , Review of Economic S t ud i e s , 21, 1-20. Samuelson, P.A. [-1966], "The Fundamental S i n g u l a r i t y Theorem f o r Non-J o i n t P r o d u c t i o n " , I n t e r n a t i o n a l Economic Review, 7, 34-41. Schweiger I. and 3.S. McGee [1961], "Chicago Banking: The S t r u c t u r e and Performance of Banks and Re lated F i n a n c i a l I n s t i t u t i o n s i n Chicago and Other A rea s " , Journa l of Bus iness , 34, 203-366. S chwe i t ze r , S.A. [1972], "Economies of Sca le and Hold ing Company A f f i l i a -t i o n i n Bank ing " , Southern Economic J o u r n a l , 39, 258-266. Schworm, W. [1980] " I n te r tempora l Dec i s i on Theory" , l e c t u r e notes f o r Advanced Microeconomic Theory, U n i v e r s i t y of B r i t i s h Columbia. - 237 -Scotb, K.E. and T. Mayer [1971], "R i s k and Regu lat ion in Banking: Some Proposa l s fo r Deposit Insurance Reform", S tan fo rd Law Review, 23, 857-902. Sea ley , C.W. [1980], "Deposit R a t e - S e t t i n g , R isk Ave r s i on , and the Theory of Depos i tory F i n a n c i a l I n t e r m e d i a r i e s " , J ou rna l o f F i nance , 35, 1139-1154. Sea ley , C.W. and O.T. L i nd ley [1977], " I nput s , Outputs, and A Theory of P roduc t i on and Cost at Depos i tory F i n a n c i a l I n s t i t u t i o n s " , J ou rna l  of F i nance , 32, 1251-1266. Shap i ro , E., E. Solomon and W.L. White [1968], Money and Banking, New York H o l t , R inehart and Winston. S i v e s k i n d , C. and K. Hurley [1980], "Choosing an Operat ing Target f o r Monetary P o l i c y " , Quar te r l y Jou rna l of Economics, 94,199-203. S t a r t z , R. [1979] , " I m p l i c i t I n t e r e s t on Demand D e p o s i t s " , J ou rna l of  Monetary Economics, 5, 515-34. Tob in , 3. [1961], "Money, C a p i t a l , and Other Shares of V a l u e " , American  Economic Review, V o l . 31, No. 2, 51, 26-46. Tob in , J . [1963] , "Commercial Banks as Creator s of 'Money ' " , i n Banking and Monetary S tud ie s , Deane Carson, e d . , Homewood, I l l i n o i s : I r w i n . Towey, R.E. [1974] , "Money C rea t i on and the Theory of the Banking F i r m " , J o u r n a l of F inance, 29, 57-72. Un i ted S ta te s Department, Bureau of I n t e r n a l Revenue [1942], B u l l e t i n F-- Income Tax, Dep rec i a t i on and Obsolescence, Est imated U se f u l L i v e s and  D e p r e c i a t i o n Rates, Washington. Un i ted S t a te s Department of Commerce [1979], Bureau of Economic A n a l y s i s , Survey of Current Business Revised Est imates of the N a t i o n a l Income and Product Accounts, Washington, D . C , Government P r i n t i n g O f f i c e , J u l y . Woodland, A.D. [1972], "The Cons t ruc t i on of P r i c e and Quant i ty Components of Inputs for Canadian I n d u s t r i e s , 1927-1969", Department of Manpower and Immigrat ion, Ottawa. Woodland, A.D. [1975], " S u b s t i t u t i o n of S t r u c t u r e s , Equipment and Labour i n Canadian P r o d u c t i o n " , I n t e r n a t i o n a l Economic Review, 16, 171-187. Woodland, A.D. [1978], "On Tes t ing Weak S e p a r a b i l i t y " , J o u r n a l of  Econometr ic s , 8, 383-398. - 238 -Z e l l n e r , A. [1962], "An E f f i c i e n t Method of E s t imat ing Seemingly U n r e l a -ted Regress ions and Tests f o r Aggregation B i a s " , Jou rna l of the  American S t a t i s t i c a l A s s o c i a t i o n , 57, 348-368. 

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