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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.Sc,  U n i v e r s i t y of Santa C l a r a , 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 t h i s t h e s i s to  as conforming  the r e q u i r e d standard  THE UNIVERSITY OF BRITISH COLUMBIA December 1982  ° Diana Hancock C h i n l o y , 1982  3E-6  In p r e s e n t i n g requirements  this thesis f o r an  of  British  it  freely available  Columbia,  by  understood that for  Library  shall  for reference  and  study.  I  for extensive copying of be  her  g r a n t e d by  shall  not  be  EffiiOQMlCS  The U n i v e r s i t y o f B r i t i s h 1956 Main Mall V a n c o u v e r , Canada V6T 1Y3  (3/81)  of  Columbia  make  further this  thesis  head o f  this  my  It is thesis  a l l o w e d w i t h o u t my  permission.  Department o f  the  representatives.  copying or p u b l i c a t i o n  the  University  the  h i s or  f i n a n c i a l gain  the  I agree that  s c h o l a r l y p u r p o s e s may  department or  f u l f i l m e n t of  advanced degree a t  agree t h a t p e r m i s s i o n for  in partial  written  SUPERVISOR - W.E. DIEWERT - iii ABSTRACT This research develops a microeconomic theory of the f i n a n c i a l firm that i s empirically implementable.  Financial firms such as banks  and savings and loan associations produce intermediation services between borrowers and lenders. a l l goods.  User costs per unit of service can be derived for  For f i n a n c i a l services, these include the e f f e c t s of reserve  requirements, c a p i t a l gains or losses, deposit insurance,  interest rates,  and service charges. Items generating more expenditure positive user costs, and are inputs. outputs.  than revenue for the firm have  Those with negative user costs are  Comparative s t a t i c s on p r o f i t s , supplies of output and demands  for input are derived for interest rates and monetary regulations. Data comprise pooled time series and cross section data f o r eighteen  banks in New York and New Jersey for the years 1973-1978. User  cost and quantity data are constructed deposits, cash, labor and materials.  for loans, demand deposits, time The f i r s t two are outputs and the  last four inputs. A s p e c i f i c a t i o n i s derived for the variable p r o f i t function, and the testing of regularity conditions such as monotonicity described.  and convexity  A test for the existence of a money supply, as a subset of  f i n a n c i a l goods i s developed.  The test imposes no prior r e s t r i c t i o n on  the form of the money supply. The empirical results indicate that convexity and monotonicity obtain, at the geometric mean of the sample. outputs are p o s i t i v e , but less than unity. negative.  E l a s t i c i t i e s of supply for E l a s t i c i t i e s of demand are  Bank response to any monetary policy action can be calculated,  - iv -  and  some experiments are reported  on.  An alternate model i s derived to permit imperfect the f i n a n c i a l firm market for outputs and inputs.  competition  in  The model i s shown to  y i e l d testable predictions, and price taking behavior for these banks i s ruled out. The results indicate that i t i s possible to develop and implement a model of f i n a n c i a l firm behavior.  Such a model i s required to ensure  accuracy in the effectiveness of monetary p o l i c y .  - 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  viiI  ACKNOWLEDGEMENTS C H A P T E R  1.1 1.2 1 .3 1.4 1.5 1.6 1.7 1.8  C H A P T E R  1  -  x  I N T R O D U C T I O N  2.3 2.4 2.5  2.6  S U M M A R Y  Need o f Microeconomic Theory o f F i n a n c i a l F i r m s I s s u e s i n Technology and R e g u l a t i o n o f F i n a n c i a l Firms User Cost D e r i v a t i o n A Model o f the F i n a n c i a l F i r m Data and Data C o n s t r u c t i o n S p e c i f i c a t i o n and H y p o t h e s i s T e s t i n g Empirical Results I m p e r f e c t C o m p e t i t i o n and the F i n a n c i a l F i r m Notes 2  -  I S S U E S  I N  F I N A N C I A L  2.1 2.2  A N D  T E C H N O L O G Y  A N D  R E G U L A T I O N  1 5 7 7 9 10 11 12 13  O F  F I R M S  Introduction Cost F u n c t i o n Approach 2.2.1 Output S e p a r a b i l i t y ; 2.2.2 N o n - j o i n t Technology P r o f i t F u n c t i o n Approach O u t p u t s , I n p u t s and t h e " C l a s s i f i c a t i o n Problem" R e g u l a t i o n and the F i n a n c i a l F i r m 2.5.1 Reserve Requirements 2.5.2 I n t e r e s t Rate C e i l i n g s 2.5.2.1 D e p o s i t I n t e r e s t Rate C e i l i n g s 2.5.2.2 Loan I n t e r e s t Rate C e i l i n g s -Usury Laws 2.5.3 Federal Deposit Insurance Corporation Premium Rates C o n c l u d i n g Remarks Notes  14 16 17 18 20 24 26 27 29 29 30 32 33 35  - vi -  CHAPTER 3 - USER COST DERIVATION FOR FINANCIAL FIRMS 3.1 3.2  CHAPTER 4.1 4.2  User Costs f o r Assets and L i a b i l i t i e s Implementation Problems 3.2.1 E x p e c t a t i o n s of Future P r i c e s Notes  ••  37 42 42 45  - A MODEL OF THE FINANCIAL FIRM Introduction An I n t e r t e m p o r a l P r o d u c t i o n Model of I n d i v i d u a l F i n a n c i a l Firm Notes  4-7 the 47 69  CHAPTER 5 - DATA AND DATA CONSTRUCTION 5.1 5.2 5.3 5.4 5.5  5.6 5.7  Introduction Labor S e r v i c e s Materials Services Physical Capital Services. User Costs f o r F i n a n c i a l Commodities 5.5.1 Loans 5.5.1.1 Introduction 5.5.1.2 Investments 5.5.1.3 Real E s t a t e Mortgages 5.5.1.4 Instalment Loans 5.5.1.5 C r e d i t Card Loans 5.5.1.6 Commercial, A g r i c u l t u r a l and Other L o a n s . . . 5.5.1.7 User Cost f o r Aggregate Loans 5.5.2 Cash 5.5.3 Demand D e p o s i t s 5.5.4 Time D e p o s i t s 5.5.5 Non-deposit L i a b i l i t i e s 5.5.6 Net Loans 5.5.7 Financial Capital Variable Profits Concluding Remarks Appendix - Chapter 5 - F u n c t i o n a l Cost D a t a On C a p i t a l Notes  72 75 79 84 94 94 94 94 97 98 99 100 100 105 106 112 115 118 121 121 123 126 130  CHAPTER 6 - SPECIFICATION AND HYPOTHESIS TESTING 6.1 6.2 6.3  Introduction P r o f i t F u n c t i o n and Net S u p p l i e s Regularity Restrictions  131 133 136  - vii -  6.4  6.5  6.6  Tests of Bank Technology 6.4.1 Introduction 6.4.2 Existence of Monetary Subagqregates 6.4.2.1 Introduction 6.4.2.2 Money Supply D e f i n i t i o n s : Cash and Demand Deposits.. 6.4.2.3 Money Supply D e f i n i t i o n : Cash, Demand and Time Deposits Econometric Issues.. 6.5.1 Exogeneity of Prices and Quantities 6.5.2 Pooling Time Series and Cross Section Data -- Bank Effects Concluding Remarks Appendix - Chapter 6 Notes.  .  139 139 142 142 143 148 149 149 151 153 155 158  CHAPTER 7 - EMPIRICAL RESULTS 7.1 7.2 7.3 7.4 7.5 7.6 7.7  7.8  Introduction E l a s t i c i t i e s of Transformation, Demand and Supply.... Regularity Tests Tests of Monetary Aggregation Estimation of Transformation, Supply and Demand E l a s t i c i t i e s Rate of Return on Capital Policy Implications: Monetary Policy and Bank Behavior 7.7.1 Introduction 7.7.2 Interest Rate Ceiling Deregulation 7.7.3 Reserve Requirement Costs 7.7.4 Deposit Insurance -- FDIC Regulation Concluding Remarks Notes  159 161 164 171 178 187 189 189 190 192 194 196 198  CHAPTER 8 - IMPERFECT COMPETITION AND THE FINANCIAL FIRM 8.1 Introduction 8.2 .Noncompetitive Bank Behavior: The Context 8.3 Imperfect Competition and the Financial Firm 8.4 S p e c i f i c a t i o n . 8.5 Empirical Results 8.5.1 Hypothesis Testing on Competitive Behavior... 8.5.2 Output Demand and Input Supply E l a s t i c i t i e s . . 8.6 Policy Implications 8.6.1 Costs of Noncompetitive Behavior 8.6.2 Monetary Policy 8.7 Concluding Remarks Notes  200 201 204 211 215 215 217 221 221 224 225 226  CHAPTER 9 - CONCLUDING REMARKS  227  BIBLIOGRAPHY  230  - viii  -  LIST OF TABLES Page T a b l e 5.1  5.2  5.3  5.4  5.5  5.6  O i v i s i a P r i c e I n d i c e s f o r Labor ( T o r n q v i s t s p e c i f i c a t i o n 1973=1.00) Cross Bank T o r n q v i s t Labor P r i c e s I n d i c e s (Bank 1 normalized at u n i t y ) . . . . Labor Input and Wage Data Current D o l l a r s Price Indices, 1973-1978  Materials  and Intermediate  Tornqvist Price Indices, Materials Intermediate I n p u t s , 1973=1.00  and 85  User Cost and Q u a n t i t y Index, M a t e r i a l 1973-1978  S e r v i c e L i v e s by Type of Asset  5.9  Asset P r i c e and Q u a n t i t y I n d i c e s , 1973-1978  5.12  Inputs, 83  5.8  5.11  80  81  Asset  5.10B  1973  1973-1978,  5.7  5.10A  78  Prices for Physical Capital  Services, 86  (1972=100)  ....  91 Capital  Stock, 95  Loan S t a t i s t i c s - User Costs (per c e n t , net r e t u r n a f t e r d i s c o u n t i n g ) Three Sample Years Loans Balances O u t s t a n d i n g , Three Sample Years  89  Millions  of  101 Dollars 104  Reserve Requirements on Demand D e p o s i t s Banks November 1972 - November 1978  of Member  Reserve Requirements on Demand D e p o s i t s Banks, Average Annual  of Member  108  Statistics  109  5.13  Demand Deposit  5.14  Maximum I n t e r e s t Rates Payable on Time and Savings D e p o s i t s at F e d e r a l l y Insured Commercial Banks  113  5.15  Time Deposit  116  5.16  Borrowed and Purchased Funds and Other L i a b l i t i e s . . .  Statistics  110  119  - ix -  5.17  Net Loans, User Cost and Q u a n t i t i e s .  120  5.18  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  .124  5.19  Variable Profits  Table 6 . 1 6.2 Table 7 . 1  125  Test S t r u c t u r e , R e g u l a r i t y  140  Conditions  150  T e s t i n g f o r Money Supply D e f i n i t i o n s Test S t a t i s t i c s , Symmetry and E q u a l i t y of Variable Profit  Function  166  7.2  Parameter E s t i m a t e s , V a r i a b l e P r o f i t  7.3  R e l a t i v e E x p e n d i t u r e s , Outputs and I n p u t s  170  7.4  C o n v e x i t y Test  172  7.5  Money Supply Aggregates  M l , Parameter E s t i m a t e s . . . .  174  7.6  Money Supply Aggregates  M2, Parameter E s t i m a t e s . . . .  175  7.7  E s t i m a t e s of E l a s t i c i t i e s o f T r a n s f o r m a t i o n and R e l a t i v e E x p e n d i t u r e s E s t i m a t e s 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  180  Classification Complements  185  7.8 7.9 Table 8 . 1  of P a i r s —  Function  Substitutes  Parameter E s t i m a t e s , Bank Supply Functions  and  and Demand  8.2  Parameter E s t i m a t e s , T e s t s o f C o m p e t i t i v e Taking i n Separate Markets  8.3  Test S t a t i s t i c s , C o m p e t i t i v e Behavior and Input Markets ( x /OF)  Price  168  179  216 218  in Output 2 19  8.4  Parameter E s t i m a t e s , T e s t s of C o m p e t i t i v e Bank B e h a v i o r , A l l Markets  220  8.5  P r i c e E l a s t i c i t i e s of Demand f o r Outputs and Supply f o r I n p u t s  222  -  X  -  ACKNOWLEDGEMENTS  I would like to acknowledge with gratitude the help of my visor, W. Erwin Diewert.  His own  example to follow, p a r t i c u l a r l y  super-  scholarship has provided me with an  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 Shearer.  Ronald  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 c a r e f u l l y 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 B r i t i s h Columbia Computing Centre.  CHAPTER 1 INTRODUCTION AND SUMMARY  1.1  Need for Microeconomic Theory of F i n a n c i a l Firms This research develops a microeconomic theory of f i n a n c i a l firms.  A f i n a n c i a l firm i s assumed to be a p r o f i t maximizing entity engaged i n the production of intermediation services between borrowers and lenders. These services are related d i r e c t l y or i n d i r e c t l y to the financial and l i a b i l i t i e s held by the firm, such as loans and deposits.  assets  The  f i n a n c i a l firm issues i t s own l i a b i l i t i e s , t y p i c a l l y deposits of various types.  Services other than f i n a n c i a l 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  i n s t i t u t i o n s " are used to describe these firms. The focus of this research i s on national banks subject to regulation by the central bank, though the theory developed can be applied to other f i n a n c i a l firms.  This permits an examination of money  supply aggregates and regulatory p o l i c i e s such as reserve requirements. The need for a microeconomic theory of the f i n a n c i a l firm has been pointed out by Tobin [1961] The i n t e l l e c t u a l gulf between economists' theory of values of goods and services and their theories of value of money i s 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 t h e o r e t i c a l apparatus i s 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 u t i l i t y 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  firms' decisions.  involves financial  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 l i a b i l i t y 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 recipient, but also service charges, reserve requirements, deposit and penalties, together with the discount rate.  insurance  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 developed among t h e s e physical  capital,  estimation in  are l a b o r employed  for physical services.  i n managerial  m a t e r i a l s and s u p p l i e s .  o f t h e bank t e c h n o l o g y .  r e g u l a t i o n s or monetary p o l i c y  Notable  and p r o c e s s i n g f u n c t i o n s ,  The u s e r  This permits  c o s t s enter the  an a n a l y s i s o f c h a n g e s  on l o a n s , d e p o s i t s and e m p l o y m e n t i n  banking. S e c o n d , a method o f c l a s s i f y i n g Outputs are those expenditure  with negative  f o r the firm.  H e n c e i t c a n be r e a d i l y The policy  determining has  Inputs  determined  model p e r m i t s  on f i n a n c i a l  user  outputs  c o s t s , or generate  are those  and t h e r o l e  t h e money s u p p l y .  The t h e o r y  as f i r m s .  Explicit  money s u p p l y  aggregates  exist,  t h e money s u p p l y .  Relatively  there  financial  little  i s a plethora of literature  m a r k e t s t r u c t u r e on p e r f o r m a n c e . firm behavior  when t h e r e i s no t h e o r y  w i t h which  t o whether determine  financial  and l e n d e r s  firms  i s examined.  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 r e g a r d i n g t h e impact  of  I t may be p r e m a t u r e t o a s k how i n market s t r u c t u r e  to describe that behavior.  develops  an e m p i r i c a l m o d e l w h i c h c a n s t a t i s t i c a l l y  petitive  behavior  output  financial  firm decisions  i s a f f e c t e d by v a r i a t i o n s  i n both  a t t e n t i o n has  a t t e n t i o n h e r e h a s been g i v e n  c r e a t e money and i n t e r m e d i a t e b e t w e e n b o r r o w e r s  firm,  less  b a n k s and o t h e r  where f i n a n c i a l  i s relatively  costs.  o f t h e e f f e c t s o f monetary  The method and e f f i c i e n c y  Though t h e r e  user  o f money demand by c o n s u m e r s  o f money, v i e w i n g  institutions  with positive  than  of intermediary decisions i n  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 .  been g i v e n t o t h e s u p p l y  more r e v e n u e  whether goods a r e i n p u t s o r o u t p u t s .  the investigation  firms,  and i n p u t s i s d e v e l o p e d .  and i n p u t  markets.  This  research  test  f o r noncom-  - 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 r m has been p l a n t e d by p o r t f o l i o t h e o r y i n a n a l y z i n g tutions.  the b e h a v i o r of f i n a n c i a l  Banks have not been t r e a t e d as f i r m s , but as r a t i o n a l  i n an environment  c h a r a c t e r i z e d by r i s k or u n c e r t a i n t y .  and the r o l e they p l a y  output m i x , i n p u t demands ation.  It  riskless  is usually  equilibrium  and s c a l e s i z e have been o m i t t e d from c o n s i d e r -  assumed t h a t the f i n a n c i a l f i r m has u n l i m i t e d ,  been performed on asset  Extensive  research  a l l o c a t i o n between a l t e r n a t i v e i n v e s t m e n t s  However, the l i a b i l i t y  r e l a t i v e l y less  investors  Production  in determining  a b i l i t y t o borrow and o b t a i n l e v e r a g e .  portfolio.  insti-  The M a r k o w i t z -  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 a p p a r a t u s . and c o s t c o n s t r a i n t s ,  sup-  attention.  s i d e o f the b a l a n c e sheet has  has in a  received  F u r t h e r , a t h e o r y of f i n a n c i a l f i r m s 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 a p p l y i n g p o r t f o l i o t h e o r y . It  should be noted t h a t t h i s model i s based on the r i s k l e s s  c l a s s i c a l theory of the f i r m .  It  neo-  can be used as a b u i l d i n g b l o c k f o r a  more complete model which i n t r o d u c e s u n c e r t a i n t y and p o s s i b l y  risk  aversion. The n e o c l a s s i c a l approach d e r i v e s e x p e c t e d user c o s t s , h i g h e r moments of these d i s t r i b u t i o n s may a l s o p l a y a r o l e .  but the The  i n c l u s i o n of such h i g h e r moments r e q u i r e s d a t a not t y p i c a l l y a v a i l a b l e . It  remains the case t h a t f i n a n c i a l f i r m s have expected r i s k  measurable by expected u s e r c o s t s . i higher  returns.  Higher  risks  are compensated by  An o b j e c t i v e of the r e s e a r c h i s t o measure these  c o s t s , dependent not o n l y o n i i n t e r e s t r a t e s but a l s o  user  reserve  r e q u i r e m e n t s , expected c a p i t a l g a i n s or" l o s s e s and d e p o s i t rates.  premia  insurance  - 5 -  1.2  Issues i n Technology and Regulation o f F i n a n c i a l 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 i s that output i s  not a predetermined variable.  Further, without a c l a s s i f i c a t i o n rule to  select between outputs and inputs, outputs cannot be easily determined. Cost functions for f i n a n c i a l firms are t y p i c a l l y estimated with outputs aggregated, although this i s not a requirement. output permits the estimation of economies of scale.** issue i s what prices are used in the cost function.  Aggregation of The important  User costs include  interest rates and regulatory and other cost variables.  I f interest  rates only are used, the data are subject to measurement error and the resulting estimates are biased.  I t i s impossible  to analyze the e f f e c t s  of reserve requirements and monetary policy on the banking system. The  alternative starting point for bank technologies  i s the p r o f i t  function.  The p r o f i t function, as the maximum of p r o f i t s subject to the  production  function constraint, i s more appropriate  f i n a n c i a l firms.  for banks and other  The problems with the p r o f i t function arise more in  .specification and estimation than in theory.  Some of these problems are  discussed below. F i r s t , i f a second order  form such as the translog or generalized  Leontief or quadratic i s used, i t i s necessary to check regularity conditions.  These include linear homogeneity in output and input  •prices, monotonicity and convexity.  I f the convexity  or the linear homo-  geneity in prices properties f a i l to hold, then the estimated p r o f i t  - 6 -  function i s not consistent with the maintained assumption of p r o f i t maximizing  behavior. Second, the variable p r o f i t function depends on prices, or user  costs of outputs and  inputs, and the quantities of fixed inputs.  There  i s l i k e l y to be substantial m u l t i c o l l i n e a r i t y in these user costs, whether in time series, cross section or pooled data. be ameliorated  i f demand or supply  system of estimating equations,  This situation can  equations are also included in the  but otherwise i t i s d i f f i c u l t to identify  parameters. Third, the argument on user cost data applies to the p r o f i t function.  If there i s measurement error in user cost, biased parameter  estimates a r i s e .  Furthermore, i f the e f f e c t s of regulations on user  costs are excluded, i t i s impossible  to analyze monetary policy e f f e c t s .  Chapter 2 examines the p r i n c i p a l areas of regulation that affect user costs.  For example, reserve requirements, as administered  Federal Reserve, act as a tax on f i n a n c i a l firms so covered.  by the  Required  reserves earn no return to the f i n a n c i a l firm and there i s foregone revenue. . Deposit the banks.  insurance  increases the user cost of servicing deposits to  Interest rate regulations place l i m i t s 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 e f f e c t s on interest rates and the quantities of f i n a n c i a l goods. Chapter 2 reveals that previous work on the estimation of bank technologies  i s incomplete, and that the regulations require modelling  as  - 7 -  a part of the profit maximizing  1.3  structure.  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 c l a s s i f i e d 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 i s  one d o l l a r per period.  Goods with a negative user cost, with  expenditures f a l l i n g below revenue per unit, are outputs. Liability  items, such as time or demand deposits, involve interest  expenditures by banks. requirement,  5  Further unit costs are incurred for the reserve  in foregone revenue, and deposit insurance, while service  and penalty charges are earned. revenue i s earned.  On asset items such as loans, interest  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 p r o f i t function estimation.  This permits  outputs and inputs to be distinguished.  1A  A Model of the Financial Firm A model of producer behavior i s developed  in Chapter 4 where  labor, materials and physical capital demands, and asset and holding decisions are simultaneously determined.  liability  The s p e c i f i c a t i o n  d i f f e r s from previous neoclassical models in that i t i s based on the  - 8 -  theory of intertemporal production of Hicks [1946] and u t i l i z e s the user costs derived in Chapter 3. f i n a n c i a l firm's production  Time plays an essential role in the process, and an intertemporal model i s  needed, p a r t i c u l a r l y for analyzing asset and  liability  decisions.  Each  f i n a n c i a l i n s t i t u t i o n holds an inventory of various f i n a n c i a l assets, liabilities,  and c a p i t a l .  There are revenues and costs associated  holding this inventory over time. choose the input-output production period.  The f i n a n c i a l firm i s assumed to  combination which maximizes p r o f i t during  the  The model developed considers regulatory controls  through their effect on relative user costs. production  with  The duality between the  p o s s i b i l i t y set and the p r o f i t function i s employed to derive  comparative s t a t i c s yielding testable predictions, and to obtain the functional forms for the estimating equations.  It i s found that the  holdings of an asset do not decrease when the rate of interest payable to the f i n a n c i a l firm increases.  A similar conclusion obtains If expected  c a p i t a l gains increase, or i f the service charge rate c o l l e c t e d 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 i s found that  deposits are non-increasing  i f their required reserve ratio increases, or  i f the interest rate payable increases. the insurance premium increases.  A similar conclusion obtains i f  However, i f the service charge rate per  d o l l a r increases, then deposits are non-decreasing. Comparative -statics for the cross e f f e c t s of the components of each user costs are indeterminate.  It i s unknown a p r i o r i what the  effect on time deposits is when the required reserve ratio on demand  - 9 -  deposits changes.  This i s because the off-diagonal elements of the  matrix of second order p a r t i a l derivatives of the p r o f i t evaluated  function  at the optimum cannot be sign-determined using the regularity  properties of the p r o f i t function.  Further analysis of the cross e f f e c t s  of the components of each user cost requires examination of empirical point  estimates. P r o f i t s for the f i n a n c i a l firm are non-decreasing when there i s an  increase i n : (1) the interest rate payable to the firm on assets held; (2) the c a p i t a l gains on assets held; (3) the service charge rate on loans; and  (4) the service charge rate on deposits.  non-increasing user cost:  P r o f i t s are  i f there i s an increase in the following components of  (1) the default rate on loans; (2) the required reserve  ratio  on deposits; (3) the interest rate payable by the f i n a n c i a l firm on liabilities;  1.5  and  (4) the insurance  premium rate on  deposits.  Data and Data Construction The data and their derivation are described  in Chapter 5.  The  major data source for the study i s developed by the Federal Reserve Bank of New  York's Functional Cost Analysis Program.  yearly data for eighteen  commercial banks over the period 1973-1978.  banks are located in the states of New are more appropriate  The sample comprises  York and New  Jersey.  The  Panel data  than cross-sectional data for our purposes because  they permit variation in user costs over time and permit the testing of s p e c i f i c bank e f f e c t s . Data are constructed  for three physical, or non-financial  commodities used in bank production.  These are labor input, the services  -  of intermediate  10  -  inputs and raw materials, and the services of c a p i t a l .  User costs and the relevant quantities for f i n a n c i a l commodities are constructed.  For the s p e c i f i c a t i o n , four types of f i n a n c i a l  commodities are distinguished, namely loans, cash, demand deposits time deposits.  and  With the exception of cash, the quantity of each i s an  index comprising  a number of other f i n a n c i a l commodities.  component a separate user cost must be constructed. variable p r o f i t s are also constructed  For each  Quasi-rents  or  for each bank in each year.  The c l a s s i f i c a t i o n test i s then applied to the data. sample points, loans and demand deposits are outputs.  For a l l  Cash, time  deposits, labor and materials are inputs. 1.6  S p e c i f i c a t i o n and Hypothesis Testing The  functional form used i s a translog variable p r o f i t function.  Prior to testing hypotheses on bank technology, certain conditions must be s a t i s f i e d . monotonicity  These include symmetry of the quadratic parameters, and convexity.  Monotonicity  requires that variable p r o f i t s  be increasing in output prices, and decreasing  in Input p r i c e s .  Convexity i s s a t i s f i e d i f the Hessian matrix of second derivatives of the variable p r o f i t function i s positive semi-definite. Chapter 6 derives the e l a s t i c i t i e s of transformation e l a s t i c i t i e s of supply for outputs and demand for inputs.  and It i s possible  to calculate e x p l i c i t l y 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 e f f e c t s of monetary policy on banks to be derived.  - 11 -  A s t a t i s t i c a l test i s developed for whether a money supply and  i f so, what i t s components are.  demand and time deposits. money.  exists,  Candidates for inclusion are cash,  The test i s generalizable to any d e f i n i t i o n of  The test i s based on a test due to Woodland [1978].  is not subject to the bias noted by Blackorby, which occurs when the Berndt and Christensen  Primont and Russell [1977]  [1974] test for the  existence of an aggregate in a translog model i s used. of the Berndt and Christensen  This test  test in this context  Usual application  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 p o s s i 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 i n Chapter 7. estimating system.  Symmetry i s imposed on the  Given t h i s , both monotonicity  and convexity  hold for  a l l data points. The matrix of e l a s t i c i t i e s of transformation p r i n c i p a l diagonal elements are p o s i t i v e . supply,  i s well behaved. A l l  Own price e l a s t i c i t i e s of  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 r e l a t i v e l y close to unity, while that for time deposits i s less than one. Responses to changes in monetary regulations are examined. S p e c i f i c a l l y , the provisions of the 1980 Monetary Control Act are applied to the sample period, by allowing the interest rate c e i l i n g 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 F i n a n c i a l Firm The theory  i s extended to account for market imperfections facing  f i n a n c i a l firms in Chapter 8.  The demand for output i s permitted  be perfectly e l a s t i c , and similar f l e x i b i l i t y i s permitted  on the  not to supply  of inputs. Previous models impose price-taking in output and input markets. Also, the e l a s t i c i t i e s are a l l estimated, information.  and do not require a p r i o r i  The model developed commences from the production  function,  and i s not s t r i c t l y comparable to the variable p r o f i t function model. This i s because a translog s p e c i f i c a t i o n i s used, and the form i s not self-dual. Tests are developed separately for price taking in loans, cash, demand deposits, time deposits and labor. the eighteen New accepted markets.  York and New  In the empirical results for  Dersey banks 1973-1978, price taking i s  in the labor market, but not accepted  in the remaining four  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 i t is not the  case. Price taking i s imposed in a l l markets, and the estimates  with those when price taking i s not imposed.  The s p e c i f i c  compared  simulations  are for responses to monetary policy in affecting cash, demand deposits and time deposits.  In some cases, the difference in results i s small,  while in others the error can be as large as 20  percent.  NOTES hobin  [ 1961].  2  Klein  [1971].  3  S e e Barnett  [1981].  T h i s i t s e l f i s not a requirement, f o r economies of s c a l e e s t i m a t e have been d e r i v e d f o r m u l t i p l e output t e c h n o l o g y , although there i s no agreement on procedure. One p o s s i b i l i t y i s to e v a l u a t e the marginal c o s t of each output, and to sum. See Caves, C h r i s t e n s e n and Swanson [1980] and Panzar and W i l l i g [1977]. I n the case of demand d e p o s i t s , there may be a p r o h i b i t i o n a g a i n s t p o s i t i v e i n t e r e s t payment. However, p o s i t i v e i n t e r e s t r a t e s apply on n e g o t i a b l e order of withdrawal (NOW) accounts. 5  -  14 -  CHAPTER 2  ISSUES IN TECHNOLOGY AND REGULATION OF FINANCIAL FIRMS 2.1  Introduction The  s t r u c t u r e o f technology  between v a r i o u s point  a s s e t s and l i a b i l i t i e s  regulation  Moreover,  by p o r t f o l i o theory i n a n a l y z i n g  tions.  but  such i n f o r m a t i o n  the n e o c l a s s i c a l  substitutability  of interest  is  and d e r e g u l a t i o n of the f i n a n c i a l  Traditionally,  and M a l k i e l [ 1 9 7 3 ] , Hart  of  sector.  the behavior of f i n a n c i a l  not as p r o d u c e r s , but as r a t i o n a l  stems from the omission  of p r o d u c t i o n and cost  constraints  financial  The  firms o p e r a t e , and the r o l e of these c o n s t r a i n t s  firm.  The second i s  l i t e r a t u r e of the l i a b i l i t y  input demands  the r e l a t i v e n e g l e c t  i n the  s i d e of the balance s h e e t .  authors have argued that  first  under which in deter-  and s c a l e s i z e of  t h e o r y of f i n a n c i a l f i r m s must take account of p o l i c y Several  investors  or u n c e r t a i n t y . approach.  e q u i l i b r i u m output mix,  Aigner  apparatus.  two problems with t h i s  mining  Kane  [ 1 9 8 0 ] , have adopted  There are at l e a s t  financial  funds  A number of w r i t e r s ,  1  and McCurdy  i n an environment c h a r a c t e r i z e d by r i s k  institu-  the a l l o c a t i o n of  p o r t f o l i o theory as t h e i r a n a l y t i c a l  theory views f i r m s  of  model of the f i r m has been s u p p l a n -  and i n v e s t m e n t s .  and Oaffe [1974], Berndt  from the  r e l e v a n c e i n the  [1965], P a r k i n [1970], P y l e [ 1 9 7 1 ] , Hyman [ 1 9 7 2 ] ,  Markowitz-Tobin  Portfolio  loans  not only  a l s o f o r the conduct  The primary focus of p o r t f o l i o theory i s  between heterogeneous  the  is  of e f f i c i e n c y i n the f i n a n c i a l s e c t o r ,  monetary p o l i c y .  ted  and p o t e n t i a l  the  portfolio  Further, a regulations.  p e r f e c t c o m p e t i t i o n may not be the  - 15 -  relevant behavioral mode in asset and deposit markets.  2  Mason [1979]  argues that the assumption of quantity-setting behavior i s not appropriate  for financial firms, and that p o r t f o l i o theory  prices as exogenous.  tends to view  Hart and daffe [1974] argue that p r i c e - s e t t i n g  behavior cannot be adequately treated within a p o r t f o l i o model. Various  studies u t i l i z i n g the concepts of the r i s k l e s s  neoclassical theory of the firm have been proposed to describe the operations  of financial firms in order to correct d e f i c i e n c i e s of  p o r t f o l i o analysis.  Most of these studies do not consider the e f f e c t s  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 s c a l e . Another area relates to the conduct of monetary p o l i c y .  4  Specifically,  the issue i s the relationship between the technology of a f i n a n c i a l firm and money c r e a t i o n .  5  Another problem i s the relationship between  regulations on f i n a n c i a l i n s t i t u t i o n s and the theory of money creation. The methodology used has varied.  In some cases, a reduced form i s  derived and estimated without a direct linkage to economic theory'. other cases, derived.  6  the economic model and underlying  In  In  technology have been  essence, the research on f i n a n c i a l firms can be divided  into those using cost functions and those employing p r o f i t  functions.  Section 2 discusses the cost function approach, and section 3 discusses the p r o f i t function approach. One of the main confusions arises from disagreement concerning  i n the theory of the f i n a n c i a l firm appropriate measures of outputs  16  -  and it  inputs.  -  If neither input nor output can be appropriately  is d i f f i c u l t to speak of a production  defined,  function relating the  two.  Section 4 discusses this c l a s s i f i c a t i o n problem. Section 5 discusses firms. 2.2  three types of regulations on  The chapter closes with some concluding  financial  remarks.  Cost Function Approach Duality theory  for production  s p e c i f i c a t i o n of any production  and cost structures permits the  technology in terms of an  eguivalent  cost function (McFadden [1978]), assuming cost minimizing behavior. Econometrically,  this permits the estimation of the cost structure  the c h a r a c t e r i s t i c s of the underlying run multiproduct  production  structure.  The  and  short  variable cost function can be written as: C = C(z,w,f)  (2.1)  where C i s minimal short run total variable costs,z i s a vector of outputs, w i s a vector of variable input prices and inputs, exemplified  f i s a vector of fixed  by c a p i t a l .  The cost function s a t i s f i e s the properties that i t is a nonnegative  function, p o s i t i v e l y l i n e a r l y homogeneous, concave, continuous  and nondecreasing in input prices, w, continuous in z (Diewert [1982]). to the firm and  and s t r i c t l y  increasing and  Assuming that z and w are exogenous  i t s stock of capital i s given, (2.1)  estimates of the underlying  yields unbiased  technology once an appropriate  form and stochastic s p e c i f i c a t i o n have been given.  functional  By imposing r e s t r i c - .  tions in the estimation, i t i s possible to test hypotheses on technology.  17 -  The c o s t  f u n c t i o n approach has been employed by r e s e a r c h e r s  mainly  concerned w i t h the degree of economies of s c a l e and the i m p l i c a t i o n s f o r e n t r y and b r a n c h i n g r e g u l a t i o n . financial  The emphasis  i s on whether e x i s t i n g  f i r m s should be allowed to expand by b r a n c h i n g , or i f new  f i r m s should be a l l o w e d to e n t e r . scale researchers  To o b t a i n e s t i m a t e s of economies of  have e i t h e r assumed an output aggregate  t h a t the f i r m has a n o n - j o i n t t e c h n o l o g y . measured f o r the output aggregate  exists,  or  The economies of s c a l e were  or f o r each i n d i v i d u a l p r o d u c t .  2.2.1 Output Separability One group of s t u d i e s on the t e c h o l o g y of the f i n a n c i a l f i r m imposes ex ante output a g g r e g a t i o n .  p  One procedure f o r measuring  output  q  has been t o use t o t a l d e p o s i t s as a p r o x y .  An a l t e r n a t i v e measure  been t o use t o t a l a s s e t s h e l d by the f i n a n c i a l f i r m . [1981] uses both these output p r o x i e s .  1 0  has  Goldschmidt  As a t h i r d a l t e r n a t i v e ,  Greenbaum [ 1 9 6 7 ] , Powers [1969] and S c h w e i t z e r [1972] c o n s t r u c t  output  measures t h a t a s s i g n weights to the v a r i o u s components of the e a r n i n g assets p o r t f o l i o . Using the m u l t i p r o d u c t v a r i a b l e c o s t f u n c t i o n , a g g r e g a t i o n outputs (2.1)  i m p l i e s the e x i s t e n c e of an aggregator  the  such t h a t  can be w r i t t e n C =  Since  f u n c t i o n h(z)  of  C(h(z),w,f).  = C^h^, where s u b s c r i p t s  (2.2)  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  output a g g r e g a t i o n c o n d i t i o n , C  n  h (z) n  m  h (z) m  C  (2.3)  - 18 -  for any outputs n and m independently of w and f. The output aggregation condition implies that the ratio of the short run marginal costs for any two outputs must be independent of variable input prices and c a p i t a l .  Since this condition implies r e s t r i c t i o n s on the variable  cost function, i t 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  s p e c i f i c a t i o n s 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 e x p l i c i t consideration of the structure of the underlying  tech-  nology (Benston [1965], B e l l and Murphy [1968], Dugger [1975] and Longbrake and M e r r i l l [1974]). function i s non-joint multi-input  It i s assumed that the transformation  in inputs.  firm be represented  Let the technology of a multiproduct, by a transformation  function T(z,x) = 0  where z and x are M and N dimensional vectors of the quantities of outputs and inputs respectively.  A transformation  inputs i f there exist individual production Z  i  =  f  i  (  x  LT ' " ' i N X  )  1  =  function i s non-joint in  functions,  >--->  1  (2-4)  M  M such that T(z,x) = 0 i f and only i f z. = f. and Ex.. = x. for i=l J 1  j = 1,...,N where z = ( z ^ , — >(v|)> z  x  E  1  1 J  ( |»-''> ^) 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 B e l l and Murphy [1968] view the f i n a n c i a l  -  19  -  f i r m as r e p r e s e n t e d by a number of s e p a r a t e p r o d u c t i o n processes  in  estimating  is  a model of bank b e h a v i o r .  measured by number of accounts. deposits,  instalment  securities,  loans,  safe d e p o s i t  f o r each p r o d u c t .  The products are demand d e p o s i t s ,  business  loans,  boxes and t r u s t  divided into administration, analyzed s e p a r a t e l y .  The output of each process  business  The o b j e c t i v e i s  real estate  business.  loans,  Overhead  costs  development, and occupancy  are  to e s t i m a t e economies of  scale  The form of the e q u a t i o n estimated f o r each of  d i r e c t banking s e r v i c e s ,  time  and f o r each c a t e g o r y of i n d i r e c t cost  the  is  d e r i v e d from an u n d e r l y i n g Cobb-Douglas p r o d u c t i o n f u n c t i o n . Adar, Agmon and O r g l e r [1975]  argue that  interdependence may  a r i s e from the j o i n t use of c e r t a i n i n p u t s by many p r o d u c t s . In banks, j o i n t h e s s i n p r o d u c t i o n i s e v i d e n t i n the j o i n t use of i n f o r m a t i o n by d i f f e r e n t departments, e . g . , i n e v a l u a t i n g a loan a p p l i c a t i o n of a d e p o s i t o r . Another example i s the j o i n t use of g e n e r a l "brand name" type advertisement. A test  f o r the e x i s t e n c e of j o i n t n e s s  m u l t i p r o d u c t cost relation,  f u n c t i o n can be d e v e l o p e d .  in production u t i l i z i n g It  u t i l i z e s the  following  12  M C(z.j , . . . ,z^,w,f)  { = I C..(z.,w,f) j=1  i f F is  non-joint  in  inputs  M < £ C.(z.,w,f) j=1  J  J  i f F involves jointness p r o d u c t i o n , j=1,...,M.  in  the  -  3ointness  in production  20  -  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 f l e x i b l e functional form for the multiproduct  variable cost function and  separability, jointness in production, structure.  then test for output homogeneity and a Cobb-Douglas  These tests would be based on parametric r e s t r i c t i o n s .  Woodland [1978] has developed a test for weak s e p a r a b i l i t y . Cowing [1980] has suggested a test for the existence of jointness in production i f a multiproduct  transloq variable cost function i s postulated.  Hall  [1973] has derived a functional form for joint cost functions that contains separability and non-jointness  as parametric r e s t r i c t i o n s .  test for output homogeneity using the variable cost function non-linear estimation of the degree of homogeneity. assumptions can also be  The  involves  Other alternative  considered.  2.3 P r o f i t Function Approach Duality between p r o f i t and transformation specification of any production  functions allows  technology in terms of an  the  equivalent  p r o f i t function (Diewert [1974]), assuming that the producer chooses the input-output  combination which maximizes p r o f i t .  applications i t is convenient to introduce due to Samuelson [1953-4].  For econometric  the variable profit  The variable p r o f i t  function may  function  be defined  as follows: ir(v,w:f) = max  {vz-wx  : (z,x:f)eS}  (2.6)  where n is maximized variable p r o f i t , z i s an M dimensional vector of  - 21  outputs,  -  x i s an N d i m e n s i o n a l v e c t o r of v a r i a b l e i n p u t s ,  representing  f is a vector  the q u a n t i t y of f i x e d i n p u t s , v i s a v e c t o r of  p r i c e s , w i s a v e c t o r of input p r i c e s and 5 r e p r e s e n t s technologically  f e a s i b l e set of i n p u t s and o u t p u t s .  output  the  Hotelling's  Lemma  can be used i n order to d e r i v e systems of v a r i a b l e output supoly i n p u t demand f u n c t i o n s ,  i f the v a r i a b l e p r o f i t  function  and  satisfies  r e g u l a r i t y c o n d i t i o n s and i s d i f f e r e n t i a b l e w i t h r e s p e c t to v a r i a b l e 13  output and input  prices.  S t a t i c p r o f i t maximizing b e h a v i o r  i s a s t a n d a r d assumption  c o n 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  in  [1970] and Towey  [1974] f o c u s on r e c o n c i l i n g the t h e o r y of money c r e a t i o n w i t h the t h e o r y of the f i r m .  Mingo and Wolkowitz [1977] and S e a l e y  c o n c e n t r a t e on the a l l o c a t i o n o f r e s o u r c e s output.  and L i n d l e y  [1977]  and e q u i l i b r i u m l e v e l s of  A t h i r d group (Adar, Agmon, and O r g l e r  [1978]) c o n s i d e r a l t e r n a t i v e t y p e s of p r o f i t  [1975] and  Mullineaux  functions.  Those i n t e r e s t e d i n r e c o n c i l i n g the theory of the f i r m w i t h the t h e o r y 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 q u a n t i t y of d e p o s i t s the banking excess  industry.  as the output  of  Roth models assume that banks d e s i r e to hold no  r e s e r v e s on the d e p o s i t s  they expect to r e t a i n .  Hence  3 ea =  I (l-k.)D. j=l and k^ i s the r e s e r v e r a t i o on the j t h J  where ea = e a r n i n g a s s e t s , deposit type, j=1,...,3. and s e r v i c e c h a r g e s .  (2.7)  1  Revenues are composed of e a r n i n g s  on a s s e t s  Pesek [1970] c a l c u l a t e s average c o s t s measured  per  - 22 -  d o l l a r o f demand d e p o s i t s u s i n g f u n c t i o n a l c o s t  data  prepared  by  the  F e d e r a l Reserve Bank o f Boston f o r 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  d e p o s i t q u a n t i t i e s and a v e c t o r of s e r v i c e s per d o l l a r o f d e p o s i t s performed. Sealey  and L i n d l e y [1977] and Sealey  [1980] c o n s i d e r d e p o s i t s as  i n p u t s i n t h e p r o d u c t i o n of e a r n i n g asset o u t p u t , output i t s e l f .  r a t h e r than being t h e  The d o l l a r volume o f the v a r i o u s types of e a r n i n g  i s used as a measure of the output o f the f i n a n c i a l  firm.  f i r m i s viewed as being composed o f c o n c e p t u a l l y d i s t i n c t The  assets  The f i n a n c i a l departments.  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  inputs.  The t r a n s f o r m a t i o n f u n c t i o n i s n o n - j o i n t i n i n p u t s i n t h e  d i f f e r e n t i a b l e case i f and only i f 3 TT/3V.3V. = 0  1*7  2  . and  i  J  8^IT v. —=• 3v.  +  ^  1  i  Z 1=1 •  3^TT w. J  = 0 3w.3v. J  i = 1 , . . . ,M . ' '  , > (2.8) c  J-i,...,N i  where IT i s t h e p r o f i t f u n c t i o n and v^'s and v v / s are the output and i n p u t p r i c e s r e s p e c t i v e l y . S i n c e 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 it  technology  i s amenable t o s t 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  L i 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. [1977] and Sealey  [1980] a l s o assume a n o n - j o i n t  Mingo and Wolkowitz  technology.  Most o f t h e econometric s t u d i e s o f bank p r o f i t s a r e developed without  an u n d e r l y i n g p r o d u c t i o n  structure.  Some c o n t a i n 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 o f the p r o f i t f u n c t i o n . * One group o f 1 1  - 23 -  models contains bank assets as a proxy for bank output.  Another uses  as output, bank c a p i t a l , which is highly correlated with assets.  These  models are t h e o r e t i c a l l y misspecified because output is in the p r o f i t function. If output is endogenous and  i t s quantity i s correlated with  the error term in the profit function then simultaneous equation bias occurs.  The estimates of the parameters w i l l be biased and inconsis-  tent . Mullineaux [1978] u t i l i z e s the theory of the p r o f i t function in developing  his econometric model.  training bank production  He assumes the technology cons-  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. represented  Quantities of fixed factors f are  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 p r o f i t function is tested which is transloq  in labor input prices and Cobb-Douglas in the prices of output and inputs and the quantities of fixed factors of production.  other  Rather than  using a s p e c i f i c a t i o n which u t i l i z e s share equations to correct for c o l l i n e a r i t y in the data, he estimates a single equation usinq least squares and cross-sectional data.  A number of c o e f f i c i e n t s either  f a i l to conform in sign to a p r i o r i s p e c i f i c a t i o n s or are insignificant.  ordinary  statistically  Mullineaux tentatively interprets these results as  - ?A -  e v i d e n c e of n o n - c o m p e t i t i v e b e h a v i o r , variables  i n the m o n o p o l i s t ' s  a r q u i n q t h a t output p r i c e s are not  profit function.  For m u l t i p r o d u c t f i r m s 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 o n s i s t e n t w i t h the h y p o t h e s i s that banks are not p r i c e t a k e r s i n any of the markets f o r t h e i r products and s e r v i c e s . Of c o u r s e , banks may o p e r a t e c o m p e t i t i v e l y f o r a subset of t h e i r p r o d u c t s , i n 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 . ( M u l l i n e a u x [ 1 9 7 8 ] , p. 263) The r e s u l t s may be a t t r i b u t a b l e t o annual average Mullineaux  being p o s s i b l y  poor p r o x i e s  i n t e r e s t r a t e s used by  f o r a c t u a l market p r i c e s .  They  c o u l d a l s o be caused by m u l t i c o l l i n e a r i t y a s s o c i a t e d w i t h i n s u f f i c i e n t price dispersion  i n the c r o s s - s e c t i o n a l  f u n c t i o n a l form such as the t r a n s l o q . number and s i z e of v a r i o u s  1 5  sample to e s t i m a t e a f l e x i b l e The f i x e d f a c t o r v a r i a b l e s ,  the  k i n d s of branches may be s u b j e c t to e r r o r ,  and the parameters are not r e s t r i c t e d t o ensure the p r o f i t f u n c t i o n  is  homogeneous of degree one i n p r i c e s .  is  c h a r a c t e r i z e d by i n c r e a s i n g  The e s t i m a t e d p r o f i t e q u a t i o n  r e t u r n s to s c a l e , but t h i s v i o l a t e s a  p r o p e r t y of the p r o f i t f u n c t i o n , u n l e s s  some i n p u t s are h e l d  In c o n c l u s i o n , t h e r e are s e v e r a l hypotheses, in  fixed.  g i v e n the l i t e r a t u r e  t h i s a r e a , which are of i n t e r e s t i n an econometric model of  financial firm.  the  These i n c l u d e output s e p a r a b i l i t y , n o n - j o i n t n e s s i n  i n p u 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 and o u t p u t s of the f i n a n c i a l f i r m .  We now t u r n t o t h i s  problem.  2.fr Outputs, Inputs, and the " C l a s s i f i c a t i o n Problem" Although  i t i s w e l l known t h a t f i n a n c i a l f i r m s  the  produce  inputs  - 25 -  heterogeneous and inputs.  outputs, there has been l i t t l e consensus on their outputs The outputs used by various researchers are:  total assets,  earning assets, loans, total deposits, demand deposits in d o l l a r  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 f i n a n c i a l firm as long as the measure i s consistent with the researcher's goal. The central questions in what we term the " c l a s s i f i c a t i o n 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 i s dual to the question "what units i s output measured in?"  One can be obtained from the other i f the necessary  conditions for producer equilibrium are s a t i s f i e d . posing the problem  Another way of  i s whether stock or flow variables measure the  relevant concept of bank output and input. Our approach to tackling the c l a s s i f i c a t i o n problem  i s to develop  complete user costs of balance sheet items for the f i n a n c i a l firm.  User  costs, or rental prices, of balance sheet items are derived in Chapter 3.  An input i s 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 c l a s s i f i c a t i o n and develops appropriate  - 26 -  p r i c e s on i n p u t s and o u t p u t s , but a l s o a l l o w s e x a m i n a t i o n  of key  monetary p o l i c y i n s t r u m e n t s such as r e s e r v e r e q u i r e m e n t s ,  and  r a t e s and  r e g u l a t i o n s such as d e p o s i t r a t e and  P r e v i o u s r e s e a r c h e r s have not modelled  2.5  Regulation and The  the Financial  loan r a t e c e i l i n g s .  explicitly  r e g u l a t i o n s when e s t i m a t i n g the f i n a n c i a l  interest  firm's  these i n s t r u m e n t s  and  technology.  Firm  a n a l y s i s of r e g u l a t i o n p r o v i d e s a primary m o t i v a t i o n f o r the  development of a theory of the f i n a n c i a l f i r m .  Typically, regulations  are not i n t e g r a t e d w i t h the theory of p r o d u c t i o n f o r a f i n a n c i a l Three types of r e g u l a t i o n on f i n a n c i a l  firm.  f i r m s are d i s t i n g u i s h e d .  F i r s t , t h e r e are r e g u l a t i o n s t h a t 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 s u b j e c t t o r e g u l a t i o n by the c e n t r a l bank, moral s u a s i o n 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 c o s t s by d e p o s i t i n s u r a n c e agencies are not e a s i l y q u a n t i f i a b l e .  The  second t y p e  of r e g u l a t i o n a f f e c t s f i x e d c o s t s 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 s h o r t run i n t h i s a n a l y s i s . the i n d u s t r y through  Examples are r e s t r i c t i o n s on e n t r y t o  requirements  number and e x t e n t of branches.  on s h a r e h o l d e r s , and  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 t h e  m a r g i n a l p r i c e to the f i r m of o f f e r i n g s e r v i c e s . include reserve requirements,  l i m i t s .on the  For banks, these c o s t s  d e p o s i t i n s u r a n c e and c e i l i n g s on  interest  rates. The  f o c u s i s on the t h i r d type of r e g u l a t i o n , f o r through  changes  i n m a r g i n a l p r i c e s , the e f f e c t s on l o a n and d e p o s i t c o m p o s i t i o n can analyzed.  be  I t p e r m i t s 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 firms.  It i s p o s s i b l e t o g e n e r a l i z e the model t o accomodate  -  the  second type of A model i s  regulation,  27 -  but t h a t  d e r i v e d where r e g u l a t o r y  p r i c e s or user c o s t s of the s e r v i c e s Empirically,  the model i s  F e d e r a l Reserve System.  of  is  not  the  focus.  c o s t s are part of loans  and  marginal  deposits.  formulated f o r hanks which are members of These r e g u l a t i o n s  focused upon are summarized,  as d i s c u s s e d  in the r e l e v a n t  not grounded  in a theory of p r o d u c t i o n , which makes comparative  analysis  literature.  the  In  existing  research these  are  static  difficult.  T h i s study  focuses on t h r e e types of f i n a n c i a l  regulation  entering user costs. S e c t i o n 2.5.1 d e a l s with r e s e r v e r e q u i r e m e n t s . Section 2.5.2  i s on i n t e r e s t r a t e c e i l i n g s  and s e c t i o n 2.5.3  is  concerned with d e p o s i t insurance premium r a t e s . 2.5.1 Reserve Requirements Nearly a l l d e p o s i t o r y i n s t i t u t i o n s must keep some minimum p o r t i o n of assets in cash or otherwise l i q u i d form.  These r e s e r v e  requirements  affect the marginal p r i c e s of v a r i o u s f i n a n c i a l commodities.  If  a  commercial bank is a member of the F e d e r a l Reserve System, i t must hold i t s reserves i n cash at the F e d e r a l Reserve Bank, or i n v a u l t The  traditional  a n a l y s i s of r e s e r v e requirements  as d e t e r m i n i n g the money s u p p l y .  This neglects  is  cash.  1 6  to view them s o l e l y  o t h e r e f f e c t s of  the  reserve requirement, notably i n acting as a tax on f i n a n c i a l f i r m s and their deposit h o l d e r s (Kane [1981] p. 357).  The e x i s t e n c e of r e q u i r e d  reserves on which no i n t e r e s t r e t u r n i s r e c e i v e d by the f i r m reduces revenue.  It may also reduce the i n t e r e s t r a t e payable to d e p o s i t o r s ,  pointed out in Laurent [ 1 9 8 1 ] .  The  as  neglect of the effect of the r e s e r v e  - 28 -  requirement tax on the user costs of deposits to which they apply, hence to the structure of bank technology, may  and  have severe e f f e c t s .  The  money supply depends on s u b s t i t u t a b i l i t y between f i n a n c i a l commodities, their r e l a t i v e 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  s p e c i f i e s uniform  reserve  requirements against transactions accounts for a l l depository  insti-  tutions (banks, savings banks, savings and loan associations, credit unions).  The term "transactions account" i s defined to include demand  deposits, NOW accounts, telephone transfers, ATS purpose of uniform  and share drafts.  The  reserve requirements i s to give the Federal Reserve  better control over the money supply by eliminating changes that occur because of s h i f t s of reserves among d i f f e r e n t 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 f i n a n c i a l firm would hold different amounts of reserves against i t s government s e c u r i t i e s , or against various kinds of loans.  The advantage  claimed  reserves  for this scheme i s that by judiciously varying the  (taxes) against different types of assets, the Federal Reserve could encourage banks to extend credit to p a r t i c u l a r sectors of the economy. The  user cost framework developed in Chapter 3 can handle this  in an analogous manner to reserves on deposits.  proposal  -  2.5.2  29  -  Interest Rate Ceilings  2.5.2.1 Deposit  Interest Rate C e i l i n g s  Financial firms have t y p i c a l l y faced price r e s t r i c t i o n s on both sides of their balance sheets.  These include deposit rate c e i l i n g s ,  including the prohibition on paying interest on demand deposits, and loan rate c e i l i n g s .  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 Insurance Corporation  (FDIC) for insured non-member banks.  rate structures set by the two agencies are i d e n t i c a l .  Deposit The maximum  In practice, the  Federal Reserve sets maximum rates and FDIC p o l i c i e s 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 r e s t r i c t i o n s are binding.  The deposit  rates  are fixed below the equilibrium value that would be set in an unregulated market. The t r a d i t i o n a l reason given for deposit bank competition failures.  rate c e i l i n g s i s that  for deposits allegedly leads to a high rate of bank  According  to this view, bank competition  for deposits led  individual banks i n the 1920's and early 1930's to offer higher interest rates i n order to maintain or increase individual share of the market. The banks were forced to rely on higher y i e l d i n g r i s k i e r assets to  - 30  o f f s e t incurred deposit costs. position.  Any  -  This placed the banks in a vulnerable  adverse economic developments, either national or l o c a l ,  would be s u f f i c i e n t 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 i n s t i t u t i o n s makes them allegedly more sound. The  analysis of interest rate c e i l i n q s i s t y p i c a l l y not couched in  a production generating  framework.  What i s required i s a model capable of  demands and supplies for loans and various deposits,  functions of their user costs. rates.  as  The user costs depend on interest  If interest rate c e i l i n g s are changed, i t i s possible to  determine the effect on f i n a n c i a l firm p r o f i t s , loans and This i s an objective of this  deposits.  research.  2.5.2.2. Loan Interest Rate Ceilings -Usury Laws As in the case of deposit rate c e i l i n g s , the analysis of the e f f e c t of usury laws requires the construction of a system where the response of loans and deposits can be calculated. Almost every state l i m i t s the interest rate that f i n a n c i a l tutions can charge on certain types of loans (Minqo [1977]). c e i l i n g s have been intended rates.  insti-  Loan rate  to protect consumers from paying high loan  Examples of state usury laws are interest rate c e i l i n g s on  business and a g r i c u l t u r a l loans, and mortgage loans on real property mobile homes.  Such c e i l i n g s when binding may  of loans td consumers.  act to r e s t r i c t the  or  supply  This implies that there develops a secondary  - 31 -  market with unregulated i n s t i t u t i o n s with high r i s k , high interest rate portfolios. The t r a d i t i o n a l argument has been that deposit in concert  rate c e i l i n g s act  with loan rate c e i l i n g s to reduce loan costs to borrowers.  This implies depositors are subsidizing borrowers.  It i s argued that  regulation of deposit rate c e i l i n g s in the period from 1966 intended  to 1979  to confer benefits on interests associated with the  was  thrift  industry, the housing industry, and construction unions. The underlying regulatory strategy attempted to c a r t e l i z e competition for household savings deposits to assure a substantial flow of low-cost funds to deposit i n s t i t u t i o n s (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 [ 1 9 8 1 ] , p. 363] Elsewhere Kane thrift  [1980]  argues that the re-regulation allowed banks and  i n s t i t u t i o n s to discriminate e f f e c t i v e l y between i n t e r e s t -  sensitive and i n t e r e s t - i n s e n s i t i v e depositors.  The marginal  penalty  that interest rate c e i l i n g s imposed f e l l rapidly with depositor wealth and sophistication.  It i s further argued that the burden of  interest rate c e i l i n g s f a l l s p a r t i c u l a r l y on the young, the old, and poor whose adaptive efficiency to f i n a n c i a l change i s inherently The Depository of 1980 permits NOW  Institutions Deregulation  the  low.  and Monetary Control Act  accounts nationwide after a nine-month waiting  period, provides for a six-year phase-out of interest c e i l i n g s on time and savings accounts, and overrides state imposed usury c e i l i n g s on mortgages, a g r i c u l t u r a l and business loans.  It also eliminates  state r e s t r i c t i o n s on the rate or amount of interest that may 17 deposits, or accounts, at depository  institutions.  any  be paid on  - 32 -  2.5.3  Federal Deposit Insurance Corporation Premium Rates The remaining user cost item examined i s the premium rate for  deposit  insurance.  The FDIC insures, e f f e c t i v e January 1, 1982,  deposits of i t s member commercial commercial banks to a maximum of $100,000. The FDIC i s financed by annual insurance banks.  premia paid by i t s member  The premium rate i s thus part of the user cost of deposits.  statute, the premium for each bank i s set at 1/12 of 1 percent t o t a l , not only insured, deposits.  By  of i t s  Out of this premium income the FDIC  pays i t s operating expenses, makes an assignment of funds to i t s reserves, and returns the remainder to i t s member banks on a pro rata basis.  In 1977, a year representative of recent experience, t h i s  premium reimbursement reduced the net assessment to 1/27 of one percent.  18  It i s argued by Buser, Chen and Kane [1978] that the FDIC deliberately sets i t s e x p l i c i t insurance  premium rate below an  a c t u a r i a l l y f a i r market rate to entice state-chartered non-member banks to submit themselves voluntarily to FDIC regulatory dominion. control excess demand for insurance  To  service, or expanded risk-taking,  the FDIC i s forced to develop an implicit price structure (Merton [1977]).  FDIC entry regulation and periodic examination of individual  banks balance sheet r a t i o s function i n tandem to maintain charter and to control the moral hazard inherent in insurance.  value  Buser, Chen, and  Kane [1978] argue that the FDIC currently employs a pro-rated  structure  of i m p l i c i t premia i n the form of regulatory interference which varies  - 33 -  with a bank's p o r t f o l i o r i s k .  Scott and Mayer [1979] suggest that a  risk-rated structure of premia i s necessary to offset a s t r u c t u r a l incentive towards inordinate leverage. considered  The  i m p l i c i t premia are not  here, but user costs are developed which include as arguments  the e x p l i c i t deposit insurance  premium rates.  Changes in these rates  affect r e l a t i v e prices, and hence the quantities of loans and  deposits.  It i s thus possible to analyze quantitatively the effect of deposit insurance  premia given a specified amount of coverage.  19  2.6 Concluding Remarks The cost function approach suffers from the major l i m i t a t i o n that outputs are assumed to be exogenous.  Although i t i s well known that  f i n a n c i a l firms produce heterogeneous outputs, there i s l i t t l e consensus on what goods constitute their outputs and various researchers  inputs.  The outputs used by  include t o t a l assets, earning assets, t o t a l  deposits, demand deposits, the number of deposit and loan accounts, gross operating  income and combinations of these measures.  Although i t  i s not necessary for the application of a cost function, researchers i n the banking area have t y p i c a l l y assumed either that heterogeneous outputs can be aggregated, or a non-joint technology obtains.  These  assumptions imply r e s t r i c t i o n s on the variable cost function that can  be  tested. Another approach to estimating the f i n a n c i a l firm technology involves the p r o f i t function.  Estimation of this p r o f i t function with  t y p i c a l l y c o l l i n e a r prices as arguments may estimates.  The appropriate  lead to imprecise  s p e c i f i c a t i o n i s to include supply  parameter and  - 34 -  demand equations for outputs and inputs respectively. from not including demand and supply  The i n s t a b i l i t y  functions appears to affect the  results in Mullineaux [1978]. An advantage of assuming p r o f i t maximization i s that i t can accomodate imperfect  competition.  Most studies on the f i n a n c i a l firm  assume that the firm operates in a competitive exceptions  environment.  Three  are Klein [1971], Mullineaux [1978] and Sealey [1980].  environment i s largely determined by bank regulation.  This  Klein s p e c i f i e s  in his t h e o r e t i c a l model that private s e c u r i t i e s , loans, are in imperfectly e l a s t i c supply to the individual bank. deposit markets are not perfectly competitive.  Sealey argues that  Mullineaux also finds  evidence against the assumption of price taking behavior.  This 20  indicates that the hypothesis of competitive  markets should be tested.  Financial firms are subject to a myriad of regulations. to come to some tentative  In order  evaluation of the impact of such regulations,  a theory of the f i n a n c i a l firm i s required.  Most studies that have  examined f i n a n c i a l firm regulations, such as reserve requirements, deposit rate c e i l i n g s and deposit rate insurance institutional detail.  have concentrated  on  There has been l i t t l e analysis on t h e i r effects  on bank substitution, transformation  and production.  - 35 NOTES While here user costs for various loans constructed and the allocation of funds between considered, in the empirical s p e c i f i c a t i o n t h i s loans are aggregated. This i s both to preserve to focus on monetary commodities such as demand A  2  and investments are various assets can be i s not performed and degrees of freedom and and time deposits.  See Klein, [1971], Hart and Oaffe [1974], Mason [1979] and Sealey  [1980]. 3  In Chapter 8 a model of the f i n a n c i a l firm i s developed which tests for imperfect competition. See Schweiger and McGee [1961], Gramley [1962], Benston [1965], B e l l and Murphy [1968] and Mullineaux [1978] for results on economies of scale. 4  See Pesek [1970], Carleton and Bryan [1971], Towey [1974], Greenbaum, A l i and Merris [1976]. 5  See Klein [1971], Towey [1974], Adar, Agmon and Orgler [1975], Sealey and Lindley [1977], and Mingo and Wolkowitz [1977]. 6  With 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 i s to maximize expected u t i l i t y , or equivalently the rate of return on equity. Sealey [1980] also assumes that the f i n a n c i a l intermediary maximizes expected u t i l i t y of p r o f i t , but has a general u t i l i t y function in p r o f i t s , with f i r s t derivative p o s i t i v e . The second derivative depends upon risk preferences. 7  See Alhadeff [1954], Horvitz [1963], Schweiger and McGee [1961], Gramley [1962], Grebler and Brigham [1963], Greenbaum [1967], Powers [1969], Brigham and P e t t i t [1970], and Schweitzer [1972]. 8  9  See Alhadeff [1954], Schweiger  and McGee [1961] and Horvitz  [1963]. S e e Gramley [1962], Grebler and Brigham [1963], Brigham and P e t t i t [1970] and Murray and White [1981]. 10  n  A d a r , Agmon and Orgler [1975, p. 239].  12  Adar, Agman and Orgler [1975^ p. 240].  13  One point that should be mentioned i s that the assumption of competitive price taking behavior is' not e s s e n t i a l 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. Rather than using share equations to deal with collinearity problems, Mullineaux [1978], enters the average wage of a l l 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. 15  Federal 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. 16  See "Depository Institutions Deregulation and Monetary Control Act of 1980" by the Federal Reserve Bank of Boston. 17  I n 1980 the net annual premium was 1/30th of 1 percent of a l l deposits for deposit insurance. 1 8  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. 20  See Chapter 8.  - 37 -  CHAPTER 3 USER COST DERIVATION FOR FINANCIAL FIRMS 3.1  User Costs for Assets and  Liabilities  The user cost of a f i n a n c i a l good i s defined as the net effective cost of holding one unit of services per time period.  In the context  a consumer decision model Diewert [1974-], Donovan [1978] and [1978, 1981]  Barnett  have derived user cost formulae for interest bearing  non-interest bearing monetary assets.  of  and  These models are based on the  theory of intertemporal consumer demand of Irving Fisher [1930], and formulated for  in discrete time.  This chapter derives complete user costs  balance sheet items held by f i n a n c i a l i n s t i t u t i o n s in the context  of  an intertemporal producer decision model. Time i s decomposed into discrete periods, where the periods  are  chosen to be s u f f i c i e n t l y short so that variations in prices within the period can be neglected. constant  Interest rates, prices, and wages remain  within the i n t e r i o r of each period, but can change d i s c r e t e l y  at the boundaries of periods.  1  A l l p o r t f o l i o transactions are assumed to take place at the boundaries between intervals.  Each f i n a n c i a l firm holds an  consisting of stocks of various kinds of f i n a n c i a l assets, and c a p i t a l during each discrete time period.  inventory liabilities  The user cost i s 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 f i n a n c i a l firm no less importantly than the cost of l a b o r .  2  - 38 -  Consider for  f i r s t the i t h asset.  An interpretation of the user cost  the services of one unit of the i t h asset during period t i s to view  the banker as purchasing  the asset at the beginning  then s e l l i n g i t at the beginning to himself.  of period t, and  of the following period, possibly  Over one period, one dollar held i n asset i produces  services earning an interest rate r ^ . dollar of asset i i s s^. * 1  stand-by charges.  3  The service charge rate per  This rate includes late loan payments and  Capital gains or losses are denoted by c ^ . The 5  default rate 6^ provides for loan losses per dollar of asset.  This  includes assets marked down or written o f f , interest payments forgiven, and c o l l e c t i o n costs. The f i n a n c i a l firm purchases one unit of asset i during the current period, the cost of which i s one d o l l a r . at the beginning  I f a l l returns arise  of the following period, the present value of the y i e l d  per dollar of the asset one period hence i s (1 + r ^ + c^ + s. - 6^)/ (1 + R).  Here R i s the common discount rate applied on a l l assets and  liabilities.  The user cost of asset i i s the difference between the  current value of one dollar of the asset, and the present  value of the  return one period hence, or _ u. = 1 -  (1 + r. + c. + s. - 6.) * — 1  ( 1  R )  i = 1,...,N  r  (3.1)  An alternative interpretation of the user cost i s the net, e f f e c t i v e 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 i s an input, while i f i t has a negative user cost i t i s an output during the period. i s a c l a s s i f y i n g rule enabling the inputs and outputs guished.  This  to be d i s t i n -  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 j t h 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  i n 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 f i n a n c i a l firm pays interest. Let r.. be the interest payable by the f i n a n c i a l firm. A remaining  cost i s 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 i t s t o t a l deposits.  From t h i s premium income the  corporation f i r s t pays i t s operating expenses.  Two-fifths of the  - 40  remainder i s then  added t o t h e  premium i s c r e d i t e d p r o  -  insurance  r a t a to the  paid  d o l l a r of d e p o s i t  at the b e g i n n i n g  period  can  be  of  f i r m d o e s not  Let  the  (1-kj) per  dollar  (1-kj).  dollar  requirement  credit  Let  the  Assume t h a t t h e premium i s As  an e x a m p l e ,  the  requirements, total  the  so  deposit  r a t e f o r the j t h type  of deposit  r e c e i v e d by  i s a v a i l a b l e f o r usage.  i n cash  user  of  the  balance.  The  the  financial  remaining  6  deposit. For firm,  kj i s  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  cost of deposit  f o r u s a g e by  the  j i s b a s e d on t h e n e t  financial  A d e p o s i t o r on w i t h d r a w a l  ( 1 - k j ) o f c l a i m on reserves.  At  the  and  net  i s discounted  cost  insurance  - kj + r j - S J + The  h o l d i n g one  financial  the beginning  interest  (1  this  in vault  8  The  is  apply  the  f o l l o w i n g year.  to reserve  gain c o n t r o l over  of the j t h type  transferred  per  bj.  of  t h e c a s e o f member b a n k s o f t h e F e d e r a l R e s e r v e S y s t e m .  each, d o l l a r  cash.  reserve  balance  year.  are u s u a l l y subject  financial  Consider  be  i n the  following period.  s e l e c t e d t o be one  Deposits  k j be  the  The  i n s u r e d b a n k s , who  t o w a r d payment o f premium p a y m e n t s due premium r a t e per  fund.  user  cost  of the  premiums and  f i r m d u r i n q the c u r r e n t  r e c e i v e s one  firm  amount a v a i l a b l e  and  dollar,  k j from  period,  comprising  required  f o l l o w i n g p e r i o d , the  firm  pays  r e c e i v e s s e r v i c e charge f e e s .  to the c u r r e n t p e r i o d .  or  In present  This  value terms i t  bj)/(1+R).  i s the net  u n i t of d e p o s i t .  So  e f f e c t i v e c o s t of funds per on  the  net d e p o s i t  f o r the  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 ) .  period  of  bank  + (3.3)  - 41 -  or,  _ ii U  (1-k. + r . - s. + -  j "  _  (1_k U  ) +  J  J  V  b.)  J  J  1 + R  - (1+R)(1-k.) + (1-k. + r. - s. + b.) J  = -1 +  1 + R  J  J  J  (1+r. + b. + Rk. - s.) 1\ J  1  J  j=1,...,N  1  R  (3.4)  2  where there are N2 types of deposit and R i s the discount rate.  The  term Rkj has the interpretation of being the cost imposed by the reserve requirement.  This i s equivalent to the imposition of a tax by  the Federal Reserve for one period, for the bank i s unable to use  the  reserve requirement in i t s loan p o r t f o l i o . If the deposit has a positive user cost in a period i t i s an input, and i f i t has a negative user cost i t i s an output.  With  movements in interest rates and other determinants, a deposit can  be  either an input or output for the f i n a n c i a l firm. T r a d i t i o n a l l y , there have been two j u s t i f i c a t i o n s for considering deposit services as outputs of the f i n a n c i a l f i r m .  F i r s t , since the  services which are performed for deposit customers benefit the l a t t e r , i t has been argued (Benston [1965], B e l l and Murphy [1968], Longbrake [1974]) that possibly these services constitute outputs.  Deposit  customers derive benefits from the services they receive, and f i n a n c i a l firm produces these services. deposit services are necessarily outputs.  the  This does not imply that 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 a c t i v i t y , when one i s concerned with the macroeconomic effects of the banking system [1974]).  (Pesek [1970], Towey  This does not necessarily j u s t i f y making deposits the  microeconomic  output of the f i n a n c i a l firm or industry.  9  Deposits in f i n a n c i a l 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 i s applicable not only to deposits, but to any kind of l i a b i l i t y held by the f i n a n c i a l 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 i s necessary to estimate  expectations of the producer about asset and c a p i t a l prices in the next period, given the capital gains term in (3.1). are  These expected prices  generally unobservable, and thus analysts d i f f e r widely on how to  estimate them.  One approach i s to assume that producers have perfect  anticipations (Christensen and 3orgenson  [1969, 1970]).  Another  approach i s to assume s t a t i c expectations. Producers expect current  - 43 -  prices to prevail in the following period (Woodland [1972, 1975]).  A  10  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  3.2.2  econometric  modelling.  The Discount Rate The user cost formulae in the previous  discount  rate.  section both involve a  Usually i t i s argued that i f the firm i s a net borrower,  then R should be the marginal cost of borrowing an additional d o l l a r for one period, while i f the firm i s a net lender, R should  be the  one-  period interest rate i t receives on i t s last loan (Diewert [1980]). practice, researchers  In  have taken R to be either an internal rate of  return (Oorgenson and G r i l i c h e s [1967], Christensen 1970]) or an exogenous bond rate that may  or may  under consideration (Diewert [1980] p. 477).  and Oorgenson [1969,  not apply to the firm  Neither of these last  two  alternatives appears completely satisfactory from an a p r i o r i point of view.  3.2.3  Depreciation Rates User cost formulae for the services of one unit of c a p i t a l during  one  period usually involve a depreciation rate.  This depreciation rate  i s related to the f i n i t e length of l i f e of the c a p i t a l stock. function of physical deterioration, usage and It  vintage.  It i s a  11  i s assumed that f i n a n c i a l assets and deposits do not  depreciate or deteriorate.  Donovan [1978] considers  money due to a positive expected i n f l a t i o n rate.  "depreciation" of  He concludes  that the  - 44  user cost of money is unaffected  -  by that kind of depreciation.  Anticipated i n f l a t i o n should be taken into account by the c a p i t a l gains term in the user cost formulae.  (anticipated)  Since the anticipated  c a p i t a l gains term accounts for nominal price changes in each f i n a n c i a l 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 i s essentialy i n stantaneous so that we can ignore stock adjustment problems. See Samuelson [1947]. These assumptions follow Hicks [1946] p. 122, pp. 335-337. Pesek [1970] and Sealey and Lindley [1977] recognize that f i nancial i n s t i t u t i o n s 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. 2  Barnett [1978, 1980] assumed interest was paid at the beginning of the following period when deriving the user cost of interest-bearing money. 3  "See  Pesek [1970] p.  371.  C a p i t a l gains are due to discrete jumps in interest rates at the boundaries of i n t e r v a l s . Capital gains would be negative i f i n t e r est rates rose, positive i f interest rates f e l l . 5  Nearly a l l f i n a n c i a l firms must keep some minimum portion of assets in cash or otherwise l i q u i d form. These reserve requirements are generally based upon the types of deposit l i a b i l i t i e s the f i n a n c i a l firm has. If a commercial bank i s a member of the Federal Reserve System, i t must hold i t s reserves in cash at the Federal Reserve Bank, or in vault cash. 6  7 Many customers and borrowers are subject to minimum and compensatory balance requirements, respectively. In their e f f e c t s 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 f i n a n c i a l firm i s 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]). W i t h the recent upsurge of world-wide i n f l a t i o n and interest rates, i t has become more d i f f i c u l t to ignore c a p i t a l gains and losses. 10  - 46 -  ^ C a p i t a l stocks c o n s t r u c t e d on the b a s i s of d i f f e r e n t d e p r e c i a t i o n assumptions can d i f f e r c o n s i d e r a b l y . See examples t a b u l a t e d in T i c e [1967] and Creamer [1972]. 1 2  See  Diewert  [1974b]  p.  510.  1 3  The caveat i s that i f the d i s c o u n t r i s e s due to i n f l a t i o n a r y e x p e c t a t i o n s , then the user cost of monetary s e r v i c e s 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  f i n a n c i a l i n s t i t u t i o n s , with e x p l i c i t attention given to regulatory constraints on operations.  We develop a model of producer  behavior  where labor demands, physical c a p i t a l demands and asset and l i a b i l i t y holding decisions are simultaneously  determined.  The s p e c i f i c a t i o n  d i f f e r s from previous neoclassical models (Benston [1965], B e l l and Murphy [1968], Klein [1971], Towey [1974], Adar, Agmon and Orgler [1975], Mingo and Wolkowitz [1977] and Mullineaux based on a theory of intertemporal production  [1978]) in that i t i s  introduced by Hicks [1946]  and u t i l i z e s the user costs derived in Chapter 3 above.  Our model i s  unique in that i t considers regulatory controls through their effect on r e l a t i v e user costs.  We employ the duality between the production  p o s s i b i l i t y set and p r o f i t function to derive comparative s t a t i c s y i e l d ing, testable predictions, and to obtain the functional forms for the estimating  fr.2  equations.  An Intertemporal Production Model of the Individual Financial Firm Intertemporal  or dynamic optimization problems are d i s t i n g u i s h -  able from s t a t i c 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 problems.  researchers have considered  s t a t i c optimization  Bell and Murphy [1968] derive a s t a t i c cost  model, and Mullineaux  minimization  [1978] a s t a t i c p r o f i t maximization model.  plays an essential role in the f i n a n c i a l firm's production  Time  process, and  an intertemporal model i s needed, p a r t i c u l a r l y for analyzing asset and l i a b i l i t y holding decisions.  Each f i n a n c i a l firm holds an inventory  consisting of stocks of various f i n a n c i a l 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  that extends to period t+1.  of period t  The plan consists of a l i s t of input  demands and output supplies for the period.  Since the model i s in  discrete time, a structure of assumptions i s required regarding the timing of interest rate, wage rate and price changes, payments and of p o r t f o l i o transactions. (1)  These are:  Interest rates, prices and wages remain constant  within the  i n t e r i o r of each period, but can change d i s c r e t e l y at the boundaries of periods. (2)  A l l p o r t f o l i o transactions are assumed to take place at the boundaries between i n t e r v a l s .  (3)  The producer i s assumed to s e l l a l l f i n a n c i a l 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 i n t e r i o r of each period and the new issue interest rate equals  the seasoned r a t e .  5  - 49 -  (4)  Interest and service fees are paid at the beginning following period.  (5)  of the  6  Insurance premiums are paid at the beginning  of the follow-  ing period. The model i s short-run periods.  in that we consider only two time  With active secondary markets in each period, the  7  financial  firm can review i t s past decisions in light of the current market situation and alter i t s input demands and output supplies accordingly. Although we s h a l l not f i x the time i n t e r v a l in the theoretical model, i t a  could be set as short as one day. choose the input-output production period.  The f i n a n c i a l firm i s assumed to  combination which maximizes p r o f i t during  The assumption of p r o f i t maximizing behavior  l i e s the models of Pesek [1970], Towey [1974], Adar, Agmon and [1975], Greenbaum, A l i , and Merris [1977], Sealey Mingo and Wolkowitz [1977] and Mullineaux  [1978].  the under-  Orgler  and Lindley [1977], 9  Assume that producers take prices, wage rates, and user costs as given, and optimize with respect to quantity variables they c o n t r o l . The producer's p r o f i t maximization model for period t may follows, with the dot denoting ir =  max  - {u*y  - V»z + w^x  T J an N  be written as  an inner product : Cx/y,z)eS  x'/y/z, _> 0, w » 0, v~C 0}  "x,7,z~ with  1 0  (4.1)  1  + N  2  dimensional  vector of user costs for the f i n a n c i a l  firm's balance sheet holdings during period t.  The f i r s t N i  -  50  user costs w i l l be for the firm.  -  types of assets held by the  The last N 2 user costs w i l l be for the N 2 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 i s an Hi dimensional  vector representing the assets held by the  f i n a n c i a l 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. a non-negative Ni+ dimensional  z  vector of period t outputs which  are not balance sheet holdings such as safe-deposit boxes. S  the financial firm production p o s s i b i l i t y set, which i s 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 negat i v e 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 follows,  of Debreu as  - 51 -  -  max  {u«y +• v z  + wx  : (x,y,z)e  > • • •  ^ =  with  u  ),  '  S,  y. > 0 i f  J  l  z ^> 0, x <_ 0,  u. < 0 and l  < 0 i f u. > 0, v » 0, w » 0, u » 0} (4.2)  T T ( U , V , W )  a non-negative Nj_ + N2 d i m e n s i o n a l v e c t o r of transformed user c o s t s f o r the f i n a n c i a l f i r m s b a l a n c e sheet h o l d i n g s period  w  t.  a non-negative N3 d i m e n s i o n a l v e c t o r of p e r i o d t  p r i c e s for variable inputs v  a non-negative  (e.g.  wage r a t e s )  (purchase)  (w = w).  dimensional v e c t o r of p e r i o d t p r i c e s  outputs which are not balance sheet h o l d i n q s  y  during  for  (v = v ) .  an Ni + N2 dimensional v e c t o r r e p r e s e n t i n g balance sheet ings.  Outputs are measured p o s i t i v e l y  Inputs are measured n e g a t i v e l y determined,  (y > 0 i f  (y <^ 0 i f u >> 0 ) .  the qoods are renumbered so that  u «  hold-  0).  Once so  the f i r s t  Hi  components of the v e c t o r y r e p r e s e n t a s s e t s held by the financial  f i r m , while the l a s t N2 components r e p r e s e n t the  liabilities  held by the firm d u r i n g p e r i o d  t.  a n o n - p o s i t i v e N3 d i m e n s i o n a l v e c t o r of p e r i o d t  (x = - x ) .  inputs  - 52 -  z  a non-negative are  N  dimensional  4  not balance sheet  v e c t o r of  holdings  such as  p e r i o d t outputs safe-deposit  which  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  assumed to be convex, c l o s e d , non-empty,  set,  which  and c o n t a i n s  is the 0  vector. Equation are  (4.2)  is  the p r o d u c e r ' s  profit  a f u n c t i o n of the p r i c e v e c t o r  function, IT.  (u,v,w)  Given the p r o d u c t i o n p o s s i b i l i t i e s d e f i n e d by (4.2) (i)  ir i s  will  satisfy  non-negative  if  dimensional 0 vector, (ii)  IT is  input  non-decreasing  prices,  (iv)  TT i s  which we denote by n ( u , v , w ) . set  the f o l l o w i n g  (u,v,w) (ii)  i n output a (proper)  »  0  ir i s  S,  the p r o f i t  regularity  + N  N  + N  2  (iii)  TT i s  function  conditions:  + rV  3  non-decreasing  prices,  Maximum p r o f i t s  t  h  e  N  1  +  i n output  N  2  +  prices,  non-increasing  convex f u n c t i o n and (v)  TT i s  in  homogen-  12 eous of degree one i n  input  and output  prices.  We are now i n a p o s i t i o n to s t a t e to d e r i v e f u n c t i o n a l output are fies  supply  given  forms f o r  equations  a functional  systems of  consistent  input  which w i l l  enable  demand e q u a t i o n s ,  with p r o f i t m a x i m i z a t i o n .  form for a p r o f i t  the above f i v e c o n d i t i o n s  a result  and i s ,  function  TT(U,V,W)  in a d d i t i o n ,  r e s p e c t to output  (0,0,0).  and input p r i c e s  which  =  y  .( %V) u  at the p o i n t  i =  1,...,N  satis-  differentiable  (u,v,w  Then we have,  9Tr(u%!w*)  and  Suppose we  * * * with  1 +  N  2  us  )  »  - 53 -  (  # * * -±^= J  zAu%W)  j = 1,...,  (4.3)  N  J  and  * ** (u,v,w)  , * * *\ = x (u,v,w )  k = 1,...,N  k  where y^(u,v,w ) i s the profit maximizing amount of output i (of input i  *• * *  * * *  i f y.(u,v,w ) < 0), z.(u,v,w ) i s the p r o f i t maximizing amount of output # * * j,  and x (u,v,w ) i s the p r o f i t maximizing amount of input k given posik  * * * t i v e prices (u,v,w ).  This result i s due to Hotelling [1932, p. 594].  P r o f i t 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 i n  our model of the f i n a n c i a l firm given exogenous prices and user costs. Hotelling's lemma i s useful from an econometric point of view since i t permits the derivation of functional forms for demand and supply functions consistent a functional form for  with p r o f i t maximization simply by choosing  and d i f f e r e n t i a t i n g i t with respect  output prices, including user costs.  to input and  Also, t h i s lemma and duality  theory permit the derivation of comparative static  results.  1  Using the duality between the production p o s s i b i l i t i e s set and the p r o f i t function, we know the p r o f i t function.  function i s a proper convex  Let p = (p ,.. - ,P ) = (u ,...,u 1  N  1  N  + N  , v ,...,v 1  N  , w^...^ )  -  denote the v e c t o r of p o s i t i v e outputs  and i n p u t s ,  transformed user c o s t s  where N = Ni + N  Denote the N by N matrix of  S*,  a twice c o n t i n u o u s l y then TT i s  of ir i s  + N 3 + Mi+.  semi-definite  derivatives  2  a positive  2  and only  for a l l p £ S * .  for  Then u(u,v,w) = i r ( p ) .  [ 3 TT( p) / 9p^3p,. ],  a convex f u n c t i o n over S i f  positive  and prices  i,j  That  with  = 1,...,N.  d i f f e r e n t i a b l e f u n c t i o n over  [3 ir(p)/3p^3pj ] is  this  2  second order p a r t i a l  r e s p e c t to p of the f u n c t i o n TT by TT i s  54 -  the convex the Hessian  is  if  matrix  (4.4)  1 6  implies, [ 8 T r ( p ) / 8 p . 8 p ] >_ 0  for i = 1 , . . . , N .  2  i  Alternatively,  _> 0  for  i = 1,.. . ,N 1 + N  3 ir(u,v,w)/3w.3w. >_ 0  for  j = 1,...,N  2  2  J  3 3v  3 TT(U,V,W)/3V 2  Using  (4.5)  s i n c e p = (u,v,w)  3 ir(u,v,w)/3u.3u.  (4.3)  > 0  for k =  1,'...^^  which we o b t a i n e d by a p p l y i n g H o t e l l i n q ' s  convexity conditions  (4.6)  we have the f o l l o w i n g  2  (4.6)  3  .  lemma and the  comparative  static  results,  3y.(u,v,w 3u  ) —  1  y. _> 0 > 0 if  i  (i.e.  if  1  y  L  u. < 0)  i = 1 , . . . , N +N :  < 0  (i.e.  if  u.  2  (4.7)  1  >  Q  )  * * *)  3z.(u,v,w — — 5 3v.  > 0 where z . i s  -  j  an output  j = 1,...,N 3  (i.e.  z . > 0)  J -  If  set  if  semi-definite matrix  1 5  (4.8)  - 55 -  3 w.  2^ 0 where x,  is  an input  ( i . e . x.  < 0)  (4.9)  k k = 1  Equation  (4.7)  summarizes  item with r e s p e c t to a change item i  is  user c o s t negative), supply  the response of  in i t s  own user c o s t .  an o u t p u t , or has a n e g a t i v e user c o s t , increases  (i.e.  and hence i s  E q u a t i o n (4.8)  Similarly,  (4.9)  demand f o r that  transformed  becomes more  the balance sheet and i t s  item do not  if  user  if  the p r i c e of  input by the f i r m does not  We now t u r n our a t t e n t i o n to c r o s s  cost  increases  f i r m does not d e c r e a s e . input k i n c r e a s e s ,  the  increase. e f f e c t s , or response of  supply or input demand when the p r i c e of another output or changes.  item  i n c r e a s e , or the  the p r i c e of output j  by the f i n a n c i a l  i m p l i e s that  sheet  rise.  implies that  then the supply of output j  If  an i n p u t ,  h o l d i n g s of the balance sheet  demand f o r the input does not  balance  sheet  item i do not d e c r e a s e , and the  of the i t h output does not d e c l i n e .  increases,  If  and i t s  the untransformed user cost  h o l d i n g s of balance sheet  has a p o s i t i v e user c o s t ,  the i t h balance  output  input  We begin by d e f i n i n g the e l a s t i c i t y of t r a n s f o r m a t i o n  between  commodities m and n as  T f ( p * ) 3 T r ( p * ) / 3 p 3p 2  n  (4.10)  [3TT(p*)/3p ][3TT(p*)/3p ] m  n  - 56 -  * * * ). R e c a l l p* = (u,v,w  I f the mth p r i c e c o r r e s p o n d s  n o r m a l i z a t i o n of 3 y . ( p * ) / 3 p , m  if  y . >_ 0 or chanqe  the chanqe i n the supply of the i t h output  i n demand f o r the i t h  input  pect to a chanqe i n the nth p r i c e or user c o s t . corresponds change price.  to u. then n is a 1 mn  i f y . < 0 with  res-  I f the n t h p r i c e  to v. then n i s a normalization of 3z.(p*)/3p o r the J mn J n  i n the supply of output j w i t h  respect to a chanqe i n t h e nth  the mth p r i c e corresponds to w, then n i s a normalizak mn  If  t i o n of 3 x ( p * ) / 3 p , the change i n demand f o r the kth input with k  n  to a change i n the nth p r i c e . that n is mn  invariant  Assuming tions ted at  The n o r m a l i z a t i o n s have been chosen so  to s c a l e changes in u n i t s  * * * T T ( U , V , W  above, T T ( * ) p  )  =  respect  Tr(p*)  > o, the f i r s t  satisfies  and so that  the f i v e  n = n •— •> mn nm  regularity  condi-  order p a r t i a l d e r i v a t i v e s of rr e v a l u a -  at p* are n o n - z e r o , and that * i s  twice c o n t i n u o u s l y  differentiable  p*:  (i)  the symmetric e l a s t i c i t y of t r a n s f o r m a t i o n matrix  [n L  positive  s e m i - d e f i n i t e of rank at most e q u a l  particular n  1, mn• mn J  is  to N - l ; i n  > 0 f o r every m, mm — ' J  (4.11)  N (ii)  f o r every m,  T n 9 = 0 mn n n=1  where the nth commodity r a t i o of r e l a t i v e e x p e n d i t u r e to v a r i a b l e 9  n  i s d e f i n e d as  profit  - 57 -  p*[aTr(p*)/9p  n  n  ]/ir(p*)  M  T9  for n = 1 , . . . , N . Also  n= I  commodity n i s an output  but 8  n  =1,  and  9  n  < 0 i f commoditv n i s an i n p u t .  The f i n a n c i a l firm has many inputs and outputs, tive s t a t i c s for cross-effects are indeterminate. however, does provide an addinq up property  18  0  N  if  17  so the compara-  The above theorem,  for the c r o s s - e f f e c t s . If  we consider input k, i t s commodity share of value added 6^ i s negative. We know from (4.11(1)) that n  k)<  _> 0, so n e _< 0. k|<  k  Now using (4.11(ii)) we obtain N ^, m = l^km^m  +  ^kk^k ~ ^  m*k  which implies  N  ^ kmm= " V k ^ n  e  0  (4.12)  m*1  Similarly for output j , N  I  n  4  e m  m  = -n..e.  <  o.  rn*1  Although the comparative s t a t i c s for cross e f f e c t s are indeterminate, we can test to determine whether the above adding up properties and symmetry conditions are s a t i s f i e d in an econometric estimation of  - 58 -  t h e model.  For f u r t h e r a n a l y s i s  e m p i r i c a l point  of c r o s s e f f e c t s we have to examine  estimates.  Above we developed a model of f i n a n c i a l f i r m b e h a v i o r simultaneously liability  determines  input demands,  holding decisions.  an i n d i v i d u a l balance sheet user cost.  Equation  output  supplies,  (4.7) summarized  Now we c o n s i d e r how changes i n the components  d e c i s i o n to hold that item. i n response  and asset  of the user firm's  We are e s p e c i a l l y i n t e r e s t e d i n requirements,  of  i n i t s own  item a f f e c t the f i n a n c i a l  t o a change i n r e g u l a t o r y  and  the response  item w i t h r e s p e c t to a change  c o s t of a p a r t i c u l a r balance sheet  that  such as  adjustments reserve  r e q u i r e m e n t s and FDIC i n s u r a n c e premium r a t e s . In Chapter 3 we d e r i v e d user c o s t s  f o r b a l a n c e sheet  items h e l d  by f i n a n c i a l f i r m s i n the c o n t e x t of an i n t e r t e m p o r a l p r o d u c e r model.  The user c o s t of h o l d i n g asset  a f u n c t i o n of r^,  decision  i d u r i n g p e r i o d t was found t o be  the i n t e r e s t payable t o 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 g a i n s or l o s s e s d u r i n g p e r i o d t on a s s e t  i , s^,  the s e r v i c e charge r a t e t h a t an average d o l l a r of a s s e t  y i e l d s t o the f i n a n c i a l f i r m , 6.,  the p r o p o r t i o n of l o a n s e x p e c t e d to  d e f a u l t d u r i n g p e r i o d t , and R the d i s c o u n t Recall  r a t e used by the  firm.  (3.1), — i u  =  . 1  {1 + r. + c, + s. +• 6.} i i l i (TTD  = u . ( r . , c . , s , 6., l l l i l  R).  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 t h i n d i c a t e d s i g n s ,  i  59 -  9u /3r. = 3u./3c. = 3u./3s. = -9u./36. = -1/(1 i  3u./3R  = (1  R)"^[1  +  +  = (1 + R)" [1  r  t +  c  .  +  +  s. - 6.]  R) < 0  (^. ) 13  - u.l  1  with 3Uj./3R > 0 unless u^ > 1, implying a period user cost exceeding 100 per cent. i s positive,  The transformed user cost of asset i , u^, equals u. i f u. and equals -u^ i f  i  u  u  u. > 0  = i _  i  i s negative, or  i  i = 1,...,Ni.  J  f  -u^  u^ < 0  Using t h i s d e f i n i t i o n and ( 4 . 1 3 ) we obtain the following  < 3u /3r 1  1  u. > 0  5 0  if  {_ Uj  < 3u./3c. > 0  if  1  0  > 0  i  >  0  u. > 0 {_ u. < 0 l ,Nx  o  if  if  u  < 0  u  > 0  {_  Uj  Similarly,  L  u. > 0  <  a i ^ / a f i j  1  y" v  i = 1, 3u,/3s.  results,  y. < 0 i.e. i f {  <  (4.14)  <  o .  the user cost of holding deposit j during period t was found  -  to be a f u n c t i o n o f k., the r e s e r v e r ^ , the i n t e r e s t  60  -  r a t i o on the j t h tvpe o f d e p o s i t s ,  pavabLe by the f i n a n c i a l  d e p o s i t s , b , the insurance  i n s t i t u t i o n on one d o l l a r o f  premium r a t e 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 r a t e that an average d o l l a r o f d e p o s i t  i n s t i t u t i o n d u r i n g p e r i o d t , and R, the d i s c o u n t  financial the f i r m .  j  "  =  1  +  b.,  t  b. t Rk. -  (1 I R)  7  = u.(r.,  s.,  J  r a t e used b s  s.)  1=1,...,N  1  2  k., R ) .  We can c a l c u l a t e the f o l l o w i n q p a r t i a l usinq  to the  Recall (3.3)  (1 t r. U  j >ields  derivatives  with  indicated  siqns  (3.3),  8lTj/3k. = R/(1 + R)  3u / 3 r . = 3 u . / 3 b . = - 3 u . / 3 s  3u./3R J  and  = 1/(1  + R)  = (1 + R)~ (1 + r. + b . f Rk. •} <T J 2  > 0  s.)  «7  3u./3R < 0 u n l e s s s. > I r r . + b. + Rk., an extremelv  J  J  J  J  (4.15)  ,T  implausible  occurrence.  The  user cost  u. i s c l e a r l y  and insurance premium l e v e l s by The  interest  r a t e payable r^  is  increasinq  in r e s e r v e requirements k.  both of which may be mandated. a l s o s u b j e c t to r e g u l a t i o n ,  such  as  -  cei.Li.ng r e q u i r e m e n t s  61  -  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 .  Note that d e r e g u l a t i o n o f r . , with u.  representing  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  bank.  H o w e v e r , 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 the f i n a n c i a l system i n c r e a s e , even i f the share of each f i r m decreases,  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  favorable f o r expansion each f i r m .  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  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 the net s u p p l i e s of outputs  and o t h e r  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 The t r a n s f o r m e d u = { J -u. j  u f  J  funds.  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. > 0 _ u. < 0 J  if  i n p u t s , and  j = 1,...,N  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  (4.16)  2  (4.15),  3u./3k, I 0 i f u. I 0 j j J ^ 0 if  3u./3r J  J  uJ  0 J  3u./3b. I  Ifu.U  3Uj/3s^ 5  i f u.Z  (  0  ^  1 7 )  - 62 -  3Uj/3FL i  ifIK < 0  Using the notation u as a N  L  and I + r^ *  f N  * Rk^ >  , j=1,...,N . 2  vector of normalized user costs, we  2  can rewrite the p r o f i t function ir(u,v,w).  From (4.3) which we  by applying Hotelling's lemma, the convexity  obtained  condition (4.6) and the  signs of the above p a r t i a l derivatives (4.14) and (4.17), we have the following comparative s t a t i c r e s u l t s . If the i t h asset 3y.*  3y.*  3r.  3u.  3u.  3u. l 3c. l  J  3u. l  L  3y.* 3  S  3u. l  i  '  3y.* 3  6  i  3  u  3  U  2  3u. l  3u^  i  9  i  5  2  3 * 2  3u. l  i  3y.* _  3u. l 3r.  3 *  3r.  3y.* l 3c.  is an input and has a positive user cost,  2  2  2  3u.  U  >  2  3 * 2  3u  2  (4.18)  — ± 3c. l  <0  (4.19)  < 0  (4.20)  9 u  > 0, — 3s. l 3 u  3 TT 2  >0  < 0  3 r  a * since ^ - > 0 , 3u/ i  <0  3u. l 3s. l  2  9  > 0, —  3u^  3» 3u. l  3u. i l 3c. l  3 TT  9  U  '  s i n c e — ^ - > 0 , — 3u/ 36. i l  > 0.(4.21) ~  I f , however, the i t h asset i s an output and has a neqative  user  cost then,  3y.* 3r. *y* SCj  3Uj  3w 2  3u^ 3 * 2  Suj  3r.  2  3  2  u  >0  since  1  > 0  (4.18 ) 1  2  9 r  i  SCj  7 2.0, — 3u. . a ir 2  >. 0  since  9 u  ±-!L. > 0, — 3u. 3  s  i >_ 0 C l  (4 19I)  - 63 -  3 TT  3 u  2  i  9  2  3u.  L  _  3u.  since  ^U  35. -  2  • > o —- < 0  3u. ~  ' 36  2  !  1  /, ,,i  ~  1  (  ^  2  1  If the jth deposit is an input and has a positive user cost, 3y *  3u.  _J_  =  3u.  3k.  J  3u. 2  J  3y.* _ J _ 3u.  =  2  ._J. UL_ J  3u, _1 3r.  =  J  2  J  3k.  since since  J  2 i_L_ 3u.  2  J  3y* = — J 3u. J  3u. .2 — i= - — 3b. 3u. J J  3y * = — — 3u, j  3u. i = 3s. 3u J j  2  2  3u.  — 1 >>_[) _o —*-  .2, 3u. 0, ^ - ^ ^ O , —- iJ >_ 0 3u. 3k. - } 3k. 2  JT  3u. __1 > o 3r. J  3u. — J - >_ 0 3b. J 3u. — i£ 0 3s. J  If, however, the j t h deposit  (4.22)  T J  2_ 3u. since U L _ > , - J - > 0 3u. 3r.  (4.23)  0  2  J  J  3u. since -2-1- > 0, — i > 0 3u. 3b. J J 2  (4.24)  2  g  since  2  3u  2  j  3u. > 0, — i £ 0. (4.25) 3s J  i s an output and has a negative user  then,  3 TT  3  2  3 u  2  U  since —  9 k >  3  J I!!  3u J  9 r  3 TT 3 | 3 u  2 j  3  U  r  0  3k. J  3 TT 2  . j  3  2  > , -J- , o  J  !!1  2  u/  i "  1  0  since —  3 U  > , 0  3^4  -  -J. < 3r  3u since - J l - > 0, _ 1 3u. 3r  (4.23 ) 1  0  g2  ^ ° i  2  x  < 0 ~  (4.24 ) 1  - 6k -  3y.*  — — 3r.  3 TT  3u.  3u  — >0 3r.  2  = 2  a  2  3u.  s i n c e —_>0, — _> 0. 3u. 3r.  (4.25 ) 1  2  The response of asset i with respect to a change in i t s own rate of interest i s summarized by (4.18) and (4.18 ). 1  interest payable to the f i n a n c i a l  If the rate of  i n s t i t u t i o n increases on asset i , an  input, the demand for that input does not decrease.  From (4.18 ), i f 1  the rate of interest payable to the f i n a n c i a l i n s t i t u t i o n increases on asset i , an output, then the supply of asset i i s non-decreasing. Hence, we conclude that i f the rate of interest payable to the f i n a n c i a l i n s t i t u t i o n increases on asset i , then holdings of asset i do not 19  decrease. In (4.19) and (4.19 ) are the responses of asset i with respect 1  to a change i n the expected c a p i t a l gains on asset i , c^.  I f asset i i s  an input, and i t s expected c a p i t a l gains increase, or expected losses decrease, the demand for that input i s non-decreasing.  capital From  (4.19), i f asset i i s an output and i t s expected c a p i t a l gains increase, or expected c a p i t a l losses decrease, then the supply of asset i i s nondecreasing.  Consequently, i f expected c a p i t a l gains increase, or  expected c a p i t a l 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 i n (4.20) and (4.20 ) for an average d o l l a r of asset i 1  y i e l d s S j to the f i n a n c i a l firm. asset i are non-decreasing.  If s^ increases,  then holdings of  In (4.21) and (4.21") are summarized the response o f a s s e t i w i t h respect to a change i n the expected d e f a u l t r a t e 6..  I f the expected  default rate on asset i i n c r e a s e s , and asset i i s an i n p u t , then the demand for that input i s n o n - i n c r e a s i n g .  I f a s s e t i i s an o u t p u t ,  (4.21 ) implies that i f the expected d e f a u l t r a t e 6 l  the supply of asset i i s non-increasinq.  i n c r e a s e s , then  Hence, i f the e x p e c t e d r a t e o f  default on asset i increases, then holdinqs of a s s e t i do not increase. We now turn to the l i a b i l i t y side of the f i n a n c i a l firm sheet.  balance  In (4.22) and (4.22 ) are the responses o f the j t h type of 1  deposit l i a b i l i t y to a chanqe in the required reserve r a t i o k..  The  required reserve ratio i s under direct control of the requlatory body governing  the f i n a n c i a l i n s t i t u t i o n .  The requlatory body for national  commercial banks in the United States i s the Federal Reserve B o a r d .  20  If the reserve r a t i o on the j t h type of deposit i s increased, and these deposits are inputs, then the demand for that input does not increase. If deposit j i s an output, and the reserve r a t i o k. increases, then the supply of deposit j does not increase.  Hence, i f the required  reserve r a t i o on the j t h type of deposit increases, then holdinqs o f t h e j t h type of deposit do not increase, and may f a l l .  T h i s i s an important  result because reserve ratios are used in c o n t r o l l i n g the aqqreqate money supply which i s defined in terms of currency such as demand deposits and time deposits.  and bank l i a b i l i t i e s  21  In (4.23) and (4.23 ) are the responses of the j t h type of 1  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 d o l l a r of  -  the jth type of d e p o s i t non-increasing. Depository  66  -  i n c r e a s e s , then h o l d i n q s o f those d e p o s i t s are  This r e s u l t  i s important i n a n a l y z i n g the e f f e c t of the  I n s t i t u t i o n s D e r e g u l a t i o n Act of 1980 on i n d i v i d u a l  financial  22  mst l t u t i o n s . In (4.24) and of deposit l i a b i l i t y  ( 4 . 2 4 ) are c o n t a i n e d the r e s p o n s e s o f the j t h tyoe 1  to the insurance premium  r a t e 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 i n the d e p o s i t i n s u r a n c e system which i s administered  by the Federal Deposit I n s u r a n c e C o r p o r a t i o n  (FDIC).  V i r t u a l l y a l l commercial banks are insured with the FDIC. cial  Other finan-  i n s t i t u t i o n s such as savings and loan associations and  credit  unions have similar insurance schemes where a premium i s paid dependent on deposits held.  The  insurance premium rate is thus another potential  regulatory control v a r i a b l e .  From (4.24) i f the j t h deposit  liability  i s an input, and  i t s premium b^ increases, the demand for that input i s  non-increasing.  If deposit j is an output, and i t s premium increases,  then (4.24 ) implies that i t s supply 1  i s non-increasing.  Consequently,  i f the premium on the j t h deposit increases, i t s holdings are  non-  increasinq. In (4.25) and  (4.25 ) are summarized the response of the j t h 1  category  of deposit to the service charge levied per d o l l a r per time  period.  I f the j t h type of deposit, i s an input, and  rate, s^ increases, then i t s demand is non-decreasing. an output, and i t s supply  i t s service charge If d e p o s i t j i s  i t s service charge rate increases, (4.25) implies that  i s non-decreasing.  Hence, i f the service charge rate per  - f>l d o l l a r per unit time i n c r e a s e s , then h o l d i n q s of the j t h type of d e p o s i t are non-decreasinq. Comparative s t a t i c s  f o r the c r o s s e f f e c t s of the components  each user cost are indeterminate. the  I t i s unknown, f o r example, what i s  e f f e c t on time d e p o s i t s when the r e q u i r e d  deposits chanqes.  of  r e s e r v e r a t i o on demand  T h i s i s because the o f f - d i a q o n a l elements of the  matrix of second order p a r t i a l derivatives of IT e v a l u a t e d 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 tion.  func-  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 e f f e c t s of the components of each user cost requires examination of empirical point  estimates.  Consider the i n t e r r e l a t i o n s h i p between p r o f i t s and components of the user costs.  Using (4.3), obtained  by  the  various  applying  Hotelling's lemma, and (4.14) and (4.17) which employ the user costs, the following comparative s t a t i c results are  a*  * i 8r. " 3u. 3r. i l l 3  3ir 3c. i 3 ir 3s  x  =  obtained:  3 u  dir 3u.  3  3* luj  3  U  i > 0 3c. i i u  i 3sTu  0  1  =  If.-.N!  - 68 -  j 3k7 J J 3  37r_ _ 3TT 3k. " 3u.  J 3TT  u  0  j " 3uT 8771 J J J 3  _  3TT  _  3TT_  u  0  3r.  3TT_  3  j  u  3bTJ J  3b. " 3 .  J  U  j 3s. " 3 . 377 J J J 3TT_  _  3TT_  3  J=  0  u  0  U  P r o f i t s for the f i n a n c i a l i n s t i t u t i o n are non-decreasing when there i s an increase i n :  (1) the interest rate payable to the f i n a n c i a l  i n s t i t u t i o n on assets held; (2) the c a p i t a l gains on assets  held;  (3) the service charge rate charged on loans; and (4-) the service charge rate charged on deposits.  P r o f i t s 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 f i n a n c i a l i n s t i t u t i o n on l i a b i l i t i e s ;  and (4) the  insurance premium rate on deposits. The comparative s t a t i c predictions yield q u a l i t a t i v e results from user costs embedded i n a p r o f i t maximizing framework. results follow a p r i o r i expectations.  Many of these  The value of the r e s u l t s i s that  exact quantitative measures of responses can be obtained once a functional form for the variable profit function i s 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 a l s o 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 r e q u i r e 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 c h a r acterize optimal time paths for choice variables. L e t x ( t ) be a v e c t o r 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 permissible values of t. Let * be an objective function t h a t maps the functions (s(»), a(«)) into the real numbers. A necessary condition for optimal choice of x(«) r e l a t i v e to the objective for $ i s that  3 »(x(«), <»(•)) aTxTtn— =  0  „  in 1 t = 0,1,..., +  This procedure can be used as long as the domain of x(») See Schworm [1980] for further discussion: pp. 1-3.  i s countable.  Formally, we define the time period to to be the time i n t e r v a l [ t , t + D , closed on the l e f t and open on the r i g h t . The instant t i s i n cluded in i n t e r v a l t, but the instant t+1 i s not. Producers r e a l i z e expected c a p i t a l gains (losses) at the end each period. 5  6  of  T h i s occurs at time t + 1.  A long-run Hicksian intertemporal model would consider a l l time periods u n t i l the f i n a n c i a l 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 e x i s t . However, the long-run model w i l l be required i n order to determine the correct shadow rental rates of the short-run model. 0  Because of data constraints, our time i n t e r v a l in the model w i l l be set at one year.  empirical  - 70 -  T h e assumption of c o s t m i n i m i z i n g b e h a v i o r i s out of voque mainly because of the d i f f i c u l t y i n j u s t i f y i n g the e x o q e n e i t y of the v e c t o r of o u t p u t s . The v e c t o r of bank o u t p u t s w i l l chanqe in composition as r e l a t i v e user c o s t s v a r y . Rank c o s t f u n c t i o n s t u d i e s were plagued by s e r i o u s d i f f i c u l t i e s i n d e f i n i n g the o u t p u t s of commercial banks. 3  O u a l i t y theory can be u t i l i z e d even i f t h e r e or m o n o p o 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 r m under i m p e r f e c t c o m p e t i t i o n i s developed in Chapter 8. See Diewert [19S21. 1 0  1  d e b r e u [1959] p.  is monopsonistic  38.  12  Actually, convexity of the production p o s s i b i l i t y set may be o m i t t e d and the p r o f i t 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. 2 8 9 ] . Note, however, i f we assume the production p o s s i b i l i t y set i s 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. See also Diewert [1973, pp. 290-294]. We note t h a t i f the p r o f i t function i s not d i f f e r e n t i a b l e 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 w i l l imply that the p r o f i t function has a non-empty set of supportinq hyperplanes (y,z,x) at (u,v,w) and thus the p r o f i t maximizing derived input demand and output supply functions become set valued functions or correspondences. 13  l  Exogeneity of prices and user costs w i l l be relaxed Chapter 6. l 5  in  i r defined by (4.2) using (u,v,w) = p.  See Diewert's [1977, p. 11] fourth characterization of concavity. 16  17  See Diewert [1974a] pp. 142-146.  Proofs pp. 163-164.  18  the  For one input-output the cross effect term can be signed using above theorem. See Diewert [1974a], p. 143. 1 9  Loan rate c e i l i n g s have been intended to protect consumers from paying high loan rates. Such c e i l i n g s , when binding, may r e s t r i c t c o n sumer loans. These c e i l i n g s are adjusted p e r i o d i c a l l y . I n t e r e s t r a t e s on s p e c i f i c loans have been influenced by "moral suasion" imposed f o r short periods by the regulators. This affects loan supply i n the short-run. Under the United States Monetary Control Act of 1980 a l l depository i n s t i t u t i o n s (saving banks, savings and loans, credit unions) w i l l be required to maintain reserves in a r a t i o prescribed by the Federal Reserve Board. Previously regulatory bodies d i f f e r e d between 20  -  7 1  -  d e p o s i t o r y i n s t i t u t i o n s ( e . q . The F e d e r a l Home Loan Bank r e g u l a t e d s a v i n g s and loan a s s o c i a t i o n s ) , in other c o u n t r i e s each tyoe of d e p o s i t o r y 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 d e t e r m i n i n g the r e s e r v e r a t i o on each k i n d 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 C u r i e s and Shaw [1960] and Tobin [1963] f o r i q n o r i n g t h a t banks, c r e d i t u n i o n s , s a v i n g s and loan a s s o c i a t i o n s are f i r m s . We have d e s c r i b e d f i n a n c i a l f i r m o p e r a t i o n s e x p l i c i t l y w i t h a model of the i n d i v i d u a l f i r m a p p l i c a b l e to ther p r o d u c e r s . 2 ?  I n t e r e s t r a t e s on d e p o s i t s in the U n i t e d S t a t e s have been r e g u l a t e d . Payment of i n t e r e s t on demand d e p o s i t s was p r o h i b i t e d , and R e g u l a t i o n 0 set d e p o s i t r a t e c e i l i n g s on o t h e r c a t e g o r i e s of d e p o s i t s . The D e p o s i t o r y I n s t i t u t i o n s D e r e g u l a t i o n Act of 1980 r e q u i r e s the D e r e g u l a t i o n Committee to e x e r c i s e i t s a u t h o r i t y t o p r o v i d e f o r t h e o r d e r 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 r a t e c e i l i n q s as r a p i d l y as economic c o n d i t i o n s w a r r a n t . I t s e t s out t a r q e t s f o r i n c r e a s i n g the r a t e c e i l i n q s by at l e a s t h a l f a p e r c e n t a q e p o i n t 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 y e a r s a f t e r the date of enactment.  -  72  -  CHAPTER 5  DATA AND DATA CONSTRUCTION 5.1  Introduction To estimate the parameters of the model developed  in Chapters 3-4,  it i s necessary to have observations on a wide variety of variables.  The  major data source for the study i s developed by the Federal Reserve Bank Functional Cost Analysis (FCA) program.  This program i s a co-operative  e f f o r t 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 each bank by year and with groups of other banks.  of these data within  I t i s designed "to  help a participating bank achieve the objective of increasing o v e r a l l bank earnings as well as increasing the p r o f i t a b i l i t y and e f f i c i e n c y 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, c a p i t a l , notes and debentures, borrowed money, and federal funds purchased.  There are six asset categories:  cash,  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".  Other bank functions include the provision of safe deposit boxes, trust and estate services, and on-premises e x i s t on non-banking functions.  computer services.  Data also  A non-banking function i s defined as a  s p e c i f i c a c t i v i t y contributing to earnings, which has no balance sheet  - 73 -  entry.  2  bureaus  Some examples .ire the o p e r a t i o n of and t r u s t and s a f e k e e p i n q s e r v i c e s .  insurance agencies, These  functions provide  the i s o l a t i o n of income and expenses generated by n o n - b a n k i n q , u s i n q a c t i v i t i e s other than from s a f e d e p o s i t s , services. non-banking  travel  trusts,  for  non-fund  and computer  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 a c t i v i t i e s , it is  important that income and expense  by them not be minqled w i t h the income and expenses banking f u n c t i o n s .  generated  of the s t r i c t l y  The appendix p r o v i d e s a d e t a i l e d example o f  F u n c t i o n a l Cost A n a l y s i s d a t a . Periodic reviews were conducted by the Federal Reserve Bank of New York to ensure comparable, uniform and precise reporting.  Care was t a k e n  to ensure a c c u r a c y , s i n c e the information i s used both for cost a c c o u n t ing and performance comparisons between banks.  Other s t a t i s t i c a l  series  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  j o i n t 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 p o s s i b i l i t y  set at the f i n a n c i a l firm.  Use of the Functional Cost data i s important in the estimation of the model because they contain a salary breakdown between o f f i c e r s , or s k i l l e d workers, and processors, or unskilled workers, thus allowing them t o be treated as separate factors of production.  The FCA data a l s o  contain information on the use of computers, d e t a i l s on number and types of branch o f f i c e s , account c h a r a c t e r i s t i c 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 c o m m e r c i a l b a n k s i n New 1978.  yearly Functional Cost data for  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 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 .  a s s u m e d 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 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,  eighteen to  These banks are  factor markets.  They l i e  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  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  New have  been 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 are b e t t e r than c r o s s - s e c t i o n a l d a t a f o r our because more v a r i a t i o n i n p r i c e s , or user c o s t s , than  purposes  in t y p i c a l cross-  s e c t i o n s i s r e q u i r e d to estimate a v a r i a b l e p r o f i t f u n c t i o n with a f l e x i b l e form.  Since there are d i f f e r e n c e s in s t a t e r e g u l a t i o n of  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 has  been  c o n s t r a i n e d t o come from o n l y two s t a t e s , New  which  h a v e s i m i l a r r e s t r i c t i o n s on  Y o r k and New  3ersey,  branches.  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  Reserve B u l l e t i n of the F e d e r a l Reserve Board of Governors,  Federal  as do  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 . 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 I n c o m e and A c c o u n t s as p u b l i s h e d  Implicit  Product  in the Survey o f Current B u s i n e s s of the  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 .  the  These  U.S.  include  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  user  costs for c a p i t a l . The c h a p t e r and 4 d e v e l o p  i s organized  i n the f o l l o w i n g manner.  3,  the data c o n s t r u c t i o n f o r the p h y s i c a l , or 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 . of intermediate  S e c t i o n s 2,  These are labor input, the s e r v i c e s  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 s k i l l e d unskilled workers from FCA  data.  A T'ornqvist price index is then  calculated for the price of labor. for materials. stationery  Included  and  In section 3 we construct price data  3  in materials expenditures  are outlays on  and o f f i c e supplies, telephone, teleqraph, advertisinq,  postage and d e l i v e r y .  User costs for capital are constructed  in section  4 using implicit price deflators, and information on service l i v e s of various c a p i t a l assets.  Utilizing  income and expense statement  tion and user costs for c a p i t a l , quantities of c a p i t a l are  obtained.  Section 5 deals with the construction of user costs and quantities for f i n a n c i a l commodities.  informa-  relevant  For the s p e c i f i c a t i o n , four types  of f i n a n c i a l commodities are distinguished, namely loans, cash, demand deposits and time deposits. each is an index comprising  With the exception of cash, the quantity of a number of other f i n a n c i a l commodities.  each component, a separate user cost must be constructed.  For  As indicated  in Chapter 3, these rely on extensive information on reserve requirements, 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 p r o f i t s for each bank in each year. Data are tabulated in summary form in each subsection. information  is obtained  for eighteen banks over 1973-1978, and user costs  and quantities of services consumed constructed 5.2  The  for each.  Labor Services Average compensation i s calculated for processing employees and  o f f i c e r s for each bank and year.  Compensation includes salary and f r i n g e  - 76 -  benefits.  FCA data distinguish processing  salaries, officers'  salaries and fringe benefits by function, implying demand and time deposits  can be separated.  that the a l l o c a t i o n to  Processing  o f f i c e r s are also allocated to each function.  employees and  Where fringe benefits are  not specified to processors or o f f i c e r s for a function, they are allocated on a person basis.  Average compensation i s obtained by  dividing t o t a l compensation for each kind of labor by the number of workers.  Hence  E SPE^ + FBPE i=l *t NPE  t=1973,...,1978  F IE SOE. + FBOE, it it i=l W (OE) = NOE  t-1973,.,.,1978  l t :  W (PE) t  t  where i - 1,..., F represents  (5.1)  (5.2)  the various functions, such as demand  deposits and investments i n the FCA data, with  S P E  S  0  it  t  e  s  a  l  a  r  l  e  s  o f  processing  employees i n function i at time t  the salaries of o f f i c e r s i n function i at time t  E i  h  t  FBPE  the fringe benefits of processing  employees In function i  at time t FBOE  it  the fringe benefits of officers i n function i at time t  NPE^  the number of processing  NOE  the number of o f f i c e r s at time t .  t  employees at time t  -Il-  ka aggregate price of labor input is then constructed D i v i s i a Indexing procedure for each bank.  Let EXL  t  using the  denote labor compen-  sation at time t, or EXL  = P C  where PL i t  «L  = W (PE)«NPE  t  L. C  t  and Lt denote  + W (OE)«NOE t  t  (5.3)  t  respectivel* y the p r i c e and q u a n t i t y  of aggregate i. L  labor at time t. The D i v i s i a index for the price of labor i s  P  - « p [  l t  with base value P  L  t S j  (  1  9  ?  3  )  W.(PE) (PE, ^ <j  t  W (OE) ..(OEjJ^  d j l  ( 5  .  4 )  = 1, and  W (PE)'NPE s (PE) = — _ 1 t  (  5  >  5  )  W (OE)'NOE S  t  (  0  E  )  ~  " ^EXl  where s(PE) and s(OE)  represent  (5.6)  the relative shares i n t o t a l compensation  of processing employees and o f f i c e r s be derived analogously,  respectively.  A quantity index can  or by dividing the expenditure on labor by the  D i v i s i a index for the price of labor.  The calculated D i v i s i a price  indices f o r labor using a moving two period arithmetic mean share weight on s(PE) and s(OE), are i n Table 5.1 for each bank. Similar Tbrnqvist  indices were also calculated across banks using  Bank 1 i n 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 Number  1974  1975  1977  1978  1  1.166436  1.218487  1.290430  1.152978  2  1.052673  1.120276  1.220815  1.315380  3  1.034380  1.183816  1.138518  1.425856  4  0.9839331  1.123774  1.330551  1.30639  6  1.031076  1.157491  1.203251  1.075691  12  1.057684  1.134845  1.277678  1.3291 15  13  1.347334  1.297000  1.494361  1.426364  14  1.093831  1.128340  1.376768  1.390473  15  1.069191  1.170598  1.276689  1.188653  16  1.189604  1.192038  1.240170  1.356224  19  1.046269  1.175020  1.019742  1.250883  21  0.872930  0.895532  1.012204  1.113594  2?  1.057668  1.111585  1 . 174525  1.2605 34  23  1.043968  1.071801  1.027639  1.067936  25  0.967494  1.121230  1.271021  1.261261  27  1.049748  1.141093  1.342566  1.330654  28  1.091673  1.139794  1.292020  1.331671  29  1.173486  1.231121  1.428588  1.407685  4  Number coding i s as supplied by the Federal Reserve Bank of New York.  - 79 _  banks. 5.1  These were used to weight the p r i c e i n d i c e s f o r  labor  in Table  s i n c e d a t a on Rank 1 in 1973 are used as r e s p e c t i v e n u m e r a i r e s .  cross  bank i n d i c e s are in Table 5.2.  i n d i c e s are used i n the study services  These c r o s s - b a n k  f o r the p r i c e of l a b o r .  are t a b u l a t e d in summary  form in Table 5.3  The  adjusted p r i c e The d a t a f o r  labor  f o r t h r e e sample  years.  5.3  Materials Services The FCA d a t a i n c l u d e e x p e n d i t u r e s 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 , t e l e p h o n e and t e l e g r a p h , p u b l i c i t y and a d v e r t i s i n g , postage,  f r e i g h t and d e l i v e r y .  it i s necessary  and  In order to use t h e s e d a t a i n e s t i m a t i o n ,  t o decompose them i n t o p r i c e s and q u a n t i t i e s .  The hanks i n the study  are g e o g r a p h i c a l l y  l o c a t e d i n the same  F e d e r a l Reserve D i s t r i c t , and so can be assumed to f a c e the same p r i c e s in f a c t o r markets.  I m p l i c i t p r i c e i n d i c e s c o n s t r u c t e d by the  U.S.  Departments of Commerce and Labor are used f o r the v a r i o u s m a t e r i a l components.  T o t a l e x p e n d i t u r e s i n each c a t e g o r y are d i v i d e d by the  r e l e v a n t p r i c e index t o y i e l d a q u a n t i t y i n d e x . The p r i c e used f o r p r i n t i n q , s t a t i o n e r y on o f f i c e s u p p L i e s  and a c c e s s o r i e s  Department of L a b o r . at  100.  from the Wholesale P r i c e  i s the  series  Index of  The base year used i s 1972, when the index i s  For t e l e p h o n e and t e l e g r a p h , the i m p l i c i t  n a t i o n a l a c c o u n t s , as p u b l i s h e d i n the Survey t e l e p h o n e and t e l e g r a p h i s u s e d . implicit  and s u p p l i e s  5  set  p r i c e d e f l a t o r in the  of Current Business  for  For p u b l i c i t y and a d v e r t i s i n q , the .  p r i c e d e f l a t o r for services  Survey o f C u r r e n t B u s i n e s s i s u s e d .  the  i n the n a t i o n a l a c c o u n t s from the A p r i c e i n d e x , w i t h the base 100  in  - 30 -  TABLE 5.2 C r o s s Bank T o r n q v i s t Labor P r i c e I n d i c e s , (Bank 1 normalized at u n i t y ) Bank Number  Index  1  1  2  1.014  3  1.129  4  1.077  6  1.184  12  1.056  13  0.881  14  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  1973  - SI T A B L E 5.3 L a b o r I n p u t a n d 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 ($)  2,432,700  2,824,800  136,620  8,586,800  Labor quantity, L  2,308,600  2,700,900  120,520  9,325,900  1.0522  0.13882  0.8fr3fr2  1.3587  Labor price,  1 97 5 Annual wage, officers W(0E) ($)  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  1.1990  0.1fr67  Labor price, P  L  1.0062  1.59fr6  1 97 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  3,722,000  fr,36fr,200  159,280  12,582,000  2'7,680,000  32,578,000  130,070  9,769,100  Labor cost, EXL ($) Labor quantity, L Labor price, P.  .  L  1.3412  0.1fr76  Note: Labor quantity Is measured in index units.  1.1083  1.7069  -  1972,  82  i s constructed using the U.S.  postage.  -  domestic rate for f i r s t class  This index for postage, freight and delivery along with  other price data for materials is in Table 5.4  the  below.  An aggregate price of materials is then constructed using the Tornqvist indexing procedure for each bank. expenditure EXM  on materials at time t.  = P «M t M t t  = PSS «SS t t  Let EXM^  denote the t o t a l  Hence  + PTT «TT t t  + PPA  t  «PA + PPD «PD t t t  (5.7)  where P Mt and M t denote respectively the price and quantity of aggregate materials at time t. quantity i s denoted by SS  price at time t.  with PSS  t  The quantity of telephone  Stationery, p r i n t i n g and supplies t  the corresponding  and telegraph services i s TT  S i m i l a r l y , PA  price at time t. and PTT^ i t s  represents p u b l i c i t y and advertising  fc  quantity, and PD^ denotes the postage and delivery quantity with PPA PPD^  t  and  t h e i r respective prices at time t. The D i v i s i a index for the price of materials i s  t  t  t  PPA.  S  1973  PSS.  P  A  p-pAT  d j  +  PTT  PPD. S  PD  PTOT J d  (5.8)  ]  with base value P (t) = I, and PSS -SS t  'PS  =  EXM  t  PTT -TT  t  t  ' TT S  =  ~EXM^  PPA  t  ' PA S  =  ~EXM^  -PA  PPD S  PD  =  •PD "  (5  '> 9  $1  -  TABLE 5.fr  Price Indices, Materials and Intermediate Inputs, 1973-1978  Printing, Stationery 4 Supplies  100  106.5  131.88 1fr3.fr  1frfr.76 1fr6.70 151.8fr  Telephone 4 Telegraph  100  102.6  106.9  110.fr  11fr.3  115.6  117.0  Publicity 4 Advertising  100  105.fr  113.7  128.0  136.6  1fr7.3  158.9  ostage, Freight 4 Delivery  100  106.25 125.0  162.5  162.5  162.5  162.5  Spc;' ^ T X ' ''Vv  1 1n r  * ^PD  r t  "P  on m a t e r i a l s of s t a t i o n e r y city  r e s e n (  l h (  index  can be d e r i v e d analogously t  i n d i c e s f o r m a t e r i a l s are i n Table 5.5  form i n Table  5.1-  .  expenditure  telephone and t e l e q r a p h , p u b l i -  and d e l i v e r y  e x p e n d i t u r e on m a t e r i a l s , F.\M , by P  specification.  r e l a t i v e shares i n t o t a l  and s u p p l i e s ,  and a d v e r t i s i n g , and postage  quantity  '  respectively.  The  or by d i v i d i n g the  total  The c a l c u l a t e d D i v i s i a  price  f o r each bank under the  The d a t a f o r m a t e r i a l s e r v i c e s  Tornqvist  are t a b u l a t e d i n  summary  5.6.  Physical Capital Services Information  r e q a r d i n g p h y s i c a l c a p i t a l can he o b t a i n e d e i t h e r from  the balance sheet or the income and expense  statement.  On the b a l a n c e  s h e e t , c a p i t a l i s l i s t e d at book v a l u e l e s s  accumulated d e p r e c i a t i o n .  Balance sheet d a t a are not an a p p r o p r i a t e source f o r c o n s t r u c t i n g and q u a n t i t i e s f o r two r e a s o n s . measured by h i s t o r i c c o s t s 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 Second, c a p i t a l c o s t s  on the balance s h e e t .  balance sheet  are  and are not a d j u s t e d f o r p o s t - p u r c h a s e  in a d i f f e r e n t time p e r i o d . arbitrarily  F i r s t , the c a p i t a l e x p e n d i t u r e s  prices  include i n i t i a l  "Bank P r e m i s e s " ,  are  asset  its capital  aqqreqated  as an a s s e t  e x p e n d i t u r e s on bank b u i l d i n g s ,  on the  real  e s t a t e , and f u r n i t u r e and equipment l e s s accumulated d e p r e c i a t i o n . costs  are added  together.  income and expense able.  statement  i n f o r m a t i o n on c a p i t a l are p r e f e r -  The d a t a c a p t u r e the flows r e l a t e d to the c a p i t a l s t o c k .  occupancy  The  expense o f bank premises  The  i n c l u d e s 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  1974  1975  1977  1978  1  1.134208  1.249685  1.371 134  1.414840  2  1.111802  1.230382  1.377210  1.423199  3  1.118852  1.243437  1.403031  1.443664  4  1.128526  1.255438  1.413953  1.466109  6  1.169465  1.297721  1.418836  1.461923  12  1.131352  1.253476  1.395110  1.440034  13  1.114799  1.226566  1.356195  1.401012  14  1.127663  1.236259  1.358282  1.394968  15  1.126246  1.256294  1.422896  1.466637  16  1.110494  1.228877  1.362099  1.416199  1.121184  1.239348  1.367394  1.418753  1.138339  1.271443  1.428530  1.463575  1.128845  1.250466  1.38292 I  1.430213  1.126066  1.244310  1.382432  1.426618  1.128423  1.254958  1.397117  1.451547  1.129817  1.242663  1.364757  1.406885  1.111448  1.226302  1.368730  1.412366  1.143240  1.270928  1.411747  1.447325  19 21 22 23 25 27 28 29  5.6  TABLE  User Cost and Quantity Index, Material Services, 1973-1978 1—  1 97 3 Variable  Standard Deviation  Mean  Price of Materials, P  Minimum  Maximum  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  19 7 5 Mean  Standard Deviation  1.1938  Quantity of Materials, M Expenditure on Materials, EXM ($ current)  Variable Price of Materials, P  u  Minimum  Maximum  0.0174  1.1723  1.2406  516,620  566,950  19,144  1,569,900  612,450  671,740  23,751  1,876,700  1 9 7 8 Mean  Standard Deviation  1.3770  Quantity of Materials, M Expenditure on Materials, EXM ($ current)  Variable Price of Materials, P  M  Minimum  Maximum  0.0224  1.3409  1.4098  569,230  658,560  20,829  2,088,300  777,230  898,470  29,270  2,870,900  - S7 -  costs,  rent,  interest,  ment and parking  lots.  and taxes  for bank b u i l d i n g s ,  land,  The f u r n i t u r e and equipment  5  interest  fixed equip-  expense  and tax charges  includes  d e p r e c i a t i o n , maintenance,  rent,  on movable  f u r n i t u r e and equipment.  There is a l s o a computer or computer  bank  service  expense. Let E  denote the expense on c a p i t a l  n  kinds of c a p i t a l :  structures  computers  Then,  E where U and  n  n is  (n=3). = U is  n  V  8  n  K  the q u a n t i t y  of c a p i t a l  asset n, V  services  for bank s t r u c t u r e s  For banks who have on-premise computing c e n t r a l processing  the u t i l i z a t i o n rate i s  all  firms  during  its  from asset  (n=2), and  utilization  n.  [1967].  It  Utilization  is  is  constructed  The user cost  firm  r a t e R, on i t s  assumed  is  leasinq  P  nt  Rewriting  - U = }(1 nt  - d ) P . .}/(! n nt+1  (5.11) we o b t a i n  J  symbols + R).  the as  firm.  activities.  the r e n t a l  rate The  received  the p e r i o d i s equal to the discounted d e p r e c i a t e d value of In  in  derived  to earn the going  of one u n i t of the c a p i t a l good l e s s  that  a s s e t over time.  from a " l e a s i n q "  f o r c e s the " l e a s i n g "  c a p i t a l good i n the rent p e r i o d .  rate  t h e r e are d a t a on  hours per week.  asset n i n p e r i o d t  and G r i l i c h e s  (5.10)  and f u r n i t u r e and equipment.  the same f o r a given c a p i t a l  r e t u r n , or nominal d i s c o u n t  purchase cost  (CPU)  is  n  facilities  lease t h e i r c a p i t a l qoods  C o m p e t i t i o n presumably of  unit  of c a p i t a l  framework of 3orgenson though  three  n=1,...,3  the user c o s t of c a p i t a l  The user cost  There are  (n=1), f u r n i t u r e and equipment  n  data are not a v a i l a b l e  average  asset n.  the  we have, (5.11)  - S3 -  U  nt  =  <  R P  nt  +  d  n  P  nUl  "  ( P  nt , " +  V^  1 +R )  (5  "  ,?)  n = 1,2,3 t = 1973 , . . .,1978 where P  i s the purchase price o f c a p i t a l good n i n period  i t s expected purchase price i n period t *- 1, d  t, P  . is  i s i t s one-period  combined economic depreciation and obsolescence r a t e and R i s the nominal discount  rate.  Data on purchase prices for c a p i t a l are obtained from the U.S. national accounts, as published  in the Survey of Current Business.  assumed that the banks face competitive hence the same c a p i t a l prices.  It i s  physical c a p i t a l markets, and  The implicit price deflator for purchases  of commercial structures i s used for structures.  For furniture and  fixtures and for computing machinery we use the respective  i m p l i c i t price  deflator f o r private purchases of producers' durable equipment.  These  prices are i n Table 5.7. Information on service l i v e s of c a p i t a l assets Detailed information  i s limited.  on the average service lives of the equipment and  structures that make up the stock of fixed c a p i t a l , i s unavailable, information average.  as i s  on how the service lives of individual items depart from the  There are differences in the b a s i c p h y s i c a l  c h a r a c t e r i s t i c s of  c a p i t a l assets, variations among the practices o f their owners w i t h respect  to use and retirement,  and technological changes which make for a  large dispersion of service l i v e s . For fixed non-residential business c a p i t a l , estimation  of average  service l i v e s has r e l i e d on data compiled in connection with the  -  TABLE  39  -  5.7  Asset Prices for Physical Capital [1972 = 100]  1973  1974  1975  1976  1977  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:  1978  1979  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 e d e r a l income  tax  laws.  9  This  study  uses  the asset  working l i v e s a p p l i e d i n a l l n a t i o n a l accounts and U.S. c a p i t a l s t o c k studies.  They  are p u b l i s h e d  in F i x e d R e s i d e n t i a l and N o n - R e s i d e n t i a l  Business C a p i t a l in the United States 5.8.  If L  1 0  n  i s the s e r v i c e  1929-1976, and are l i s t e d i n T a b l e  l i f e of c a p i t a l asset  n, then d , the ii  one-period depreciation rate, is  d  n ~ E~ n  n=1 ,2,3  assuming a c o n s t a n t g e o m e t r i c r a t e of d e p r e c i a t i o n .  1 1  The user c o s t of c a p i t a l (5.12) and the u s e r c o s t s i n Chapter 3 a l l i n v o l v e the d i s c o u n t  r a t e R.  ( 3 . 1 ) and ( 3 . 3 )  The a p p r o p r i a t e  discount  r a t e i s t h e m a r g i n a l o p p o r t u n i t y cost of borrowing o r l e n d i n g t h e marginal d o l l a r .  Economic theory p r e d i c t s t h a t the f i r m w i l l engage i n  short-run production i f quasi-rents  are p o s i t i v e .  I f q u a s i - r e n t s are  n e g a t i v e the f i r m i s not c o v e r i n g i t s v a r i a b l e o p e r a t i n g c o s t s and i t i s more a p p r o p r i a t e not to produce than to p r o d u c e . Quasi-rents  have been c a l c u l a t e d u s i n g  as d i s c o u n t  v a r i o u s major i n t e r e s t r a t e s f a r i n a the banks. are used as the d i s c o u n t costs.  This  1 2  I f loan  r a t e s a l l the  interes*  rates  r a t e , there i s n o spread to cover v a r i a b l e  i s c o n f i r m e d by a p p l y i n o t h i s procedure t o a l l t h e d a t a  p o i n t s , and q u a s i - r e n t s t h a t the d i s c o u n t  are n e g a t i v e throughout  the sample.  r a t e should be one on a d e p o s i t category .  This  implies  Demand  d e p o s i t s have a z e r o 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 t h e i n t r o d u c t i o n o f N e g o t i a b l e Orders o f W i t h d r a w a l (NOW) accounts  input  i n 1978.  This  l e a v e s the time d e p o s i t  remaining c a n d i d a t e f o r use as the d i s c o u n t  i n t e r e s t r a t e as the  rate.  -CI-  TABLE 5.8 Service Lives by Type of Asset  Type of Asset  Commercial Buildings  Furniture and Fixtures  Office, Computing, and Accounting Machinery  Life (years)  36  15  8  As calculated in  the  Functional Cost  data,  the time deposit rate  is a blended rate of the savings deposit rate and the c e r t i f i c a t e of deposit rate.  C e r t i f i c a t e s of deposit are in large denominations,  freguently in excess of $100,000, hence the> are not marginal Therefore a blended rate includes marginal and non-marginal  dollars.  dollars.  For  this reason i t i s assumed that the marginal opportunity cost of funds i s the lowest time deposit rate paid in the sample in each year.  This rate  i s l i k e l y to have the lowest ratio of c e r t i f i c a t e s of d e p o s i t .  13  rates are 4.477 percent  The  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 gains.  the user cost calculations including c a p i t a l  I f c a p i t a l expenditure data were available on a net basis, as  "occupancy cost and service outlays less capital gains", then the quantity of c a p i t a l services would be obtained as Q = TE /U n n n  where TE  n  n n  _ i  ,  - »• • • >' 1  i s true expenditure on c a p i t a l services.  In the FCA c a p i t a l  expenditures data, as in most published series in f i n a n c i a l capital qains are excluded. n=1,...,3.  statements,  Measured expenditures are consequent \ * . r  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 c a p i t a l services  i s 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,  user cost e x c l u s i v e of c a p i t a l q a i n s . construct  cap ital service  From the 0 are c o n s t a n t ,  This procedure  i s used t o  flows.  and the assumption  the c a p i t a l s t o c k s K  that u t i l i z a t i o n r a t e s of c a p i t a l  can be c o n s t r u c t e d as 0 /V ,  n n=1,...,3. run.  n  n  The q u a n t i t y of c a p i t a l i s assumed t o be f i x e d i n the s h o r t  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 c e s market, w i t h demand  sloping,  or the  t = 1 9 7 3 , 1 9 7 8  and the p e r f e c t l y i n e l a s t i c supply  determines  E i t h e r t h e c a p i t a l i s used at a zero or c o n s t a n t the l a t t e r may be n o r m a l i z e d at u n i t y .  downward  the user  cost.  r a t e o f u t i l i z a t i o n , and  The e x p e n d i t u r e on c a p i t a l  s e r v i c e s i s thus t h e product of the f i x e d c a p i t a l q u a n t i t y and the e q u i l i b r i u m user c o s t . T h i s i m p l i e s that i n the H i c k s i a n s h o r t r u n , no response  t o t a x changes,  f o r example, t a k e s p l a c e .  A p h y s i c a l c a p i t a l aggregate K = K(K  using  K ,  r  K )  2  the T b r n q v i s t  i s then c o n s t r u c t e d , (5.14)  3  specification.  In growth  form, t h i s  is  3  A£n K  z  =  S ^ A£n K  n=1  1  n  t  n  (5.15)  t  where  S . = 0.5  3 E E n=1  nt  a n d  t.  E  nt  =  P  nt nt K  i  s  t  h  e  d  S  S  e  nt-1 3  nt  n t  t  n=1  +  V  The p r i c e f o r aggregate  d  i  u  e  o  E  f  n=1 , . . .,3 t=1973, . . . , 19.78 ^ C d  (5.16)  1  Pital  s t o c k o f type n i n year  c a p i t a l can be computed a n a l o g o u s l y ,  o r the  - 9k  -  total expenditure o n 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  capital,  yielding 3 P^. The data 5.5  = C E  n= 1  E  ]/K  t=1973, . . . , 1978.  f o r c a p i t a l a r e tabulated i n summary i n T a b l e  (5.17)  5.9.  User Costs f o r F i n a n c i a l 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 ,  estate mortgage loans, instalment  loans, credit card  commercial, a g r i c u l t u r a l and other loans. these five loan categories.  There are  real  loans, and F C A d a t a o n each o f  The user cost o f loan i i s constructed  according to (3.1) which i s ,  _ 1 + (r.+-s. + c . - 6 . ) u. = 1 - { " / -} 1  ( 1  R  )  1=1 ,... ,5  (5.18)  where r^ i s the mathematical expectation of interest payable t o the f i n a n c i a l i n s t i t u i o n , s^ is the service charge rate that an average dollar of asset i yields per losses, and 6. i.  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  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  The term ( r . + s^ + c. - 5.)  d o l l a r of loan i per time period.  represents  to default o f category  t h e expected i n c o m e from o n e  I n 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 s p e c i f i c a t i o n s are outlined in Chapter 3.  A s there a r e f i v e  observations per bank, a lagged expectations model was not  feasible.  S t a t i c expectations were not appropriate during this time period.  - 96  5.5.1.2  -  Investments Investments  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 . major p o r t i o n of the investment  p o r t f o l i o f o r FCA  The  banks 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 loans.  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 a r e i n c l u d e d as i n v e s t m e n t s  in this a n a l y s i s .  r e s t r i c t e d here to f e d e r a l funds s o l d , purchased bankers'  acceptances,  purchased  loans n o r m a l l y r e p o r t e d as 1 4  They  commercial  are paper,  c e r t i f i c a t e s o f d e p o s i t , and Commodity  Credit Corporation c e r t i f i c a t e s of i n t e r e s t . I n c l u d e d i n t h e i n c o m e 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 . exemplify t h i s type of investment.  M u n i c i p a l bonds  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 B a n k o f York i n the f o l l o w i n g manner. banks throughout  New  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  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  percent.  On t a x a b l e i n c o m e i n e x c e s s o f $ 5 0 , 0 0 0 t h e m a r g i n a l t a x r a t e i s 48 percent.  M o s t 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 approximately  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 i n c o m e s u b s t a n t i a l l y e x c e e d s 15  $50,000.  A f t e r t a x , p r o f i t s are t h e r e f o r e approximately  0.52TT, w h e r e 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. w h e t h e r £mr  Given t h i s , e s t i m a t i o n r e s u l t s are robust to  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 i s noted that £n(1-t) = -x i s a constant and w i l l 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 s e c u r i t i e s gains or losses.  These  d o l l a r values are transformed into a c a p i t a l qains rate by dividing them by t o t a l investments. The user cost of investments i s calculated in the following manner U  INV  =  M M + UNCINV/INV) + (TAX/INV) + (GAINS/INV) ]/(1+R)} (5.19)  where INV i s t o t a l investment volume in d o l l a r s , and INCINV i s interest income received,  (INCINV/INV) i s the interest rate, (TAX/INV) denotes tax  savings on tax-exempt s e c u r i t i e s and loans in rate form, (GAINS/INV) i s the c a p i t a l gains rate, and R i s the discount 5.5.1.3  rate.  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. sheet.  Loans sold but serviced do not appear on the balance  This subcategory, representing  firms, i s deleted  mortgaqes sold to other  financial  from the analysis because i t constitutes a negligible  portion of the real estate p o r t f o l i o 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, t h e i r late charges and service fee income, and interest on loans purchased but not serviced.  -  It  ?S  -  i s assumed in the e m p i r i c a l model that each bank has  income e q u a l to the a c t u a l portfolio.  income r e c e i v e d on i t s r e a l  As a proxy f o r the expected default: r a t e ,  average net l o s s r a t e i s c a l c u l a t e d .  expected  e s t a t e mortqaqe the f i v e year  The user cost of r e a l e s t a t e m o r t -  qaqe loans i s c a l c u l a t e d in the f o l l o w i n g 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 e d and l o a n s purchased but not serviced, INCREM/REML i s the i n t e r e s t r a t e charged on r e a l estate loans, FEESRE/REML i s the service fee and l a t e charge LOSSRE/REML i s the expected default rate, and R is the discount 5.5.1.4  income,  rate.  Instalment Loans  Instalment  loans consist of d i r e c t consumer l o a n s ,  i n d i r e c t consu-  mer loans, check c r e d i t , commercial and eguipment loans, and f l o o r  plan  loans which r e f e r to advances made for financinq i n v e n t o r i e s of d u r a b l e goods such as automobiles, equipment and appliances.  It  i s customary f o r  most banks having f l o o r plan loans to record them i n the i n s t a l m e n t department,  loan  since the s a l e of these items to the consumer u s u a l l y g e n e r -  ates instalment paper f o r the bank.  Typical c r e d i t e x t e n s i o n s in the  commercial and equipment category are single payment l o a n s ,  trailer  loans, commercial instalment loans and farm and o t h e r heavy equipment loans. Income from instalment loans comprises i n t e r e s t and a discount. To obtain an i n t e r e s t r a t e , t h i s income i s divided by the t o t a l d o l l a r  - 99 -  volume of  instalment  loans or INCIN/iNSTAL.  approximated by the dollar volume of  five  The e x p e c t e d default r a t e  year average net  is  losses divided  by the t o t a l d o l l a r volume, or LOSSIN/INSTAL, so U  1 N  = 1 - {[1+(INCIN/IHSTAL) - (LOSSIN/INSTAL)]/(1+R)}  (5.21)  where again R i s the discount rate. 5.5.1.5  Credit Card Loans Credit card function data are collected for card banks.  bank f u l l y funds the credit card outstanding report the number of accounts,  balances  A card  and has records to  account usage and volume of credit losses.  Merchandise or r e t a i l volume is average assets reported by c r e d i t card business generated loans to pay  from sales s l i p s , dealer discounts and  for the sales s l i p s .  volume outstanding  retail  The cash advance volume i s the average  for direct cash advances to card holders.  Merchandise  or r e t a i l volume and cash advance balances summed equals t o t a l c r e d i t card balances The  outstanding.  income earned on t o t a l credit card balances  outstanding,  CRC,  includes merchant discount, net intercharge fees, merchant charge loan interest, and cash advance interest and fees.  There are also d a t a on  f i v e year average net credit losses which are used to approximate default rate. U  C R C  where UQ^Q  the  the  The user cost for credit card loans i s calculated as  = 1 - {[1+(INCCC/CRO - (LOSSCC/CRC)]/(1+R)} i s the user cost of credit card loans, CRC  is total  (5.22) credit  card balances outstanding, INCCC/CRC i s the interest rate plus the service charge rate and LOSSCC/CRC i s 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 , ann Other Loans 1  Commercial, agr i c u 1t ur.i i and l e a s e d eguipment related  incomes a r e r e p o r t e d s e p a r a t e l y  and o t h e r and  loan f u n c t i o n .  l o a n ha I duces and  i n the c o m m e r c i a l ,  agricultural  loans an- ! i s l e d at hook  Leased >'qu i pment  i n c l u d e bank-owned equipment leased to o t h e r f i r m s , o t h e r than  p r o c e s s i n g equipment.  The a g r i c u l t u r a l  those c a r r i e d  departments.  Commercial loans i n c l u d e o v e r d r a f t s . agricultural  data  loans i n c l u d e a l l to the farm  s e c t o r except  commercial,  value  in the r e a l e s t a t e loan o r i n s t a l m e n t  and o t h e r loans i s mainly  loan  The income from interest  income.  A g a i n , t h e r e a r e a l s o data on the f i v e year averaqe net l o s s e s i n d o l l a r terms. IL  L AU  The user c o s t f o r commercial,  a g r i c u l t u r a l , and o t h e r  , i s calculated 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 c o m m e r c i a l , o t h e r l o a n s , INCCAO/COMAOL  i s the i n t e r e s t  COMAOL i s t h e c a l c u l a t e d d e f a u l t r a t e proxy 5.5.1.7  r a t e earned  on them, I.0SSCA0/ rate.  User Cost f o r Aggregate Loans  t h r e e sample y e a r s .  ment l o a n s , c r e d i t  Investments,  form  f o r each bank.  f o r the o t h e r years i n the sample p e r i o d .  c o s t of l o a n s ,  i j  -4.666 p e r c e n t  A  instal-  c a r d loans and commercial and o t h e r loans a l l have  a l s o the case  L O a N  in Table '> . '  r e a l e s t a t e mortgage l o a n s ,  n e g a t i v e u s e r c o s t s and hence c o n s t i t u t e o u t p u t s  and  a g r i c u l t u r a l and  and R i s the d i s c o u n t  Oata on user c o s t s are t a b u l a t e d i n summarv for  loans,  >  w  d  S  " 3.107 percent  i n 1978.  Conseguently  T h i s was  The average user  i n 1973, -3.782 percent  i n 1975  the mean net r e t u r n a f t e r  TABLE 5.10A -  Loan S t a t i s t i c s - User Costs (per cent, net return after  1 0 1 -  discounting)  Three Sample Years 19 7 3  Mean  Standard Deviation  Minimum  Maximum  User cost of investments, U _, 1NV  -2.803  0.473  -4.082  -2.187  User cost of mortgages, U  -2.462  0.330  -3.355  -2.089  -5.230  1.058  -6.939  -3.069  -16.559  -1.902  Variable T1  User cost of instalment U  R £  loans  IN  User cost of credit  loans,  -11.379  12.091  User cost of commercial and other loans, U ^  -3.062  0.683  -4.273  -1.390  User cost of loans, average  -3.107  0.346  -3.698  -2.354  Mean  Standard Deviation  Minimum  Maximum  User cost of investments, U ' INV  -3.631  0.58o  -4.747  -2.634  User cost of mortgages, U RE  -2.775  0.271  -3.245  -2.333  -5.792  1.167  -7.825  -2.729  -6.873  4.657  -13.217  -4.831  User cost of commercial and other loans, U  -3.844  0.782  -5.138  -1.415  User cost of loans, average  -3.782  0.451  -4.829  -2.862  U  U  CRC  1 L0AN =U  19 7 5 Variable  D r  User cost of instalment U  IN  User cost of credit U  loans  loans,  CRC  C Q L  U  1 L0AN =U  -  T a b l e 5.10A  102  -  continued  19 7 8 Mean  Standard Deviation  Minimum  Maximum  User cost of investments, U..., INV  -4.242  0.742  -5.639  -2.222  User cost of mortgages, U  -3.944  0.507  -5.672  -3.305  -6.718  0.827  -9.171  -5.194  -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  -4.666  0.509  -5.283  -3.326  Variable r  R £  User cost of instalment loans U  IN  User cost of credit U  U  loans,  CRC  1 L0AN =U  -  discounting  ranged from 3.107 percent to 4.666 percent on  Balance sheet e n t r i e s instalment  loans,  Table 5.10B. varying  for investments,  c r e d i t card l o a n s ,  The sample  REVLOAN(t)  where U(t)  = U,(t)  and N(t)  aggregate loans  N(t)  I  loans  loan  = -{U  at time t .  volumes of i n v e s t m e n t s , card loans, It dollars.  C R C  1NV  *INV + U  * C R C + IJ  The user c o s t s ,  are  in  portfolios  noted that  all  the type of l o a n .  *C0MA0l_}  (5.24)  and q u a n t i t y ^CRC  instalment  and other loans  loans,  using  the T o r n q v i s t  loans which may a l s o the user cost  denote t o t a l o u t s t a n d i n g = {iNV  is  '  credit  are measured  in  is  and length  the aggregate user  be more  of  i n d e x i n g procedure cost  risky.  c o n s t r u c t e d as f o l l o w s .  loan balances at time t .  + REML + INSTAL + CRC + C0MA0L}.  The aggregate user cost  a n c  r e f l e c t d i f f e r e n c e s i n c h a r a c t e r i s t i c s of  T h i s procedure would weight  For aggregate l o a n s ,  of  respectively.  These c h a r a c t e r i s t i c s i n c l u d e r i s k i n e s s  toward higher user cost  LOAN(t)  *REML +  the d i f f e r e n t loan q u a n t i t i e s  For these two reasons,  inappropriate.  or  REML, INSTAL, CRC, and CAO are the d o l l a r  and commercial, a g r i c u l t u r a l  is  Hh  in p e r i o d t ,  Uj^yj '-*RE' ^IN'  r e a l e s t a t e mortgages,  D i f f e r e n t user c o s t s  maturity.  T  denote r e s p e c t i v e l y the user cost  are f o r p e r i o d t and INV,  LOAN(t)  and l a r g e  denote the net revenue from loans  IN  is  e s t a t e mortgages  commercial and o t h e r  i n c l u d e s both s m a l l  U *INSTAL + U  C A Q  real  loans.  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)  U  103 -  Let  Then, (5.25)  - 105 -  U  l  (  t  )  =  U  U  or,  LOAN  CRC*  *  (t)  C R C  +  U  f U  INV*  CAO*  I N V  C O M A  +  U  ° ^ L  RE* / L  °  R E M L  +  U I  N  *  I  N  S  T  A  L  +  (5-26)  A N  substituting (5.24) into (5.25)  U  l  (  t  )  - "LOAN^)  =  -REVLOAN(t)/LOAN(t).  (5.27)  The aggregate quantity of loans at time C i s total outstanding balances LOAN(t).  loan  Summary s t a t i s t i c s on the aggregate user cost for  loans, U ^ Q ^ J , and the aggregate quantity of loans, LOAN are in Tables 5.10A and 5 . 1 0 B 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, i s constructed according to ( 3 . 1 ) and ( 5 . 1 8 ) .  The holding of  cash during the Hicksian period does not y i e l d revenue to the firm, but has an opportunity cost. "CASH"  1  -  Consequently, the user cost of cash i s  {i/Ci*)}.  < - > 5  28  where R i s the discount rate. This user cost i s applicable to excess reserves. Nearly a l l f i n a n c i a l firms must keep some minimum portion of assets in cash.  These  reserve requirements are generally based upon the types of deposit liabilities  the f i n a n c i a l firm possesses.  The banks i n this study are  members of the Federal Reserve System and hence must hold their reserves i n cash at the Federal Reserve Bank, or i n vault cash.  The required  reserves on deposits are accounted for i n the user cost calculations f o r  - 106 -  d e p o s i t s below.  These r e s e r v e s are the p r o p e r t y of the F e d e r a l  Reserve  Bank and do not have an o p p o r t u n i t y cost  to the bank as i n (5.28) because  of the p r o h i b i t i o n on use of t h i s c a s h .  F u r t h e r , s i n c e the c o s t  of  r e s e r v e r e q u i r e m e n t s i s accounted f o r by type of d e p o s i t , a d o u b l e counting arises  i f the c o s t  user c o s t of demand d e p o s i t s  i s a l s o a s c r i b e d to c a s h . i n c l u d e s the c o s t of the  For example, the reserve  r e q u i r e m e n t s on such d e p o s i t s , t o be h e l d i n c a s h .  5.5.3  Demand D e p o s i t s The user c o s t on the j t h type of d e p o s i t  t o (3.3)  which  is c a l c u l a t e d accordinq  is,  _  (1 - k. + r. - s . + b.)  u. = -(1  -  1  - k.)  + f  +  ' ^  I  j=DD,TD  J R )  1 + r. + b. + Rk. J j J  (5.29)  s. .71  w i t h DD and TD r e s p e c t i v e l y d e n o t i n q demand and time d e p o s i t s . In the case of d e p o s i t s , r a t h e r than r e c e i v i n g i n t e r e s t , t h e 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 . r^.  The d e p o s i t  i n s u r a n c e r a t e , b^,  r a t e per d o l l a r of d e p o s i t . t y p e of d e p o s i t  Interest  i s k.,  payable by the bank i s denoted by i s e x p r e s s e d i n terms o f a premium  The r e s e r v e requirement r a t e f o r the j t h  w h i l e s^ i s the s e r v i c e charge r a t e t h a t an  average d o l l a r of d e p o s i t j y i e i d s to t h e bank per time p e r i o d , w i t h R being the d i s c o u n t  rate.  For most of the sample p e r i o d , 1973 t o 1978, financial deposits.  i n s t i t u t i o n s were p r o h i b i t e d from p a y i n g N e g o t i a b l e o r d e r s of w i t h d r a w a l (NOW)  federally  insured  i n t e r e s t on demand  a c c o u n t s , which are  - 107 -  e s s e n t i a l l y demand deposits with interest payments, were authorized in only a few states. to offer NOW  Massachusetts and New  Hampshire were f i r s t  accounts on January 1, 1974.  Authorization to issue  accounts was extended to similar i n s t i t u t i o n s throuqhout New February  27,  1976,  and  considers banks in New Reserve D i s t r i c t 2. in 1978  in New  permitted  England on  York State on November 10, 1978.  York and New  NOW  Our  study  3ersey which are located in Federal  For those banks which reported NOW  interest expense  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 d o l l a r amount paid for Federal Deposit Insurance Corporation (FDIC) premiums on demand deposits.  These are converted to a premium rate by d i v i d i n g their d o l l a r  value by t o t a l demand deposits dollar volume. Information on reserve requirements Bulletin.  comes from the Federal Reserve  Demand deposits subject to reserve requirements  are gross  demand deposits minus cash items in process of c o l l e c t i o n and demand balances due from domestic banks. are these net balances.  Demand deposit balance data in the FCA  Reserve requirement  schedules are graduated, and  each deposit interval applies to that part of the deposits of each bank. The  reserve requirement  compiled  in Table 5.11.  schedules for the period 1973  to 1978  For those years in which reserve  changed, an averaqe reserve requirement demand deposits l i s t e d in the FCA data.  have been  requirements  is calculated to apply to average These are in Table  5.12.  Income i s earned on demand deposits by levying service and penalty charges.  The service charge rate on demand deposits i s c a l c u l a t e d 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 i n M i l l i o n s of Dollars. Requirements are in percent of deposits.) Net Demand Deposits ($M.)  Effective Date  0-2  2-10  10-100  1972 - November 9  8  10  12  November 16  -  -  1973 - Duly 19  -  1974 - December 12  100-400  over 400  16.5  17.5  -  13  -  10.5  12.5  13.5  18  -  -  -  -  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 i n effect 1978 - December 31  7  V.5  11.75  12.75  17.25  Sources:  Federal Reserve B u l l e t i n , 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). Net Average Yearly Demand Deposits ($M.)  1  Year  0-2  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  7  9.5  11.75  12  16.25  2-10  10-100  100-400  over 400  ... _  i  T A B L E 5.13 Demand D e p o s i t S t a t i s t i c s Three Sample Y e a r s  Variable  Mean  Penalty rate, (PEN/DD)  1  FDIC Insurance premium rate (FDIC/DD)  1  Reserve effect (R*RESREQ)  1  Service charge rate (SERVJ/DD  1  Return on $1 of demand deposit Return on $1 discounted  3  2  1  Minimum  Maximum  0  0.6060  0.1657  0.1438  0.0347  0.0062  0.0110  0.0400  0.5547  0.0775  0.4589  0.7947  0.6128  0.2917  0.1760  1.322  0.9981  0.0043  0.9866  1.0061  0.9553  0.0041  0.9443  0.9630  Quantity of demand deposits,^DO 107.68 User cost of demand deposits,  Standard Deviation  -4.4662  153.39 0.4100  3.845 -5.567  422.07 -3.7054  DD  U  19 7 5 Variable  Mean  Penalty rate, (PEN/DD)  1  FDIC Insurance premium rate (FDIC/DD)  1  Reserve effect (R*RESREQ)  1  Service charge rate (SERVJ/DD  1  Return on $1 of demand deposit Return on $1 discounted  3  2  DD  U  Maximum  0.1376  0.036  0.6285  0.0410  0.0030  0.0343  0.0463  0.5502  0.0521  0.4632  0.6014  0.6301  0.2962  0.17505  1.422  0.9977  0.0042  0.9854  1.0037  0.9538  0.0040  0.9420  0.9596  1  1  Minimum  0.1957  Quantity of demand deposits, *DO 101.62 User cost of demand deposits,  Standard Deviation  -4.6253  142.61 0.4047  3.457 -5.7973  388.97 -4.0451  111-  •able 5.13 continued  19 7 8 Variable  Mean  Interest rate, (NOWINT/DO)  1  FDIC Insurance premium rate (FDIC/DD)  1  Reserve effect (R*RESREQ)  1  Service charge rate (SERVJ/DD  1  Return on $1 of demand deposit Return on $1 discounted  3  2  U  1  Minimum  Maximum  0.0006  0.0014  0  0.0046  0.0392  0.0035  0.03235  0.0449  0.4750  0.0660  0.3831  0.6553  0.7167  0.3309  0.2158  1.6776  0.9980  0.0036  0.9884  1.0046  0.9593  0.0035  0.9501  0.9656  Quantity of demand deposits,**DD 110.41 User cost of demand deposits,  Standard Deviation  -4.071  150.48 0.3495  4.065 -4.991  400.86 -3.436  D0  'Percent.  Return on  $1 of Demand deposits = {1 - (N0WINT/D0) + (FDIC/DO) + R*RESREQ - ((SERV + PEN)/DD)}.  3  Return 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 + ( N n w i N T / n n ) + (FDIC/OD) + R*RESREO)  -  (SERV+PEN)/D0) }/(HR) where DD is total demand deposits,  (5.30)  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 i s  always negative for each bank in a l l 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 function 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 at Federally Insured Commercial Banks (percent per annum) Type and Maturity of Deposit 1.  Savings Other time deposits (multiple & single maturity unless otherwise indicated) 30 - 89 days  2.  Multiple-maturity  3. Single-maturity 90 days t o 1 year 4.  On E f f e c t Dec. 31/1978  6.  Percent  Effective Date  Percent  Effective Date  5  7/1/73  4.5  1/21/70  5  7/1/73  4.5  1/21/70  5  9/26/66  5.5  7/1/73  2 t o 2-1/2 years  8.  2-1/2 t o 4 years  9. 4 t o 6 years  5  7/20/66 9/26/66  1 t o 2 years  7.  - 113 -  Previous Maximum  Multiple-maturity  5. Single-maturity  Deposits  6  7/1/73  5.5  1/21/70  5.75  1/21/70  6.5  7/1/73  5.75  1/21/70  7.25  11/1/73  a  -  10.  6 t o 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 t o governmental u n i t s ( 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 J u l y 1, 1973 and October 31, 1973, there was no c e l l i n g f o r 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 l i m i t e d t o 5 percent of i t s t o t a l time and savings d e p o s i t s . Sales l n excess of that amount, as w e l l as c e r t i f i c a t e s o f l e s s than $1,000 were l i m i t e d 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. Source:  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, V o l . 62, January 1976, p. A10 and No. 1. V o l . 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 t o t a l time deposits  d o l l a r volume. The required reserve rate varies not only with respect to the quantity, or d o l l a r volume, of time deposits held, but also with respect to their maturity.  The FCA d i v i s i o n 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  i s equal to required reserves on time deposits plus one percent of such deposits.  16  Some income i s 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 i s U = -1 + {l + (TDINT/TD) + (FDICT/TD) + R^RESREOT T D  (SERVT/TD)}/(UR)  (5.31)  where TD is t o t a l time deposits, TDINT/TD is the interest rate payable by the f i n a n c i a l i n s t i t u t i o n s , FDICT/TD is the insurance premium rate payable on time deposits, RESREQT is their  reserve requirement, and SERVT/  TD i s the service charge rate on an average d o l l a r of time deposits.  - 115 -  The data for time deposits are tabulated in summary form in Table 5.15 for three sample years. the sample.  The data are s i m i l a r for the other years in  The user cost for time deposits i s always p o s i t i v e 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 i n a n c i a l f i r m .  With a zero discount  rate a l l of the user costs for time deposits are p o s i t i v e for each bank over the sample period, so t h 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 d e p o s i t s , 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 d i s t i n g u i s h e d 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 n a n c i a l o b l i g a t i o n s 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 U  is  = - 1 t {l + BPFINT/BPF} / ( H R )  (5.32)  where BPFINT represents the i n t e r e s t paid by the bank for borrowed and purchased funds, and BPF the t o t a l balance outstanding. p o s i t i v e , t h i s category represents an input.  I f U^p^.  is  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 = - 1 + { 1 + OLINT/OL} / (HR)  is (5.33)  - 116 T A B L E 5.15 Time D e p o s i t S t a t i s t i c s Three Sample Y e a r s 19 7 3 Variable  Mean  Standard Deviation  Minimum  Maximum  Interest rate (TDINT/TD)  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)  0.1557  0.0159  0.1343  0.1782  Service charge rate (SERV/TD)  0.0151  0.0226  0  0.1000  Return on $1 of time deposit  1.0508  0.0034  1.0464  1.0572  1.0058  0.0033  0.0015  1.0119  1  1  1  Return on $1 discounted  2  3  Quantity of time deposits,^TD User cost of time deposits, U  1  100.44 0.5794  TD  108.46  4.60  316.92  0.3268  0.1526  1.1906  Standard Deviation  Minimum  Maximum  19 7 5 Variable  Mean  Interest rate (TDINT/TD)  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)  0.1725  0.0247  0.1381  0.1964  Service charge rate (SERV/TD)  0.0159  0.0247  0  0.1091  Return on $1 of time deposit  1.0540  0.0027  1.0477  1.0584  1.0076  0.0026  1.0016  1.0118  1  1  1  Return on $1 discounted  2  3  Quantity of time deposits,^TD User cost of time deposits, TD  1  112.96 0.7630  117.82 0.2562  5.10 0.1623  333.58 1.1807  -  117 -  Table 5.15 continued  19 7 8 Mean  Standard Deviation  Interest rate (TDINT/TD)  5.073  0.4175  4.0327  5.6856  FDIC insurance premium rate (FDIC/TD)  0.0392  0.0035  0.0324  0.0449  Reserve effect (R*RESREQT)  0.1404  0.0150  0.1210  0.1645  Service charge rate (SERV/TD)  0.0166  0.0261  0  0.1040  Return on $1 of time deposit  1.0524  0.0043  1.0414  1.0585  1.0116  0.0042  1.0010  1.0175  Variable 1  1  1  1  Return on $1 discounted  2  3  Quantity of time deposits,**TD  117.88  User cost of time deposits, U * TD A  0.4164  5.41 1.0350  Percent.  Return on $1 of Time deposits = {l R*RESREQT - (SERVT/TD)}.  3  1.1565  132.15  Minimum  • (TDINT/TD) + (FDIC  Return on $1 discounted = {1 + (TDINT/TD) + (FDIC/TD) + R*RESREQT - (SERVT/TD)}/(1 + R).  ^Millions of dollars.  Maximum  425.71 1.7512  IIS  -  where the the  total  amount of  other  d a t a on o t h e r in Table 5.5.6  interest  p a i d by  liabilities  liabilities  and  As  liabilities  loans  and  lender,  borrowed and  are  purchased  is  0L1NT  U*OL.  and  Summary  funds are  between t h e  two.  The n e t  borrowed and  tabulated  loans  categories  t h e bank  Net  loans  include s e c u r i t i e s ,  and  net or  loans. lender.  investments  similar  financial  are the d i f f e r e n c e  - EPF  - OL.  real estate  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  and p u r c h a s e d  of  and  is  + REML + INSTAL + CRC + COMAOL assets  cost  As b o r r o w e r ,  liabilities.  loan p o s i t i o n of  and i n v e s t m e n t  of v a r i o u s  the balance sheet.  i n d i c a t e d as  NLOAN = INV  the user  p u r c h a s e d funds  t h e bank c a n be e i t h e r a b o r r o w e r  records  side of are  instalment,  user c o s t s f o r  investments,  commodities  borrowed  category  Expenditures  permits the d e r i v a t i o n of  t h e bank  on t h e a s s e t  Loan  OL.  in t h i s  Loans  The c a l c u l a t i o n of  For  is  bank  5.16.  Net  other  the  -  loans.  funds  and o t h e r  liabilities.  f r o m t h e l o a n and i n v e s t m e n t  portfolio  is  (5.34)  mortgages,  L i a b i l i t i e s are  T o t a l net  revenue  EXNLOAN = -UJ..... * I N V + U *REML + U... * INSTAL + U - „ * C R C INV RE IN CRC D  D C  + tl  C A 0  *C0MAOL) -  where t h e n e g a t i v e costs net  siqn  (Uppj. * B P F + IJ before the asset  t o p o s i t i v e numbers.  loans  *0L) categories  Hence EXNLOAN i s  (5.35) converts  positive.  the  user  The u s e r  cost  is  UL = EXNLOAN/NLOAN or t o t a l cost Table  of  net  revenues  d i v i d e d by b a l a n c e s  and b a l a n c e o f n e t 5.17.  (5.36)  loans,  outstanding.  and t h e i r n e t  revenues,  D a t a on t h e are  indicated  user in  Table 5.16  119 -  Borrowed and Purchased Funds and Other  Liabilities,  Sample S t a t i s t i c s Three Sample Y e a r s  1 9 7 3 Standard D e v i a t ion  Mean  Min imum  Maximum 0.208  User C o s t , Borrowed and Purchased funds  0.040  0.041  0.012  Q u a n t i t y , Borrowed and Purchased funds ($m.)  7.040  16.743  0  63.885  User C o s t , bilities  0.025  0.068  0.018  0.032  0.923  2.216  0  9.022  Other  Lia-  Q u a n t i t y , other l i a b i l i t i e s ($m.)  1 9 7 5  Mean User C o s t , Borrowed and Purchased Funds  Standard Deviation  Minimum  Maximum 0.016  0.011  0.004  0.0004  10.924  30.670  0  User C o s t , Other Liabilities  0.019  0.010  0.009  0.041  Q u a n t i t y , Other L i a b i l i t i e s ($m.)  6.099  15.087  0  54.061  Minimum  Maximum 0.042  Q u a n t i t y , Borrowed and Purchased Funds ($m.)  127.640  1 9 7 8  Mean  Standard Deviat ion  User C o s t , Borrowed and Purchased Funds  0.035  0.005  0.030  Q u a n t i t y , Borrowed and Purchased Funds (Sm.)  7.706  18.420  0  68.996  User C o s t , Other Liabilities  0.032  0.009  0.012  0.061  44.815  67.230  0.517  228.220  Q u a n t i t y , Other L i a b i l i t i e s ($m.)  - 120 Table 5.17  Net Loans, User Cost and Q u a n t i t i e s  (revenue measured as n e g a t i v e net e x p e n d i t u r e s )  19  Standard Deviation  Mean User C o s t s , Net Loans Q u a n t i t y , Net ($m.) Revenue, Net ($m.)  loans  loans  Revenue, Net Loans  ($m.)  -0.037  -0.024  202 .440  250.310  8.598  728.640  6.140  7.546  0.202  24.556  Minimum  Maximum  -0.038  0.005  -0.048  -0.029  219.960  265.190  9.178  800.550  8.264  9.886  0.269  27.230  Mean  Q u a n t i t y , Net Loans ($m.) Revenue, Net Loans ($m.)  7 5 Standard Deviation  19  User C o s t s , Net Loans  Maximum  0.004  Mean  Q u a n t i t y , Net Loans ($m.)  Min imum  -0.032  19  User C o s t s , Net Loans  7 3  7 8 Standard Deviation  Minimum  Maximum  -0.047  0.005  -0.053  -0.033  265.390  306.560  10.643  854.110  6.099  8.576  0.302  30.354  -  5.5.7  121 -  Financial Capital On the balance  completed.  Assets  sheet, a l l items  i n v o l v i n g user c o s t s a r e now  i n c l u d e f i n a n c i a l goods, and the c a t e g o r i e s  are cash and v a r i o u s l o a n s and investments. financial  liabilities  together  are equal  less  to p h y s i c a l a s s e t s and  shareholders'  equity.  of the bank.  Further, i f f i n a n c i a l assets  in  F i n a n c i a l assets  included  The l a t t e r two c a t e g o r i e s c o n s t i t u t e the c a p i t a l  c u r r e n t d o l l a r s , then t o t a l c a p i t a l  and l i a b i l i t i e s  i s measured  are r e p o r t e d  in current d o l l a r s .  A l s o , s i n c e t h i s i s a b a l a n c e sheet i t e m , i t i s a s t o c k . Total capital  is  CAPITAL = CASH + INV + REML + INSTAL + CRC + COMAOL - BPF - OL - DO - TD or  c a s h , l o a n s and i n v e s t m e n t s l e s s borrowed and purchased funds  deposits. in  (5.37) and  C a p i t a l i n p h y s i c a l and f i n a n c i a l form i s assumed t o be f i x e d  the short run.  T h i s 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 P r o f i t s v a r i a b l e p r o f i t s , or q u a s i - r e n t s f o r each bank i n each year  The are  constructed  the c a l c u l a t e d user c o s t s f o r b a l a n c e  utilizing  sheet  i t e m s , t h e i r d o l l a r v a l u e s , and e x p e n d i t u r e s on l a b o 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 **  =  ~' 1NV* U  -(U  C A S H  I N V  +  U R  E  *  R  E  M  L  * » *INSTAL 1 N  *CASH) - (U *™>) D D  - (  n T D  + U  C R C  *CRC + U  * T D ) - [(EXL  CAQ  *COMAOL}  + EXM)/(1 + R)] (5.32)  where L l ^ y , " p p > ' [ N ' ' V R C l  e s t a t e mortqaqes,  instalment  a g r i c u l t u r a l and o t h e r loans  "cAO  a  r  e  t :  ^  e  u  s  e  r  c  o  s  t  s  °f  investments,  l o a n s , c r e d i t card loans and c o m m e r c i a l , respectively.  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 v a l u e s of i n v e s t m e n t s , e s t a t e mortgages,  instalment  real  loans, c r e d i t card loans,  real  and commercial  a q r i c u l t u r a l and o t h e r loans held on the b a l a n c e sheet d u r i n q the H i c k s i a n time  period.  The term - { U  *INV + U  T  INV  *REML + U , *INSTAL +  Kh  IN  U^ *CRC + U^^COMAOL} r e p r e s e n t s the net revenue from l o a n s h e l d by the R  financial  institution.  and o t h e r l i a b i l i t i e s  The user c o s t s of borrowed and purchased r e s p e c t i v e l y are U^pp  t h e b a l a n c e s h e l d of these l i a b i l i t y t h e s e are s u b t r a c t e d from asset l o a n s and i n v e s t m e n t s .  firm -(U^^DD)  A N C  '  AN(  ^ ^  A R E  So t o t a l e x p e n d i t u r e s on  loan revenue to y i e l d net revenue from  The term -(U^ (.^*CASH) r e f l e c t s the c o s t A  h o l d i n g funds i n cash f o r m . financial  items.  and UQ^'  funds  of  S i n c e demand d e p o s i t s are an o u t p u t o f the  i s the net revenue of h o l d i n g demand  Time d e p o s i t s are an i n p u t , so -(IJ  *TD)  deposits.  i s the net c o s t of h o l d i n g them.  The e x p e n d i t u r e s on l a b o r and m a t e 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 s c o u n t e d 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 p e r i o d . V a r i a b l e p r o f i t s do not i n c l u d e the e x p e n d i t u r e 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,  variable profits  i n c l u d e a l l r e t u r n s t o c a p i t a l , and indeed the e l a s t i c i t y o f p r o f i t s t o c a p i t a l , and the r a t e of r e t u r n on c a p i t a l can be c o n s t r u c t e d 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 f o r each bank i n each year are a i l positive.  The sample s t a t i s t i c s  f o r each vear are i n T a b l e s 5.IS and  5.19,  C o n c l u d i n q Remarks  5.7  This concludes data. for  the d e s c r i p t i o n of procedures  for constructinq  The d a t a c o n t a i n v a r i a b l e p r o f i t s and user c o s t s  f i n a n c i a l and p h y s i c a l qoods.  and  quantities  The user c o s t method on f i n a n c i a l  qoods can be q e n e r a l i z e d t o a wider and f i n e r c l a s s i f i c a t i o n than applied here.  the  On the p h y s i c a l qoods s i d e ,  l a b o r , 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 a d j u s t e d f o r q u a l i t y  change.  that  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 c u r r e n t m i l l i o n s of  Year  Mean  1973  5.863  1974  Standard Deviation  dollars)  Minimum  Maximum  7.705  0.221  23.788  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 Variable Profits  ( i n current  m i l l i o n s of  dollars)  Year Bank Number  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 p r e m i s e s " as an asset on ha Lance s h e e t a.  Entered i s equipment V I t Z v=1 1=1 where <J>  1  the v a l u e of hank p r e m i s e s , f u r n i t u r e and at book v a l u e l e s s accumulated d e p r e c i a t i o n or I <t> .k . - d. $ k = E (1 -D ) <b k 1=1 i s the purchase p r i c e of c a p i t a l qood i of v V 1  V 1  1  V l  v l  1  v  l  v  i  v intaqe, k. i s c a p i t a l qood i of v i n t a q e 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 r a t e f o r c a p i t a l qood i ,  1=1,...,I A.  I n c l u d e d in bank p r e m i s e s : 1. Bank premises t h a t are a c t u a l l y owned by the bank and i t s c o n s o l i d a t e d 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 o c c u p i e d (or are to be o c c u p i e d i f under c o n s t r u c t i o n ) by the bank or i t s branches and consolidated subsidiaries. 2.  L e a s e h o l d improvements, v a u l t s and f i x e d machinery equipment.  3.  Remodeling c o s t s to e x i s t i n g bank  ' k.  Real estate acquired for future  5.  and  premises. expansion.  P a r k i n q l o t s , whether a d j o i n i n q or not a d j o i n i n g bank p r e m i s e s , that are owned by the bank and t h a t are used by customers or emp] oyees -»f the bank.  See R e p o r t s of C o n d i t i o n and Income by S t a t e Member Banks o f the F e d e r a l Reserve System t h a t Have Only Domestic O f f i c e s t h a t Have L e s s Than S100 M i l l i o n i n T o t a l A s s e t s , [ 1 9 7 8 ] , p. 22  -  R.  C.  Included  2.  The amounts assigned to l e a s e s assumpt ion t r a n s a c t i o n s .  3.  The amount of s t o c k s , bonds, or o t h e r a s s e t s 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 c o r n o r a t i o n s .  in purchase  and  Any method of d e p r e c i a t i o n conforminq to a c c e p t a b l e a c c o u n t i n g p r i n c i p l e s may be u s e d .  Cost Amount r e p o r t e d should r e p r e s e n t the amount d e d u c t i o n of mortgages or o t h e r l i e n s . Expense o f Bank P r e m i s e s ,  T h i s item income) of expense o f expense of A.  2  acquired  its  Depreciation:  Occupancy a.  i n f u r n i t u r e and f i x t u r e s :  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, b r a n c h e s , and i t s c o n s o l i d a t e d s u b s i d i a r i e s .  1.  2.  -  1.  1. D.  127  before  Net  r e f l e c t s the net expense (or i n some c a s e s net bank premises occupancy. The amount of "occupancy bank p r e m i s e s , n e t " r e p r e s e n t s the g r o s s occupancy bank premises l e s s r e n t a l income.  The g r o s s occupancy expense of bank premises  includes:  1.  Compensation ( i n c l u d i n g supplementary b e n e f i t s ) o f t h o s e o f f i c e r s and employees o f the bank and i t s c o n s o l i d a t e d s u b s i d i a r i e s who spend the major p r o p o r t i o n 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 r e c u r r i n g d e p r e c i a t i o n or j m o r t i 7 a t ion charges a p p l i c a b l e to the current: p e r i o d , whether r e p r e s e n t i n g d i r e c t r e d u c t i o n s in the c a r r y i n g v a l u e of the a s s e t s , i n c l u d i n g c a p i t a l l e a s e a s s e t s , or a d d 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.  See I b i d . , p. 70.  - Ps  3.  -  Ord inars i v n a i rs to hank premi ses and l e a s e h o l d improvement $, and the c>st leasehold not p l a c e d o n the b a n k ' s hooks as an a s s e t . i f  H.  M l c u r r e n t expenses, not i n c l u d e d above, connected w i t h the use o f bank p r e m i s e s , e . g . , the cost o f h e a t , e l e c t r i c i t y , water, o u t s i d e . j a n i t o r s e r v i c e s and s u p p l i e s , f i r e i n s u r a n c e .  5.  A l l o p e r a t i n g lease r e n t s paid on bank premises p a r k i n g Lots.  6.  i n t e r e s t on mortgages, Liens or o t h e r encumbrances o n bank premises owned, i n c l u d i n g the p o r t i o n of c a p i t a l l e a s e payments r e p r e s e n t i n g i n t e r e s t expenses, but not such expense on " r e a l e s t a t e " o t h e r than bank premises.  7.  A l l property and o t h e r taxes paid or accrued r e l u t i n q to bank premises and l e a s e h o l d improvements.  8.  Any p o r t i o n of c a p i t a l l e a s e payments r e p r e s e n t i n g executory c o s t s e . g . i n s u r a n c e , m a i n t e n a n c e , and taxes.  R e n t a l Income  b.  Includes:  r e n t a l s from r e g u l a r t e n a n t s of the b a t i k ' s building. s h o r t - t e r m r e n t a l s of o t h e r bank f a c i l i t i e s except s a f e d e p o s i t boxes.  F u r n i t u r e and Equipment  Expense  Includes: A.  3  and  A l l r e n t a l s charged f o r the use of b u i l d i n g s not i n c i d e n t to the use of the premises by the r e p o r t i n g bank, and i t s c o n s o l i d a t e d s u b s i d i a r i e s . a.  a.  r.  4.  1.  3.  i i n n n i v c n t c i i t  See I b i d . ,  Normal and r e c u r r i n g 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 charges a p p l i c a b l e to the r e p o r t p e r i o d , whether r e p r e s e n t inn d i r e c t r e d u c t i o n s in the c a r r y i n g v a l u e of the a s s e t s i n c l u d i n q c a p i t a l lease a s s e t s , or a d d 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 a c c o u n t s .  p. 7 1 .  ]?.?  -  B.  A l l operjti.no, lease r e n t s p a i d o n o f f i c e machines, i n c l u d i n g data p r o c e s s i n g equipment.  C.  Ordinary r e p a i r s to f u r n i t u r e and o f f i c e machines, including servicing costs.  0.  The p o r t i o n of c a p i t a l lease payments 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.  representing  - 130 -  NOTES 1  2  F u n c t i o n a l Cost Ibid.,  Analysis  - Average  Banks [1979]  p. i .  p. 18  The Tornqvist s p e c i f i c a t i o n for c o n s t r u c t i n g subagqreqates 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 [1976]. 3  and  The same p r i c e s a r e u s e d i n t h e n a t i o n a l a c c o u n t s . See S u r v e y 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 a n d 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 1 9 2 9 - 7 4 [ 1 9 7 5 ] , and W h o l e s a l e P r i c e s a n d P r i c e I n d e x e s " , Supplement [ 1 9 7 4 - 1 9 7 8 ] , S e e Table 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 C o n s u m p t i o n 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 v e y o f C u r r e n t B u s i n e s s , S u p p l e m e n t , 3 u l y 1 9 8 1 , p. 6 7 . 5  6  The  model w i l l  use economic d e p r e c i a t i o n  rates.  •7  F o r more d e t a i l e d i n f o r m a t i o n s e e t h e A p p e n d i x  to Chapter  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 equipment. F u r n i t u r e and e q u i p m e n t c a p i t a l r e f e r s t o m o v e a b l e f u r n i t u r e and e q u i p m e n t . Q  Specifically, Department. 1 0  85  ^The  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 h e T r e a s u r y  percent of B u l l e t i n F half-life  lives.  for a geometric  series  i s equal  to 1/d  n >  hence  d  = 2 / L . H u l t e n and W y k o f f [ 1 9 7 7 ] e s t i m a t e d e c o n o m i c 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 . In 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 approximate t h e 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 the e a r l i e s t years of the asset l i f e . 12 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 r u n may d e p e n d 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 associated with c l o s i n g or opening. T h i s i s p a r t i c u l a r l y t h e 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 t o o b t a i n a s a t e m p o r a r y s h o r t t e r m 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 e m p l o y e e 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 h e 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 b a n k , 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 , b u 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 d e p o s i t r a t e f o r each bank m each year i s a l s o t e s t e d . Those bdnks w i t h a hiqh p r o p o r t i o n of c e r t i f i c a t e s of d e p o s i t have d high time d e p o s i t r a t e and q u a s i - r e n t s f o r t h e s e i n s t i t u t i o n s ar n e g a t i v e u s i n g the time d e p o s i t r a t e as the d i s c o u n t r a t e . 1 4  S e e F u n c t i o n a l Cost A n a l y s i s p.  [1978],  1 5  Ibid.,  1 6  S e e F e d e r a l Reserve B u l l e t i n [ 1 9 7 9 ] .  p . 10.  19b.  See F u n c t i o n a l Cost A n a l y s i s [19781,  p.  8.  -  Hi  -  CHAPTER 6 SPECIFICATION AND HYPOTHESIS TESTING 6.1  Introduction The  e s t i m a t i n a system c o n s i s t s of a p r o f i t  of net suppLies  f o r outputs and i n p u t s .  p o s i t i v e net s u p p l i e s inputs.  The c o n v e n t i o n adopted  o b t a i n f o r outputs and n e g a t i v e  i s that  net s u p n L i e s f o r  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 i n p u t s and o u t p u t s a r e  d e f i n e d t o be n o n - n e o a t i v e , p o s i t i v e user c o s t s tive,  f u n c t i o n and a s c r i e s  n e q a t i v e user c o s t s o b t a i n f o r o u t p u t s and  for inputs.  Hence net demands  and net demands f o r i n p u t s p o s i t i v e .  non-neqative  f o r o u t p u t s are neqa-  The former c o n v e n t i o n  yields  p r i c e s , the a p p r o p r i a t e form f o r s p e c i f i c a t i o n and t e s t i n g  with a variable p r o f i t function. S e c t i o n 2 develops t i o n and net s u p p l i e s  the e s t i m a t i n g system.  There i s a p r o f i t  f o r two types of v a r i a b l e p h y s i c a l  l a b o r and raw m a t e r i a l s or i n t e r m e d i a t e i n p u t s .  input,  namely  P r o f i t a l s o depends on  the q u a n t i t y of c a p i t a l , assumed f i x e d d u r i n q the d e c i s i o n p e r i o d . are f o u r t y p e s of f i n a n c i a l commodities: demand d e p o s i t s outputs  and ( i v ) time d e p o s i t s .  classifiable.  The nonparametric  are i n p u t s .  There  ( i i ) cash, ( i i i )  Whether these f o u r are i n p u t s or • •> t he l a t a , is  that a l l sample p o i n t s are u n i g u e l v s i q n t e s t shows that loans and demand  are o u t p u t s of the banks throughout  time d e p o s i t s demands  loans,  i s not known a p r i o r i , but the s i q n t e s t a p p l i e d  i n d i c a t e d i n Chapter 5, c o n c l u d e s  deposits  (i)  func-  The p r o f i t  1 7 l - r ? 7 R , w h i l e cash q  f u n c t i o n , two p h y s i c a l  and two f i n a n c i a l input demands and the loans  s u p p l i e s c o n s t i t u t e seven e q u a t i o n s .  and  input  and demand  deposit  Since v a r i a b l e p r o f i t s or q u a s i -  -  _  U:>  r e n t s .ire d e f i n e d .is the d i f f e r e n c e between revenues  fin.inci.il.  fro"t  puts and e x p e n d i t u r e s on v ar i able f i n a n c i a l and ph\s i c a l a Linear  dependence,  reducino the system to s i x indepeudent  Section 3 describes tions.  inputs,  The v a r i a b l e p r o f i t  there is  equations.  the s t r u c t u r e of t e s t s on the e s t i m i t i n g function  out-  equa-  i s s p e c i f i e d to have the t r a n s L o q  form, w i t h the Logarithm of p r o f i t s q u a d r a t i c  in the Logarithm of p r i c e s  o f v a r i a b l e qoods and q u a n t i t i e s of f i x e d goods.  The f i r s t  group of  t e s t s determines whether the p r o f i t f u n c t i o n and the net s u p p l i e s  satisfv  some r e g u l a r i t y  F o r the  conditions.  The f i r s t  is eguaLity  and symmetry.  t r a n s l o g f u n c t i o n , i t i s r e g u i r e d that the second o r d e r m a t r i x o f p a r t i a l d e r i v a t i v e s w i t h r e s p e c t to p r i c e s be symmetric.  The e g u a l i t y  restric-  t i o n s are between the demand f u n c t i o n s and the v a r i a b l e p r o f i t  function  parameters.  Under symmetry  and e g u a L i t y ,  the v a r i a b L e p r o f i t  may be o b t a i n e d by i n t e g r a t i n g the net supply larity  test  profits,  is for monotonicity,  and i n c r e a s e s  functions.  that i n c r e a s e s  in output p r i c e s  A further  in input p r i c e s  increase p r o f i t s .  c o n v e x i t y o f the p r o f i t f u n c t i o n in p r i c e s  function  is detaiLed.  1  regu-  reduce  \ test for  Tests for  m o n o t o n i c i t y and c o n v e x i t y are d e r i v e d both at a Local p o i n t o f a p p r o x i m a t i o n and f o r a l l the d a t a in the sample. sample-wide  t e s t s of convex i ' y and m o n o t o n i c i t y .  The l a t t e r are T  hese r e q u i r e  "valu-  a t i o n at each d a t a p o i n t . Once the r e g u 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  behavior.  T h i s i n c l u d e s t e s t s on response of banks to monetary  and t e s t s on t h e e x i s t e n c e of monetary  f o r t e s t s on performance and  subaggregates.  poLicy  F o r example, the  - in e x i s t e n c e of v a r i o u s d e f i n i t i o n s of nones depends deposits  and time d e p o s i t s can be aqgreg at e d .  separability  commodity o u t s i d e  policy  The r<>lev .ml  i s whether the r e l a t i v e user c o s t s of an\  commodities w i t h i n a subaqqreqate  are d e s c r i b e d  on whether c a s h ,  it.  is  independent  a p p l i c a t i o n s of the model.  :  of the q u a n t i t y  grate  important potent, i a l  Prior estimation structures  from incomplete c o n s t r u c t i o n of user  the markets  of r i \  subaqqreqat " s  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 ( P a r k i n [ 1 9 7 0 ] , Berndt [ 1 9 9 0 ] ) , apart  for  p a i r of f i n a n e i a l  The t»*sts f o r e x i s t e n c e of monetary  in s e c t i o n 4, point inq to the mos  Vest  demand  costs,  f o r f i n a n c i a l commodities w i t h those  f o r the  and McCurdy do not  inte-  for other  inputs  such as l a b o 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 o n 5 some econometric i s s u e s are d e s c r i b e d , the e s t i m a t i o n p r o c e d u r e .  The data i n v o l v e  longitudinal  over 1973 - 1978.  There e x i s t s  the p o s s i b i l i t y  of  systematic  6.2  w i t h i n each hank,  in the d i s t u r b a n c e  The  The o t h e r  p r i n c i p a l e c o n o m e t r i c i s s u e i s the p o t e n t i a l presence of covariances  on  Reserve  bank e f f e c t s , a f f e c t i n g the l e v e l s of p r o f i t s and net s u p p l i e s . s t r u c t u r e of e s t i m a t i o n w i t h bank e f f e c t s i s d e v e l o p e d .  with  observations  the f i n a n c i a l performance of banks i n the New York F e d e r a l District  together  contemporaneous  terms.  Profit Function and Net Supplies The bank has a technology  deposits,  involving  two o u t p u t s ,  and f i v e i n p u t s , namely cash, time d e p o s i t s ,  raw m a t e r i a l s .  loans,  and demand  labor, c a p i t a l  User c o s t 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 s o p o s i t i v e , and q u a n t i t i e s v a r i a b l e inputs negative. commodities  are:  The q u a n t i t i e s and p r i c e s of  these  of  and  -  Uj)  loans: service  134  service quantity  and user cost  ( x ^ , U^)  demand d e p o s i t s : u n i t of serv i c e  service quantity  ( x ^ , U^)  cash: service quantity u n i t of s e r v i c e  and user  ( x ^ , U^)  time d e p o s i t s : of serv i c e  ( x ^ , IJ^)  l a b o r : e f f i c i e n c y u n i t s of p r o c e s s i n q l a b o r , and wage per e f f i c i e n c y u n i t .  (x^,, Ug)  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 : index and p r i c e per u n i t of s e r v i c e  and user c o s t  service quantity  and user  per  cost  per u n i t  and m a n a g e r i a l  efficiency  f i x e d d u r i n g the p e r i o d of p r o d u c t i o n at l e v e l  observations  are a l s o  x^.  indexed by bank and y e a r , but these a r e  The  suppressed  n o t a t i o n a l convenience. Among t h e f i n a n c i a l commodities X j , . . . , x ^ ,  the s i g n t e s t  sample i n d i c a t e s l o a n s and demand d e p o s i t s c o n s t i t u t e o u t p u t s . and time d e p o s i t s c o n s t i t u t e i n p u t s .  Net loan revenue x^Uj  n o n - n e g a t i v e w h i l e the analogous demand d e p o s i t E x p e n d i t u r e s on cash and time d e p o s i t s  term i s  profit  whiLe  Hence  cash  x-,U^ •  are X..U-, and x, U, and t h e s e 3 3 4 4  i n p u t s are measured n e g a t i v e l y .  from f i n a n c i a l o p e r a t i o n s .  f o r the  is  4  negative since  costs  cost  per  with c a p i t a l  for  of  per u n i t  7. \.:>  i  = i  as  v i e Ids  !  The s u b t r a c t i o n of p h y s i c a l  f o r l a b o r and raw m a t e 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  are  input  1 15  and t h i s  i s the dependent  variable  -  in the \ a r i a b l e p r o f i t f u n c t i o n .  v a r i a b l e p r o f i t f u n c t i o n i s ir ( U , \  ) where II = (IJ . , . . . ,l I.) c o n s t i t u t e s  +  k  the v e c t o r of user c o s t s  I  n  for v a r i a b l e commodities.  The t r a n s l o q 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 where a and g w i t h a p p r o p r i a t e s u b s c r i p t s denote  Jlnir* = a + 0  +  6 E 1 = ]  I  a. fcnU. + a, v i K  3.  K  £nl). £ n x  Inx + 1/2 K  6 E 1 = 1  6 E J = 1  0 ii  + 1/2 B ( £ n x ) . K|<  function  is,  parameters  £ntl i  2nlJ t  (6.2)  1  K  A p r o p e r t y o f such a f u n c t i o n i s homogeneity variable  in-  R  of deqree one in p r i c e s of  i n p u t s and o u t p u t s i m p l y i n g the r e s t r i c t i o n s  E  a. = 1  6 E  8  ' <  r>\  and  .1=1  = 0  for i=1,...  f  6.  (6.4)  J  The o u t p u t share s u p p l i e s of  loans and demand d e p o s i t s  are  The e x p l a n a t o r y v a r i a b l e s are the user c o s t s of f i n a n c i a l c o m m o d i t i e s , l a b o r and raw m a t e r i a l s , in l o g a r i t h m s , and the l o g a r i t h m of the q u a n t i t y of  capital.  136  Demand shares f o r 3*  inputs are  Tf *  aInTr- - i p r = respectively  a  3..4nU  i* ^  .  t  f o r c a s h , time d e p o s i t s ,  i =l , . . . , 6  Labor and raw m a t e r i a l s .  Also  9 An ir*/9fcnU. i s n e q a t l v e f o r i n p u t s , with x^ measured n e q a t i v e L v . equations  (6.2),  t h e s e seven,  (6.5)  and (6.6)  From  i t i s p o s s i b l e to e s t i m a t e the p r o f i t f u n c t i o n . r e d u c i n g the number  e s t i m a t i n g e q u a t i o n s to s i x , s i n c e the seven e q u a t i o n system  of  i s depen-  However, a l l parameters i n v o l v i n g m a t e r i a l s can be r e c o v e r e d ,  g i v e n 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  6.3  The  c o n s t i t u t e the e s t i m a t i n g s y s t e m .  E x c l u d e d i s the m a t e r i a l s demand s h a r e ,  dent.  (6.6>  homogeneity.  Regularity Restrictions The f i r s t set of t e s t s i s t o 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 s o c i a t e d s u p p l i e s obey c e r t a i n r e g u l a r i t y  conditions.  If  subuggre-  these are s a t i s f i e d , t e s t s on the e x i s t e n c e of a monetary  g a t e , and bank b e h a v i o r w i t h r e s p e c t 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 u n c t i o n has ?% f r e e 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) the  are imposed.  parameters e s t i m a t e d in the v a r i a b l e p r o f i t f u n c t i o n (6.2)  be i d e n t i c a l t o those i n the net supply  ^hJT= -P-= X  l  Y  1=1  i  + 1  \  6  f u n c t i o n s (6.7) below:  i j '""j  +  5  iK  £ n X  K  i=  Further, need not  -  -  137  The v a r i a b l e p r o f i t f u n c t i o n s a t i s f i e s  the t r a n s l o g p r o p e r t y of symmetry  if 6^ Again,  = 6^  i , j = l , . . . ,6.  i n e s t i m a t i o n o n l y f i v e of these e q u a t i o n s  supply e q u a t i o n s  (6.8)  are u s e d .  The  have seven parameters each, or 35 i n t o t a l .  symmetry r e s t r i c t i o n s (6.8)  are ten i n number.  If  five  The  b o t h symmetry  and  e q u a l i t y obtain, then, "i  =  Y  i  l . j - l5  - « g  iK  = <5  iK  and t h e r e are 35 such r e s t r i c t i o n s . conditions  (6.9)  The s a t i s f a c t i o n of a l l of  i m p l i e s t h a t the p r o f i t f u n c t i o n may be o b t a i n e d by  i n t e g r a t i n g the s u p p l y  functions.  The next sequence of t e s t s i n the d e t e r m i n a t i o n of p r o p e r t i e s i s f o r m o n o t o n i c i t y and c o n v e x i t y i n p r i c e s . requires  these  regularity Monotonicity  t h a t the p r o f i t f u n c t i o n be i n c r e a s i n g i n o u t p u t p r i c e s  decreasing i n input p r i c e s .  F o r the t r a n 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 o r d e r a p p r o x i m a t i o n around the p o i n t u n i t y . v e r s i o n approximates  TT*(U,X  )  K w i t h Jlnu = 0 and £nx  =0.  and  local  The homogeneous of degree  around U=l,  one  f o r U = (U ,... ,U ) and x = 1 6 K  At the same t i m e , the t e s t s  of  monotonicity  JT\. and c o n v e x i t y are a l s o developed f o r a l l p o s s i b l e parameters are e s t i m a t e d .  d a t a p o i n t s , once the  1,  - 13ft -  L o c a l m o n o t o n i c i t y at the p o i n t of expansion o,, a  2  > 0  a , a , a , a  < 0  3  This test  i s t e s t e d by  for monotonicity  .  (6.10)  does not reduce the number of parameters  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 The sample-wide t e s t of m o n o t o n i c i t y demand d e p o s i t expressed  revenues be p o s i t i v e .  neqatively  in ( 6 . 7 ) ,  space.  r e q u i r e s t h a t output  and  S i n c e the i n p u t e x p e n d i t u r e s  sample-wide m o n o t o n i c i t y  is  in  are  determined  from x.U./n* > 0 l l  i=1,2 '  -x.U /ir* > 0  i=3  i  ,6.  (6.11)  These are not p a r a m e t r i c r e s t r i c t i o n s , and thus cannot be s u b j e c t e d t o statistical  inference.  The r e m a i n i n g r e g u l a r i t y c o n d i t i o n i s c o n v e x i t y i n p r i c e s . t h e case of m o n o t o n i c i t y , t h e r e are l o c a l at the expansion sample-wide v a r i a n t s .  In both c a s e s ,  The H e s s i a n  in  and  the H e s s i a n m a t r i x of second  v a t i v e s must have p r i n c i p a l minors a l l n o n - n e g a t i v e . has t y p i c a l  point  As  derimatrix  element  2 * 3x. 3 n l 3U.3IJ. ~ 3IJ. i J .7 a  " H.. "ij  i,j=1,...,6.  (6.12)  The l i n e a r homoqeneity makes the Hessian m a t r i x s i n q u l a r , column can be d e r i v e d from the remaining e l e m e n t s .  and one row and  This Hessian  has e l e m e n t , s c a l e d by the p o s i t i v e f a c t o r ir*/U.u\, w i t h the form  matrix  transloq  -  e (e H  - 1) + S  -  V i where e^ = profits.  X^U^/TT*,  139  +  -  i-J i,j=l,...,6  hi  (6.13)  the ratio of expenditures on good i to variable  This i s derived in the Appendix, together with the Hessian for  an arbitrary variable p r o f i t function. When [U] = 1 and x^ = 1, e^ = a^, and the meters. point.  The scaling factor  TT*/U^UJ  = exp (CQ)»  i n (6.13) are parai s also constant, at this  Hence convexity at the point of expansion  i s tested by the  requirement M where  > 0  i=l,...,6  (6.14)  are the p r i n c i p a l 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 i n theory. Sample-wide convexity can be "tested" i f the p r i n c i p a l minors of H are non-negative.  At each sample point, the  equations (6.13).  This completes the regularity t e s t s , summarized i n  Table 6.4  6.4.1  are obtained from the  6.1. T e s t s o f Bank Technology  Introduction The prior set of r e s t r i c t i o n s determines  variable p r o f i t function.  the r e g u l a r i t y of the  The more relevant tests for policy purposes  concern the existence of monetary subaggregates and whether technologies excluding f i n a n c i a l commodities or having incomplete user cost computations are v a l i d 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 C o n d i t i o n s ( w i t h l i n e a r homogeneity r e s t r i c t i o n s d e l e t e d ) F r e e Parameters 1.  Unrestricted  2.  Symmetry  3.  Symmetry &  63 6.. = 6..  Equality (Integrability) 35  4.  i  a  =  Y  i  8 . . = <$. .  i»j=1 ,...»5 i,j=1,...,5  restrictions  28  Monotonicity Expansion p o i n t  >^ 0 a. < 0 l —  Sample-wide  xM.J-n* >_ 0 - x U / i r * >_ 0 i  4.  53  Convexity  (in  X ( <  •Note:  '  '  i=1,2 i=3,...,5  28  _> 0  ) = 1  Sample-wide (any  i=3 , . . . ,5  prices)  Expansion point (U,  i  i=1,2  28 M^ _> 0  i=1,...,5  U,x ) K  Sample-wide m o n o t o n i c i t y and c o n v e x i t y are not based on p a r a m e t r i c restrictions. A l s o , one of the v a r i a b l e goods i s removed, g i v e n l i n e a r homogeneity.  HI  -  -  Any tests for subaggregates are subject to the problem raised in Blackorby, Primont and Russell [1977, 1978],  There i t i s shown that the  test of weak separability in the translog i s a j o i n t one, simultaneously requiring a linear logarithmic form.  The linear logarithmic  subaggregate  implies that the form has extremely r e s t r i c t i v e substitution p o s s i b i l i ties. being  Further, because a structure may exhibit weak s e p a r a b i l i t y without linear logarithmic, tests imposing both j o i n t l y are l i k e l y to lead  to rejection of the former when i t i s true.  Woodland [1978] has proposed  a p a r t i a l solution, namely to express the variable p r o f i t function as 1 ),f 2 ir*(f 1 (U (x2 )) where x2 denotes the quantities of goods included i n , 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 ) i s the index of the remaining goods, £nir*(U ,x ) = * n f ( U ) + £nf (x ) 1  2  1  1  2  (6.15)  2  1 2 3 and neither f (•) nor f (•) need be l i n e a r logarithmic. context  In the translog  this implies that the second order cross terms between members of  groups 1 and 2 are zero. There are two main issues in implementation. subaggregate must appear as x  2  F i r s t , goods i n the  in the variable p r o f i t 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) i s free from simultaneous equations bias. estimation  Otherwise, a procedure of f u l l  information  such as three stage least squares i s 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  p r o f i t function ir*(f (U ), f(x )) i s different  from the previous case,  and there i s 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 e f f e c t i v e conduct of monetary policy i s whether the money supply can be aggregated^  There  is controversy on what constitutes the money supply, whether narrowly or broadly defined, but less empirical testing on whether these forms exist. * 1  I f no money subaggregate exists, the notion of adopting a rule  at the central bank r e s t r i c t i n g the growth of some monetary d e f i n i t i o n may have no p r a c t i c a l policy effect on either nominal or real v a r i a b l e s . The presence of some monetary subaggregate among f i n a n c i a l firms provides an indication as to what should be regulated by the central bank i n terms of target c o n t r o l .  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 e f f e c t i v e . Rather, i t provides information on which f i n a n c i a l commodities can be viewed as constituting the money supply.  I f no monetary subaggregate i s  ,  0  VOA**^*^  -  143  -  found to e x i s t , i t does undermine to some extent  the conduct of monetary  policy. The  test i s applied to the variable p r o f i t  function of the banks,  and corrects for the bias in hypothesis testing for subaggregation a r i s ing in using second-order functional forms such as the translog and quad ratic.  The  presence and existence of a monetary subaggregate requires  stringent r e s t r i c t i o n s , tending to lead to rejections of the hypothesis that a monetary subaggregate exists when the null hypothesis i s t r u e .  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  d e f i n i t i o n exactly paralleling M1-B, supply  since 1979.  the target d e f i n i t i o n of the money  However, this target was  not the focus of Federal  Reserve policy during the sample period 1973-1978, when narrowly defined money was 6.4.2.2  the object of central bank control. Money Supply D e f i n i t i o n s :  The  Cash and Demand Deposits  f i r s t test i s for the existence of a money d e f i n i t i o n includ-  ing cash and demand deposits, or M1, throughout the'sample period. be separable  an object of monetary control  If money under M1 i s shown to e x i s t , and  from the remaining financial and physical commodities enter  ing bank production, monetary p o l i c y .  then i t i s appropriate  to examine the conduct of  If no M1 construct arises, the entire thrust of mone-  tary policy i s undermined. f  The supply  proposed aggregating structure does not require the money  to be linear logarithmic.  Furthermore, the  It develops a test in Woodland [1978].  money supply can be recognized  in an i n t u i t i v e form.  -  144  -  Let the money components potentially in Ml be predetermined f i n a n c i a l firm.  Then i f these are  to the  and x^, cash and demand deposits,  the unrestricted variable profit function i s TTMU , 1  X , 2  X ) 3  = max { u ^ x : 1 x 1  xeS, U »  0, x »  0}  where a dot denotes an inner product, and (x*,U*) denotes and price of variable goods other than monetary ones. outputs and x^< 0 for inputs.  Since x  6  2  (6.16)  the quantity  Also x* > 0 for  and x^ are given, both are non-  negative. The transformation function i s T(x) = 0 and S i s the production possibly set. If a money supply containing cash and demand deposits e x i s t s , T(x) = T*(f j(x2»x.j), x * ) . to narrowly defined money.  ^  e  index i s f ^ ( x x ) which can correspond 2 >  3  By the i m p l i c i t function theorem, the  transformation function can be expressed i n terms of one of i t s arguments.  Selecting the money supply  f (x ,x ) = h^x )  (6.17)  1  1  2  3  or f ( x , x ) - h ^ x ) = T(x) = 0. 1  1  2  3  Rearranging,  Let h^ exhibit constant returns to scale. ( 6 . 1 6 ) becomes  ( x )/f ( x ,x ) = 1. 1  1  2  3  Under these r e s t r i c t i o n s  - 145 -  * 1 i l l 1 TT (U ,x ,x ) = max{U «x : h ^ x ) = f^x^x.^)} 2  (6.18)  3  1 = gjCU , f ( x , x ) ) K  1  2  3  = g (U ,l)f (x ,x ) 3  (6.19)  = g*(U )f (x ,x ).  (6.20)  1  1  1  2  1  1  2  3  The equality (6.19) follows the linear homogeneity of h^ : i f f ( x , x ) were changed to X f ^ x ^ x . j ) for some X > 0, then because of the 1  2  3  l i n e a r homogeneity of h^, i t can be seen that the i n i t i a l l y variable p r o f i t s would be multiplied by X also.  optimal  Note that l i n e a r  homogeneity of f^ i s not required i n order to obtain the decomposition of if* into the expression defined by (6.20).  Thus we have generalized the  Woodland [1978] test f o r s e p a r a b i l i t y to the case of a nonhomogenous f ^ .  The index g^ has the interpretation of the variable p r o f i t per unit of money.  This permits a comparison of bank e f f i c i e n c y , through the  * levels of g p Under linear homogeneity i n user costs, TT^(u* ,x ,x ) = 2  f^(x ,x )g^(u^) 2  3  normalizing on one  * * iT^ = -rr^/Ug, g^ = gj^/Ug and u be appropriate ex ante.  element.  1 1 = U /U^.  If  3  i s selected,  In empirical applications, i t may  to normalize user cost or price data and variable p r o f i t s  - 146 -  Taking  logarithms of the normalized  variable p r o f i t  function  1 1 fcrnr^u ,x ,x ) = £ n f ( x , x ) + £ng (u ) 2  3  1  2  3  (6.21)  1  which i s the sum of one function containing only monetary goods, Inf^ , and another containing the remaining goods. A translog s p e c i f i c a t i o n of Jin T r ^ ( u \ x^, x ) yields 3  1 inir. = a' + 1  1  1 a. £nz. +1/2  E  1=1  0  1  1  1  E  £ i=1 j=1  1  1 r  B. . £nz. £nz.  J  1  (6.22)  *  where z^ , i=1,...,l denotes the mixed prices and guantities (u^,  x.,, x , u^, u,., u ^ ) . If cash and demand deposits constitute 7  3  money, then (6.20) requires that the second order terms between these and the remaining goods be zero. p}  Hence  = 0  2  1=1,4,5,7  (6.23)  3 . =0 1  3  or eight parametric  restrictions.  For estimation, supply equations are  added to assist in identifying the parameters. 3£mr *nz.  x.u. TT  I = al + E  Hence  • g1 J. £nz. j  1  1  1—  1y**•  (6.24) ?  *  Since cash and demand deposits are exogenous in quantity, an increase i n either increases variable p r o f i t .  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/3x are both non-negative. 3  - 147 -  The v a l i d i t y of the r e s t r i c t i o n s (6.23) supports the construction of a money supply of cash and demand deposits. aggregate  The money supply  in logarithmic form i s  £nf.  1  1 Znx + 1 / 2 l 31 U n x 2 )  1 £nx +  =  2  3  22  +  2  1  £nx  2  Inx^  + 1/26 ' (Jlnx ) . 2  3  3  3  The Woodland [1978] test requires the additional r e s t r i c t i o n s : a  2  + a  3  = 1, 3  + e  2 2  but the test developed  2  3  = 0 and f3  23  + e  3  3  (6.25)  = 0.  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  r e s t r i c t i o n s on the variable p r o f i t function yield separability tests requiring a Cobb-Douglas form. 1  In (6.25), this requires the  1  additional r e s t r i c t i o n  = $  1 2 3  = &  33  =0.  A money supply can e x i s t  without being Cobb-Douglas, and whether cash and demand deposits have a unit e l a s t i c i t y of substitution can be tested. sum money supply of x  2  + x  form, on the parameters.  3  The conventional simple  involves further r e s t r i c t i o n s , of a l i m i t i n g  This can also be tested approximately, as a  l i m i t i n g case. Any test for a money supply which simultaneously requires a Cobb-Douglas structure thus tends to be biased against acceptance. proposed  The  test i s not biased, and provides more accurate determination of  whether a money supply e x i s t s .  -  6.4.2.3  Money Supply D e f i n i t i o n :  148 -  Cash, Demand and Time  The t e s t f o r a monetary subaggregate deposits  and time d e p o s i t s  t h i s case i s f ^ 2 ' 3 ' X  deposit  X  X  M2 c o n t a i n i n g c a s h , demand  f o l l o w s by e x t e n s i o n .  4^*  ^  Deposits  The money supply  in  analogy w i t h the cash and demand  form, the v a r i a b l e p r o f i t f u n c t i o n i s *  TT (U  2  2  where U  * 2 x ^ , x^) g ( U )  x ^ , x^) = f ( x ,  \,  ,  2  ?  2  (6.26)  2  r e p r e s e n t s t h e v a r i a b l e user c o s t s of non-monetary goods.  A  t r a n 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 u n c t i o n y i e l d s _ lnv~ = a„ + 2  0  I _ I I E a. Inz. + 1/2 E E i=1 i=1 j=1 1  1  _ p. . Inz. inz. 1  J  1  where z = ( u ^ , x ^ , x ^ , x ^ , u , u ) , w i t h u^ = U^lU^, 5  ?  (6.27)  J  = U^/Ug, Uj =  '*  U /Ug and i r ^ =  K^/U^.  7  The e x i s t e n c e of a monetary subaggregate  c o n t a i n i n g c a s h , demand  and time d e p o s i t s r e q u i r e s t h a t the second o r d e r &-j> i,j=1 , . . . ,5 terms between money and non-money  ^12  =  ^13  =  ^14 ° =  1  terms be z e r o .  =  1  '  5  '  The r e s t r i c t i o n s a r e  7  (  o r n i n e i n a l l . As b e f o r e , t h e r e s t r i c t i o n p e r m i t s t e s t i n g f o r a monetary subaggreqate  without r e q u i r i n g a Cobb - Douglas form.  The money supply M2 i s Jlnf, = L  4 _ 4 E a. Jinx. + 1/2 E i=2 i=2 1  4 _ E 0 . . inx. Inx. j=2  6  '  2  8  )  -  where  though  4 _ 4 E a. = 1 and E 1=2 i=2 this  involves  is  not  all &  _ B .  149 -  = 0 for j = 2 , . . . , 4  ;  r e q u i r e d by the t e s t .  = 0,  sum M2 c o n v e n t i o n a l l y J  under  homogeneity,  J  The Cobb-Douglas money form  i,j=2,...,4,  and can be t e s t e d .  used x., + 2  + x, i s 4  3  The simple  a limiting  testable  a  case. Finally, containing  f o r completeness a t e s t  cash only can be performed.  of a monetary In  this  * * 0 0 f u n c t i o n i s TTQ = f p / 2 ^ ^ ^ ^ where U i s remaining goods.  second order terms.  The t e s t The t e s t s  involves  case the v a r i a b l e  the user cost  x  the  subaggregate  similar  profit  v e c t o r of  r e s t r i c t i o n s on the  are summarized i n T a b l e  6.2.  6.5 Econometric Issues Exogeneity of P r i c e s and Q u a n t i t i e s  6.5.1  The  p r i c e s of v a r i a b l e  inputs  are U,=  (U^,...,Ug).  l a b o r and m a t e r i a l s may be regarded as o u t s i d e individual rates,  bank.  The  For  and r e g u l a t i o n s  r e s e r v e requirements and d e p o s i t nested system under t h i s  multivariate  the d e t e r m i n a t i o n of  such as d e p o s i t insurance  an  the v a r i a b l e p r o f i t  demands f o r f i n a n c i a l  s p e c i f i c a t i o n can be estimated as a  f u n c t i o n , net s u p p l i e s  inputs  and l a b o r ,  £, with d i s t r i b u t i o n N ( 0 , E ) , where N ( « , « ) a six-by-six  rate  provisions.  r e g r e s s i o n model with non-zero contemporaneous  normal,, and E i s  for  User c o s t s f o r f i n a n c i a l goods depend on i n t e r e s t  loan l o s s p r o v i s i o n s  ceilings,  User c o s t s  let  of  covariances.  f i n a n c i a l outputs,  and  t h e r e be an a d d i t i v e e r r o r  denotes  the m u l t i v a r i a t e  c o v a r i a n c e matrix with non-zero  off-  Table 6.2  150 -  - T e s t i n g f o r Money Supply  Definitions Free  Parameters  1.  Unrestricted  28  2.  Cash (5 r e s t r i c t i o n s )  23  ^0 3.  0 2  f  U  )  q  0  ( U  1'  U  3' V  Cash and demand d e p o s i t s  1  11  4.  =  =  f  1  ( x  2'  X  3  )  g  l  (  u  l '  U  Cash, demand d e p o s i t s  V  V  U  7  (8 r e s t r i c t i o n s )  5'  u  ^2  f  2  ( x  2'  X  20  7*  u  and time  deposits  (9 r e s t r i c t i o n s )  =  }  19 3'  \^  g  2  ( u  2 1' 5' u  "7*  -  d i a g o n a l elements.  -  151  E s t i m a t i o n of a l l nested forms can be performed by  the contemporaneous c o v a r i a n c e or seemingly u n r e l a t e d procedure of Zellner  [1962].  I t e r a t i n g on E u n t i l  i t becomes a d i a g o n a l m a t r i x  yields  g  e s t i m a t e s w i t h maximum l i k e l i h o o d p r o p e r t i e s . Tests changing  f o r monetary subaggregates  assumptions,  variables.  cannot be performed w i t h o u t  g i v e n t h a t the r e g r e s s o r s  There are two p o s s i b l e s o l u t i o n s .  t h a t each non-nested model not only corresponds  c o n t a i n a mix of  (u,x)  The f i r s t i s to assume 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 s o t o 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 r e g r e s s o r s  c o n t a i n i n g a mix of p r i c e s and  may be viewed as exogenous,  q u a n t i t i e s (Woodland [ 1 9 7 8 ] ) . forms d i f f e r , comparisons  The problem i s t h a t s i n c e the s t r u c t u r a l  between d i f f e r e n t s e t s of t e s t s i s  difficult,  although estimation i s s i m p l i f i e d . A second s o l u t i o n i s t o view the exogenous  v a r i a b l e s as being  e n v i r o n m e n t a l l y d e t e r m i n e d , and to be the same r e g a r d l e s s tion.  The non-nested models then c o n t a i n endogenous  regressors,  v a r i a b l e s from x as  w i t h non-zero c o v a r i a n c e w i t h d i s t u r b a n c e t e r m s .  a p p r o p r i a t e e s t i m a t i o n procedure i s  on a l l exogenous  by"being  T h i s procedure has the  advantage of e n s u r i n g c o m p a r a b i l i t y of r e s u l t s between models  6.5.2  squares,  v a r i a b l e s , and then the i t e r a t i v e procedure  a p p l i e d on the r e l e v a n t c o v a r i a n c e m a t r i x .  a l t e r n a t i v e monetary  An  i t e r a t i v e t h r e e stage l e a s t  w i t h the dependent x v a r i a b l e s purged on the f i r s t round regressed  of s p e c i f i c a -  positing  subaggregates.  P o o l i n g Time S e r i e s and Cross S e c t i o n Data - Bank E f f e c t s The o b s e r v a t i o n s c o n s t i t u t e pooled time s e r i e s and c r o s s  section  - 152 -  d a t a on e i g h t e e n banks i n t h e New York F e d e r a l Reserve 1973-1978, w i t h s i x e q u a t i o n s dependent  variables  ( £ m r ,  for each.  X ^ U ^ / T T ,  District  L e t y denote the s t a c k e d l i s t o f  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 y e a r s . denotes  the l i s t  A corresponding  of exogenous v a r i a b l e s  Under l i n e a r homogeneity constant,  additive error i s e.  Further, X  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 .  i n v a r i a b l e good p r i c e s , X c o n t a i n s t h e  f i v e r e l a t i v e p r i c e s , t h e q u a n t i t y o f c a p i t a l and twenty-one  second o r d e r v a r i a b l e s , or 28 i n a l l . A t y p i c a l observation i s y = X T + e _ •'nt nt nt  (6.29)  where T i s a 168 by u n i t y stacked v e c t o r o f parameters and n=1 , . . . ,N w i t h t = 1 9 7 3 1 9 7 8 .  I f t h i s i s rearranged  as a m a t r i x w i t h 28 parameter  rows and s i x e q u a t i o n columns, t h e parameters t o be e s t i m a t e d a r e  r = 75 KK  Mr  '15  <3IK'  .6 5K  0.  (6.30)  0  The above form may be e s t i m a t e d as a m u l t i p l e r e g r e s s i o n variables  are exogenous,  or by a f u l l  genous v a r i a b l e s are r e g r e s s o r s . effects,  model i f a l l X  i n f o r m a t i o n method i f some endo-  However,  the e s t i m a t e s of T are b i a s e d .  i f t h e r e are s y s t e m a t i c  bank  -  Unbiased  153  -  estimation of r with pooled time series and cross section  data requires the insertion of bank e f f e c t s . 10 A t y p i c a l observation becomes y  nt  dependent variable mean, over time, of the nth bank.  An equivalent  method of estimating this model i s to introduce a bank dummy variable matrix Z with parameter 9. This model permits the examination of systematic bank effects in 9. Also, by s t 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 i s unbiased even i f there i s intercorrelation between X and Z. Both models are used and compared i n estimation, to examine whether bank effects arise.  If 9 = 0, then the estimation can proceed  without bank e f f e c t s . 6.6 Concluding Remarks This concludes the discussion of s p e c i f i c a t i o n , hypothesis testing and estimation.  A few remarks may be made on alternative research i n  s p e c i f i c a t i o n of bank technology.  Mullineaux [1978] also uses the FCA  data to estimate a bank profit function.  Only the bank p r o f i t  specified as translog i s estimated, with no supply functions.  function, The large  number of parameters cannot easily be i d e n t i f i e d with only the p r o f i t function, and a m u l t i c o l l i n e a r i t y problem may arise.  B e l l and Murphy  [1968] use a Cobb-Oouglas specification to estimate bank technology, with a l l the concomitant  implications of constant shares i n compensation and  unit e l a s t i c i t i e s of substitution.  - 154 -  The advantage tions provide restriction  i d e n t i f i c a t i o n f o r the v a r i a b l e p r o f i t  i s placed on s u b s t i t u t i o n  f i n a n c i a l goods. also without  of the s p e c i f i c a t i o n used i s that the supply  possibilities  The e x i s t e n c e of monetary  a priori  restrictions.  function.  func-  No  between p h y s i c a l  or  suhaqqregates can be t e s t e d  - 155 -  Appendix-Chapter 6 Derivation of Hessian for Variable P r o f i t Function T h i s note d e r i v e s profit  function.  the H e s s i a n m a t r i x f o r an a r b i t r a r y v a r i a b l e  The r e s u l t i s then s p e c i a l i z e d t o the t r a n s l o g  form.  s i m i l a r d e r i v a t i o n of the Hessian f o r the t r a n s l o g v a r i a b l e p r o f i t tion has  i s c o n t a i n e d i n K o h l i [1975, p.29]. form  ) where  T T ( U , X  materials  TT  The v a r i a b l e p r o f i t  A  func-  function  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 t h e u s e r c o s t o f  and u = ( u ^ , u^, u^, u^, u,_) i s the r e l a t i v e user cost, o f  variable inputs.  C a p i t a l i s measured by x^.  The c o n v e n t i o n here i s u^>  0, i=1,...,5 and x^ > 0 f o r o u t p u t s and x.< 0 f o r i n p u t s ,  i=1,..,5,  w i t h TT > 0. Now 3TT -5—  i=1,...,5  = x.  3u.  1  1  (6.A.1)  and  3u.3u. 1  i,j=1,...,5  3u.  J  J  the l a t t e r being a t y p i c a l H e s s i a n element. e  i  ~ ^^ x  l t  *  t n e  e x  P  e n  f o r the n o r m a l i z i n g  ~„  diture  s h a r e , i=1,...,5.  So i n (6.13) i n t h e t e x t , T h i s i m p l i e s e^ =  XMJTI,  f a c t o r o c c u r s i n both numerator and denominator.  Now  x.u.  3JtniT  -T-T— = 3£nu. 1  and  (6.A.2)  1 1  IT  = e. 1  •  1  c  1=1,...,5 '  \  i\  (6.A.3)  - 156 -  TT x . = u.  32.mr 3£nu.  1  (6.A.4)  i='l , . . . ,5  1  implying  3x. l  •x  3u. J  =  , -1  U .  l  -1 = u.  u.  3TT 3£mr 3u. 3£nu. + J i  TT  -r3u. J  -  X  i 3u. J  3e. 3u. l I x. e. + ir - 5 — - x. - 5 — "j l 3u. I 3u. J J  x.e. 3e. J i ,i  x. 3u. i i  J  J  TT  u.u.  3u.  3e.  3U.  3e. l e .e. + u. -~— J J u.  This i s the qeneral  1  3  Tf  3U .  u . x. 3u . 3 i i. TT 3u .  form of t h e H e s s i a n ,  t h e s i g n i s determined by the bracketed  i,  j=1,...,5.  (6.A.5)  and s i n c e n/u.u. > 0 i J term.  For the t r a n s l o g , 3e. 3.. i _ _iJ 3u . u. J J usinq the equations  (6.A.6)  i n the t e x t .  O f f 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 H e s s i a n element becomes i J 3x.  1  3u. J  TT  u.u. J  [ e . e . + 3..] i j i j  i,j="1 ,..-,5,  1  On the p r i n c i p a l d i a g o n a l , 3u^/3u.-= 1, so  (6.A.7)  - 157 -  3x 3u. "  (6.A.8)  [ e. + 0. . - e. J i " i i i  u.2i  l  = - 2 - ^ - 1 )  +  B  U  ]  u. I  T h i s y i e l d s the H e s s i a n m a t r i x , p r o p o r t i o n a l t o  e  e  1  (  V  1  1 2  +  1 5  +  6  )  +  *12  P  11  e  e  1 2 e  +  2 V (  e  i2  1 )  e  +  6  22-'--  6  1 5 e  2 5 e  +  +  3  3  15  25 (6.A.9)  H =  6  e  3  15  e e 0  c  2 5  + 8-  c  25  . . . . e ( e , - - 1 ) + 8,c  3  3  and i f t h e p r i n c i p a l minors o f t h i s m a t r i x a r e n o n - n e g a t i v e , i s convex  i n output and i n p u t user c o s t s  f o r a l l sample  C o n v e x i t y at the p o i n t of expansion r e l i e s on t h e r e s u l t  c  33  the function  points. t h a t when u^=1,  i = 1 , . . . , 5 and x^ = 1, e^ = a., i = 1 , . . . , 5 and a l l elements of H a r e replaced  accordingly.  -  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 u n c t i o n y i e l d s 3 T T / 3 U = x where u is- the v e c t o r of n o r m a l i z e d user c o s t s , and IT i s n o r m a l i z e d v a r i a b l e p r o f i t . M o n o t o n i c i t y r e q u i r e s t h a t x be p o s i t i v e f o r o u t p u t s and n e g a t i v e f o r i n p u t s . The n o t i o n 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], F u r t h e r i s s u e s on i n t e g r a b i l i t y are e x p l o r e d by Hurwicz [ 1 9 7 1 ] , and a t e s t on aggregate consumer e x p e n d i t u r e d a t a f o r the U n i t e d S t a t e s performed i n C h r i s t e n s e n , Oorgenson and Lau [ 1 9 7 5 ] . See a l s o B l a c k o r b y , Primont and R u s s e l l [ 1 9 7 8 ] . 3  This  result  i s d e r i v e d i n Woodland [1978,  387].  ^The i s s u e s as to what the a p p r o p r i a t e t a r g e t of monetary p o l i c y i s , and what forms of subaggregates are c a n d i d a t e s are w e l l summarized i n S i v e s k i n d and H u r l e y [1980] and Berkman [ 1 9 8 0 ] . B l a c k o r b y , Primont and R u s s e l l [1977] show t h a t i f the f u n c t i o n f o r f i r m 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 o f a Cobb-Douglas, r e q u i r i n g u n 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 c u r r e n t c o n t e x t . The problem i s somewhat f i n e s s e d i f the form i s used as an a p p r o x i m a t i o n . 5  F o r these purposes, i t should be noted t h a t 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 f o r monetary subaggregates. If c a p i t a l is fixed, then i t e n t e r s the f i x e d subaggregate being t e s t e d . As an example, i n s t e a d of an M1 form c o n t a i n i n g cash and demand d e p o s i t s , t h e r e i s a form w i t h c a s h , demand d e p o s i t s and c a p i t a l . S i n c e these t h r e e are i n q u a n t i t y form, the t e s t of M1 subsequently w i l l r e q u i r e a Cobb-Douglas form. 6  Here U^ i s the r e l a t i v e user c o s t of c a p i t a l . n o r m a l i z a t i o n i t i s U , and u 7  7  Without  = U /U . 7 6  Q  The f u l l system a l s o c o n t a i n s a demand f u n c t i o n f o r raw materials. The d e l e t i o n of t h i s demand f u n c t i o n i n the n o r m a l i z a t i o n 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 u n c t i o n makes the c o v a r i a n c e matrix nonsingular. 9  1 0  S e e Kmenta and G i l b e r t  The discussion  [1968].  i s c o n t a i n e d i n 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  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 f o r the  e i g h t e e n banks i n 1973-1978 are examined. discussions the  the p o l i c y  f o r monetary c o n t r o l , i t i s d e s i r a b l e to o b t a i n e s t i m a t e s o f  responsiveness  of the supply of loans and demand d e p o s i t s ,  o u t p u t s , w i t h r e s p e c t t o own user c o s t s . the  To focus  Analogously,  i n p u t demand f u n c t i o n s f o r c a s h , time d e p o s i t s ,  the  the c u r v a t u r e of  l a b o r 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 t e c h n o l o g y and e x i s t e n c e  o f monetary and o t h e r s u b a g g r e g a t e s , t h e r e i s the e s t i m a t i o n of substitutability  and t r a n s f o r m a t i o n between goods f o r 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  as the r e l a t i v e p r i c e r a t i o of t h a t p a i r changes. measures  f o r an i n p u t  Transformation  t h e c o n v e r s i o n of i n p u t s t o o u t p u t s , or of a l l o c a t i n g  between a p a i r of o u t p u t s .  pair  resources  For the f i n a n c i a l f i r m , t h i s i n c l u d e s  the  t e c h n o l o g y by which time d e p o s i t b a l a n c e s are c o n v e r t e d t o l o a n s , or the u t i l i z a t i o n of cash b a l a n c e s , and the c o n v e r s i o n of these t o producing  revenue  items.  E s t i m a t e s of the e l a s t i c i t i e s of t r a n s f o r m a t i o n and the own and c r o 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 e q u i r e d .  For  o u t p u t 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 , w i t h compensated s u p p l i e s upward s l o p i n g .  For i n p u t s , own p r i c e e l a s t i c i t i e s of demand  are n e g a t i v e , w i t h demand c u r v e s downward s l o p i n g .  These e s t i m a t e s  have  - 160 -  i m p l i c a t i o n s f o r monetary p o l i c y .  If  loan s u p p l i e s  are shown to be  i n e l a s t i c w i t h r e s p e c t to i n t e r e s t r a t e s a f f e c t i n g the loan user the conduct of monetary p o l i c y may be undermined.  cost,  Even i f a monetary  subaggregate  can be c o n s t r u c t e d , i t may be i n s e n s i t i v e to i n t e r e s t  rates.  l e a d s to i m p l i c a t i o n s on whether i n t e r e s t r a t e s s h o u l d be  This  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 o f 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 a n s f o r m a t i o n 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 . n e o c l a s s i c a l production technology, points.  For an a r b i t r a r y  these are dependent upon d a t a  In the t r a n s l o g c o n t e x t , these v a r i a b l e e l a s t i c i t i e s are  constructed.  At a n o r m a l i z a t i o n p o i n t 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 p a r a m e t r i c , and s t a t i s t i c a l i n f e r e n c e can be a p p l i e d . S e c t i o n 3 r e p o r t s on the r e g u l a r i t y t e s t s on the t e c h n o l o g y ,  for  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 , m o n o t o n i c i t y , and c o n v e x i t y . performed.  T e s t s on whether bank e f f e c t s are present  are  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 .  S e c t i o n 4 t e s t s f o r the e x i s t e n c e of a money supply  aggregate.  In s e c t i o n 5 the e s t i m a t e s on the e l a s t i c i t e s of t r a n s f o r m a t i o n and supply  and demand are r e p o r t e d , f o r the most r e s t r i c t i v e  accepted. ules.  subaggregate  Loans and demand d e p o s i t s have upward s l o p i n g supply  Cash, time d e p o s i t s ,  demand s c h e d u l e s .  l a b o r and m a t e r i a l s have downward  schedsloping  The adding up r e s t r i c t i o n s permit- the e s t i m a t e s  for  -  161 -  m a t e r i a l s t o be c o n s t r u c t e d 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 w i t h r e s p e c t to p h y s i c a l c a p i t a l can be o b t a i n e d as 3£mr(u,x K  )/3£nx , as w e l l as the ex post r a t e of r e t u r n on K  capital. In s e c t i o n 6 some i m p l i c a t i o n s of the r e s u l t s monetary p o l i c y are d i s c u s s e d . interest  f o r the conduct  of  I n c l u d e d are the e f f e c t s of changes  in  r a t e s through F e d e r a l Reserve a c t i v i t y , as w e l l as changes  in  reserve reguirements.  The t h e o r y d e v e l o p s a c o s t of a r e s e r v e  requirement as part of the user c o s t of each d e p o s i t .  Changes i n  r e s e r v e r e q u i r e m e n t s can be examined f o r e f f e c t s on l o a n s and o t h e r financial  goods.  S e c t i o n 7 p r e s e n t s some c o n c l u d i n g remarks on the e m p i r i c a l results.  The r e s u l t s i n d i c a t e t h a t i t i s p o s s i b l e to c o n s t r u c t  e s t i m a b l e and t e s t a b l e model o f a f i n a n c i a l f i r m .  Such a model  an appears  c e n t r a l t o any complete e x a m i n a t i o n o f 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 r e l e v a n c e are the e l a s t i c i t i e s of transformation.  These may be used t o d e r i v e p r i c e e l a s t i c i t i e s o f  s u p p l y f o r o u t p u t s and demand f o r i n p u t s . financial  Consequently,  the response  of  f i r m p r o d u c t i o n w i t h r e s p e c t t o user c o s t s can be o b t a i n e d .  S i n c e the u s e r c o s t s depend on i n t e r e s t r a t e s as w e l l as v a r i a b l e s such as d e p o s i t  regulated  i n s u r a n c e r a t e s and r e s e r v e r e g u i r e m e n t s ,  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 d e f i n e d i n ( 4 . 1 0 ) ,  the e l a s t i c i t y of t r a n s f o r m a t i o n between  goods i and j , i , j = 1 , . . . , 6 i s n . . =  TTTT. ./TT.TT  ., where v..  is  3 TT/3U.3U. 2  162  -  and  is  V a r i a b l e p r o f i t s and user c o s t s  3TT/3U^.  t o the user c o s t of m a t e r i a l s . 3TT  -  From the d u a l i t y  are measured r e l a t i v e  results,  and x . >_ 0 i f i i s an output  x.i = 3u  x. < 0 i f  (7.1)  i i s an i n p u t  1=1,...,5 w i t h the f i v e v a r i a b l e s being i n o r d e r l o a n s , demand d e p o s i t s ,  V a r i a b l e p r o f i t s TT and u s e r c o s t s u are both  t i m e d e p o s i t s and l a b o r .  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. = i  3 * 3u^3uj  3e. e . e .j + u J 3u j  2  u.u. i  for i=1,...,5. elasticity  J  cash,  Substituting  (7.1)  TT  X . U . / T T  i  3u.  u .x. J  i  i  (7.2)  3U ,  and ( 7 . 2 ) , the t r a n s f o r m a t i o n  is  e.e. + u i j J 3u, u.  1+  u.x. J i  3e.  1 e.e. i J  —e-.e. i  3e.  (7.3)  3U ,  3u.  1  TT  3u. J J  1  TT  3u." i  1  u . x . 3u. J J  i»j 1»•••»5 • =  1  For the t r a n s l o g , 3 e . / 3 u . = 3. . / u . w i t h 6.. beinq the second i  J  parameter between i and j .  • i j  J  order  i j  S i n c e 3u./3u. = 1 f o r i = j ,  and o t h e r w i s e  is  zero  1 + —= 2  e. (7.4)  n..=  i,j=1,...,5.  1 + 6  i j e  -  163 -  These own t r a n s f o r m a t i o n e l a s t i c i t i e s are n o n - n e g a t i v e each d a t a p o i n t . e  i  =  and vary w i t h  At the p o i n t of n o r m a l i z a t i o n where [u] = 1,  then  i ' i 1 »•••>'>, and the e l a s t i c i t i e s are independent of the  a  =  data.  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  c o n s t r u c t e d given that (4.10) -  6 E j=1  e. = 1 and J  6 E j=1  n . . e . = 0 as d e r i v e d i n 1 J  J  (4.12).  The e l a s t i c i t i e s of supply and demand f o r r e s p e c t i v e o u t p u t s and inputs  are  e. + l  e,  - 1  i=j (7.4)  w.. = n. . e . = e. I  i,j=1,...,5  e^  and a g a i n , these are p a r a m e t r i c where [u]=1, w i t h e^ = a ^ , With e^ >_ 0 f o r o u t p u t s , u i ^  i s non-negative  s l o p i n g compensated supply c u r v e . n o n - p o s i t i v e , w i t h demand c u r v e s  i=1,...,5.  f o r o u t p u t s , w i t h an upward  I n p u t s have e . _< 0 , so u ) „ i s f o r i n p u t s downward s l o p i n g .  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 o b t a i n e d from  6 E  For  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 g u a n t i t y responses to changes i n user c o s t s .  The e f f e c t of monetary p o l i c y measures  changes i n r e s e r v e r e q u i r e m e n t s , d e p o s i t interest  insurance p r o v i s i o n s  r a t e s themselves can be a n a l y z e d .  such as or  -  7.3 R e g u l a r i t y  164  -  Tests  The f i r s t r e g u l a r i t y t e s t s are f o r symmetry and e q u a l i t y .  I n the  case of symmetry, t h i s r e q u i r e s the second o r d e r terms i n the supply demand f u n c t i o n s to be e q u a l .  and,  E q u a l i t y r e q u i r e s t h a t the parameters i n  these f u n c t i o n 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  function. All  t e s t s are performed on two a l t e r n a t i v e models,  w i t h bank  e f f e c t s e x c l u d e d and i n c l u d e d .  respectively  With bank e f f e c t s i n c l u d e d ,  dummy v a r i a b l e s are u t i l i z e d by bank i n each e g u a t i o n .  These  are  removed i n the model w i t h o u t bank e f f e c t s , so i t i s p o s s i b l e to t e s t f o r such phenomena.  An e q u i v a l e n t bank e f f e c t s model i s to t r a n s f o r m the  d a t a as d e v i a t i o n s from the sample mean, by bank, f o r dependent independent If  and  variables.  bank dummy v a r i a b l e s are i n c l u d e d , w i t h e i g h t e e n banks and s i x  e q u a t i o n s , even the removal of one bank t o a v o i d s i n g u l a r i t y t h e a d d i t i o n of 108 p a r a m e t e r s .  involves  On e s t i m a t i o n of the u n r e s t r i c t e d  model w i t h these e f f e c t s , the banks were shown to be grouped i n t o Using  the o r i g i n a l number codes s u p p l i e d by the New York F e d e r a l  Bank w i t h the d a t a , the aroups  z i = 1 f o r bank 6 Z2 = 1 f o r banks 3 or 15 z  3  z  H  z  5  Reserve  i n the dummy s p e c i f i c a t i o n used a r e , w i t h  bank 29 used as a n o r m a l i z e r (7.6)  five.  = 1 f o r banks 1,2,4,21,25 or27 - 1 banks 16 or 28 = 1 f o r banks 1 4 , 1 9 , 2 2 , o r 2 3 .  The dummies are z e r o f o r cases complementary to those s p e c i f i e d .  -  Applying  165  the l i n e a r homogeneity  in prices  the m a t e r i a l s user cost as a numeraire, f o r the no bank e f f e c t s  -  the e s t i m a t i n g e q u a t i o n s  =  +  a.  0  5  Z  a.  1 = 1  i  £nu. i  a,  +  K  £nx.. + - r K 2 1  5  +  0. £nu. £nx  E  j=1  are,  case  5 £mT  r e s t r i c t i o n , and u s i n g  J  K  +  T  £  0  KK  5  (£nx  £nu. i  Eg..  E  .  1 = 1  K  )  xj  = ]  £nu. j  2  (7.7)  and x  i i i — u  =  Y  i  +  .  E  6 1  ij *  n  u  j  +  6  iK  t n x  K  1=1,...,5.  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  =  (7.8)  T T * / U .  and u =  U/U.,  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 .  bank e f f e c t s model i n c l u d e s the f i v e dummy v a r i a b l e s additionally.  6  Data on the exogenous v a r i a b l e s  i n each  are e n t e r e d as  The  equation deviations  from t h e i r g e o m e t r i c means. T e s t s f o r the presence of bank e f f e c t s , symmetry reported i n Table 7.1.  and e q u a l i t y  P a n e l A r e p o r t s the l o g a r i t h m of the  f u n c t i o n w i t h 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  are  likelihood  the l o g a r i t h m  of  t h e l i k e l i h o o d f u n c t i o n w i t h o u t 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 P a n e l C. is  rejected.  In a l l c a s e s ,  Thus the dummy v a r i a b l e s  the h y p o t h e s i s are r e t a i n e d  of no bank e f f e c t s throughout.  2 The t e s t s t a t i s t i c s used are a s y m p t o t i c a l l y d i s t r i b u t e d as x • Berndt  and S a v i n [1977] have shown t h a t t h e r e are t h r e e  alternative  2 forms o f 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 y m p t o t i c a l l y as x •  In  descending  o r d e r of magnitude,  these are the Wald, l i k e l i h o o d r a t i o and Lagrange  multiplier  A t e s t which i s not accepted under the Lagrange  forms.  3  - 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 Variable P r o f i t Function  £nl_ ( l o g a r i t h m Degrees of Test Critical o f l i k e l i h o o d freedom (DF) S t a t i s t i c Value function) (X /DF) (0.01) 2  A  Bank e f f e c t s i n c l u d e d 1. U n r e s t r i c t e d  750.93  2.  725.83  10  5.02  2.32  648.09  35  5.88  1.70  Symmetry  3. Symmetry and Equality B  Bank e f f e c t s e x c l u d e d 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 E f f e c t s , by Model 1. Unrestricted  -  30  6.63  1.79  2. Symmetry  -  30  6.64  1.79  30  6.18  1.79  3. Symmetry and Equality  - 167 -  m u l t i p l i e r form i s not accepted a f o r t i o r i under the two Hence the results are reported for this form.  alternatives.  The hypothesis of  symmetry and equality i s rejected, but i s 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.  F i r s t , m u l t i c o l l i n e a r i t y exists in the variable p r o f i t  function by i t s e l f , rendering i t d i f f i c u l t to i d e n t i f y the and increasing their standard errors.  It may  parameters,  be easier to accept this  hypothesis If share equations are eliminated, as in Mullineaux but the cost i s imprecise parameter estimation.  [1978],  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 p r o f i t  function.  The variable p r o f i t function parameters, indicated in Table 7.2.  The bias in parameter estimates a r i s i n g when  bank e f f e c t s are excluded i s demonstrated. the sample, capital.  with symmetry imposed, are  At the geometric means of  Is the e l a s t i c i t y of variable p r o f i t s with respect to  Without bank e f f e c t s this i s 0.840, but i t changes to 0.879  with bank e f f e c t s .  The return on c a p i t a l i s 3ir/3x^ = ^ / ^<X  1I  X  At  the geometric; mean, for a given */x^ the no bank e f f e c t s model leads to an upward bias in the realized return on c a p i t a l .  I The remaining a elements are e l a s t i c i t i e s of variable p r o f i t s with respect to user costs of variable goods.  Loans and demand deposits are  outputs, as indicated lhlthe c l a s s i f i c a t i o n tests, and increases in loan  - 168 -  Table 7.2 Parameter Estimates, Variable P r o f i t Function (Asymptotic standard errors i n parentheses)  Parameter Intercept l a a  2  3  A  a  k  5  A  "K Pll 013 014 015 B  1K  022 023 024  625 g  2K  033 034  035  3 ^  *4K P55  B  KK  Bank effects included  Bank effects excluded  14.638 1.280 0.515 -0.073 -0.201 -0.416 0.840  0.409) 0.073) 0.061) 0.013) 0.032) 0.070) 0.235)  14.474 1.251 0.601 -0.081 -0.175 -0.492 0.879  (0.155) (0.028) (0.023) (0.005) (0.012) (0.026) (0.106)  0.070 -0.284 -0.006 0.153 0.054 -0.074  0.061) 0.033) 0.015) 0.023) 0.037) 0.044)  -0.076 -0.068 -0.191 0.188 0.097 -0.077  (0.081) (0.018) (0.036) (0.027) (0.047) (0.020)  0.291 0.020 -0.002 0.053 -0.081 -0.035 -0.002 -0.010 0.006  0.055) 0.036) 0.004) 0.036) 0.037) 0.033) 0.004) 0.010) 0.008)  0.197 0.041 -0.001 0.006 0.009 -0.021 -0.001 0.004 -0.010  (0.059) (0.039) (0.004) (0.004) (0.017) (0.044) (0.004) (0.013) (0.004)  -0.140 -0.005 0.000  0.010) 0.013) 0.019)  -0.146 -0.022 0.012  (0.010) (0.015) (0.008)  -0.075 0.141  0.039) 0.040)  -0.072 0.059  (0.042) (0.018)  0.013  (0.058)  -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 c a p i t a l . Given linear homogeneity, data are normalized by the user cost of materials. Intercept refers to the variable p r o f i t function constant term a^.  - 169  -  returns and demand deposit returns increase p r o f i t s . sample mean, a one percent  At the geometric  increase in loan user costs with bank effect  included increases p r o f i t s by 1.28  percent, and a similar increase for  demand deposits raises profit by 0.515  percent.  respectively cash, time deposits and labor.  Goods 3,4  and 5 are  These are inputs under the  c l a s s i f i c a t i o n 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, confirm monotonicity  at the geometric mean.  > 0 for an output  3TT/9U£  6  i  =  i  X  U  i ^  =  the results on the ou parameters, 1=1,...,  a j l n l T  /  and  3TT/8U^  Monotonicity  < 0 for an input.  requires  Now  1=1,...,5  8 £ n u i  (7.9)  so 3TT/3 , = u  i  l  e.Tr/u..  (7.10)  l  Given that u^ > 0 by d e f i n i t i o n and TT > 0 by inspection for a l l data points, sign  (3TT/3U^)  = sign (e.), i=1,...,5.  For a l l the sample  points, e^ i s s t r i c t l y positive for loans and demand deposits, and  negative for labor, time deposits and cash. used to calculate the r e l a t i v e expenditure negative for a l l observations. expenditures.  Table 7.3  6 The constraint I e.= i=1  for materials, and this i s reports these  For every observation, monotonicity  cates that the f i n a n c i a l firm technology  1 is  relative  applies.  This i n d i -  exhibits p r o f i t increases when  the user costs of loans and demand deposits increase.  P r o f i t s decrease  - 170 -  T a b l e 7.3  R e l a t i v e E x p e n d i t u r e s , Outputs and I n p u t s ( M o n o t o n i c i t y T e s t , Bank E f f e c t s I n c l u d e d )  Mean  Standard Deviation  Minimum  Maximum  1.280  0.232  0.888  1.790  -0.073  0.037  -0.190  -0.032  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  Loans Cash Demand Deposits  Relative expenditure i s 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 i s reported in Table 7.4.  The matrix i s singular for the s i x  by six case, given linear homogeneity of the variable p r o f i t  function.  Accordingly, the row and column corresponding to materials are dropped. Along the p r i n c i p a l diagonal, a l l elements are p o s i t i v e .  To determine  positive semi-definiteness of the matrix, the p r i n c i p a l minors are calculated, starting from the f i r s t row and column.  The p r i n c i p a l  minors are 0.42912, 0.03249 , 0.00813 , 0.00009 and 0.00011. * The results 1  from the p r i n c i p a l minors indicate that the variable p r o f i t function i s 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 p r o f i t function obeys the r e s t r i c t i o n s of mono-  t o n i c i t y and convexity at a l l data points, normalized around the geomet.  .  n c mean.  5  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. there i s no aggregation problem i n this one good case. 1  other money aggregates.  Furthermore, Hence we turn to  Table 7.4  172 -  Convexity Test - Hessian Matrix of Variable P r o f i t Function (H..)  Cash  Loans  Demand Deposits  Time Deposits  Labor  0.4291  -0.0988  0.3755  -0.1047  -0.4787  -0.0988  0.0985  -0.0724  0.0125  0.0199  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  Loans  Cash  Demand Deposits  Note: Hessian matrix element i s , from (7.2) H ij  For  so H  3^Tf  TT  3u 3u^  UM.  i  translog,  J  3 3u.3u. 1  + u.  - 5 —  j 3u,  J  1  J  a.a. 1  a  i  +  -  j i x  —  —  -  TT  ** i -5— 3u u  and at [u] = 1,  +  J  u  j  Ze.JZu^ =  TT  ij  e.e.  3e^  0. . ij  = a.,  i=1,...,5.  Uj  hi ~ i a  i  =  J  Table elements are reported without the scaling factor  T T / U ^ U ^ .  The sixth  row correponds to materials, and i s dropped given the l i n e a r homogeneity.  -  173 -  The M1 forms containing cash and demand deposits are indicated in Table 7.5.  Variable profit for this form, n  demand deposits.  i s the return to cash and  The dependent variables in the return to cash and  return to demand deposit equations are respectively u^x-,/^ and U  33^ 1 " X  /  1T  Since these sum to unity, the cash equation i s deleted.  The unrestricted model, with symmetry imposed i s reported i n the 2 f i r s t column.  The test s t a t i s t i c i s x /8, and i s 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  s t a t i s t i c s are reported as the computed x~ divided by the number of degrees of freedom. statistic.  This obtains for both the c r i t i c a l value and test  The f l e x i b l e functional form M1 supply i s not accepted.  Cobb-Douglas form involves the additional r e s t r i c t i o n s that Inx^ fcnx^ do not enter the demand deposit equation.  The  and  The test s t a t i s t i c for a  Cobb-Douglas, compared with the unrestricted model i s 19.17.  The  2 c r i t i c a l value of x /11 at one percent i s 2.32.  Comparing the  Cobb-Douglas with the translog, the s t a t i s t i c s 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 i s 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 i n Table 7.6.  Table 7.5  Money Supply Aggregates M1, Parameter Estimates (asymptotic standard errors in parentheses)  Variables  (UiXi/Tf! )  Unrestricted  Loans Intercept £nui £nx £nx  0.140 (0.076) -0.208 (0.078) -0.688 (0.176)  0.891 (0.003)  0.898 (0.003)  -0.383 0.008 -0.035 -0.006 -0.151 0.029 0.119  (0.055) (0.078) (0.034) (0.002) (0.025) (0.024) (0.042)  -0.332 (0.035) 0.067 (0.076)  -0.334 (0.035) 0.140 (0.076)  -0.138 (0.024) 0.028 (0.023) 0.039 (0.041)  -0.159 (0.024) 0.010 (0.033) 0.012 (0.041)  -0.843 -0.232 0.026 -0.001 0.029 0.039 0.153  (0.056) (0.079) (0.035) (0.003) (0.024) (0.034) (0.042)  -0.875 (0.035) -0.238 (0.078)  -0.876 (0.035) -0.208 (0.078)  0.028 (0.023) 0.033 (0.033) 0.140 (0.042)  -0.159 (0.070) 0.047 (0.033) 0.138 (0.042)  -1.645 (0.088) -0.705 (0.176)  -1.647 (0.088) -0.688 (0.176)  £nu7  (0.138) (0.177) (0.087) (0.003) (0.042) 6.153 (0.042) 0.410 (0.121)  0.039 (0.041) 0.140 (0.042) 0.479 (0.121)  0.012 (0.041) 0.138 (0.042) 0.509 (0.121)  AnL  613.02  539.19  517.18  5  £nu7  Demand Deposits Intercept £nuj £nx £nx Jlnuit £nu 2  3  5  £nu7  Time Deposits Intercept fcnuj £nx £nx 2  3  £n^  £nu  5  £nu7  Labor Intercept £nui £nx £nx 2  3  £nui+  £nu  5  £nu7  Capital Intercept £nui £nx £nx 2  3  *nuit  £nu  Note:  0.067 (0.076) -0.238 (0.078) -0.705 (0.176)  (0.003) (0.006) (0.003) (0.003) (0.002) (0.003) (0.003)  £nu  (-115X5/1^)  2.252 (0.137) 0.790 (0.303)  0.875 -0.032 -0.076 0.067 -0.006 -0.001 0.021  £nui+  (-Ui^/l^ )  2.245 (0.137) 0.934 (0.303)  (0.215) (0.305) (0.135) (0.006) (0.078) (0.079) (0.177)  2  x  Cobb-Douglas  2.041 1.137 -0.129 -0.032 0.008 -0.232 -0.783  3  (U3 3/*l)  Flexible form (translog)  5  -1.325 -0.783 0.234 0.021 0.119  -0.064 (0.002) , 0.064 (0.002)  The dependent variable i s noted in parentheses i n the l e f t column. User costs and quantities are measured p o s i t i v e l y i n the data.  Table 7.6  Money Supply Aggregates M2, Parameter Estimates (asymptotic standard errors i n parentheses)  Variables  (U  1  X  1  /TT  2  Unrestricted  Loans Intercept £nuj £nx £nx  )  1.425 1.133 -0.129 -0.425 0.427 -0.028 -0.250  (0.086) (0.092) (0.054) (0.025) (0.027) (0.038) (0.069)  0.648 -0.425 -0.084 0.207 -0.181 -0.029 0.106  (0.021) (0.025) (0.013) (0.014) (0.015) (0.014) (0.017)  Time Deposits Intercept Irnii £nx *nx Anx^ Jlnu Jlnu  0.256 0.427 0.025 -0.181 0.211 0.035 -0.095  (0.022) (0.027) (0.014) (0.015) (0.016) (0.015) (0.018)  Labor Intercept Anuj £nx £nx Inx.^ Jlnu £nu  -0.591 -0.028 0.057 -0.029 0.035 0.056 0.012 -0.966 -0.250 0.200 0.106 -0.095 0.012 0.009  2  3  £nu  5  inuy  Demand Deposits Intercept £ n u !  (U X /TT ) 3  3  2  & n x  2  £nx  3  £nxi  (ui x /n ) t  4  2  +  £nu  5  & n u  7  2  3  5  7  (-U5X /Tr ) 5  2  2  3  5  7  (-U X /TT ) 7  7  2  Capital Intercept Jlnu^ Jlnx Anx 2  3  Anus Jlnu 7  £nL Mote:  For in  Flexible form (translog)  Cobb-Douglas  1.641 (0.054) 0.793 (0.083)  1.642 0.792  -0.164 (0.035) -0.558 (0.066)  0.718  (0.013)  -0.171 (0.035) -0.538 (0.066)  0.693 (0.020)  -0.018 (0.003) 0.032 (0.004) -0.014 (0.004)  0.220  (0.022)  0.183  (0.014)  -0.016 -0.014 0.030  (0.002) (0.004) (0.005)  (0.032) (0.038) (0.021) (0.014) (0.015) (0.028) (0.025)  -0.662 -0.164  (0.020) (0.035)  -0.663 (0.023) -0.171 (0.035)  0.052 (0.025) 0.100 (0.023)  0.068 (0.025) 0.085 (0.023)  (0.090) (0.069) (0.057) (0.017) (0.018) (0.025) (0.075)  -1.236 (0.057) -0.558 (0.066)  784.79  0.100 (0.023) 0.422 (0.063)  -1.236 -0.538  (0.067) (0.066)  0.085 (0.023) 0.416 (0.063)  691.43  M2, time d e p o s i t s a r e i n c l u d e d i n the money s u p p l y . the quantity *  (0.057) (0.083)  619.87 An g r e a s e  i n c r e a s e s v a r i a b l e p r o f i t s , so t h e i n t e r c e p t  coefficient is positive.  - 176 -  The translog f l e x i b l e form i s 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.  F i n a l l y , the Cobb-Douglas compared with the translog has 2  test s t a t i s t i c 2 3 . 8 5 .  The hypothesis i s not accepted, since x /6 at the  one percent l e v e l i s 2 . 8 0 . Both monetary aggregates M1 and M2 are not accepted  statistically.  However, the Cobb-Douglas form i s always rejected i n favor of the f l e x i b l e money supply.  The results confirm the bias in testing  separability noted by Blackorby,  Primont  and Russell  Suppose money supply forms are imposed.  [1977].  For the translog form, in  column 2 of Table 7 . 5 , the cash parameters can be recovered by the 1 linear homogeneity r e s t r i c t i o n s = 1 - 0.891 = 0 . 1 0 9 . As estimated i n 1 1 equation B.^ = -0.064 and B ^ = 0 . 0 6 4 .  the demand deposit  supply index, where x^ = /*2 x  1  The money  S  3  g^trans) = x  —  ?  exp(0.891 £nx  —  3  + 0.064(fcnx ) 3  ?  /2)  and under the Cobb-Douglas structure, i t i s g^CD) = x exp(0.898 fcnx^) . 2  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 o b s e r v a t i o n s Inx-,  = 0.42  -  i n 1978, measured i n d e v i a t i o n form are  and £nx^ = 0 . 9 2 .  On a base of u n i t y at the g e o m e t r i c mean f o r the index and the cash quantity g^(trans) s i m p l e sum  = 2.433653 and g.^(C0) = 2.384525.  The commonly used  is  g^sum) =  x  + 2  x  3  and i n index form, the 1978 o b s e r v a t i o n i s 2.458222.  The e r r o r from  u s i n g a s i m p l e sum monetary form i s about 1 p e r c e n t , and over 2 p e r c e n t f o r the Cobb-Douglas.  The former o v e r s t a t e s monetary growth because  of  the p e 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 u n d e r s t a t e s i t . Whether an o v e r s t a t e m e n t of money supply of 1 p e r c e n t i s l a r g e or s m a l l depends on p o l i c y w e i g h t s .  In an environment where money supply  targets  are being u s e d , a c t u a l growth..oJaserved t o be above a g i v e n upper bound may not prove t o 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  Indices  are, using  the  e s t i m a t e s i n the second column o f Table 7 . 6 , w i t h x ^ = x^/x^ or t h e r a t i o o f time d e p o s i t q u a n t i t y t o cash  g,(trans) 2  = x,exp(0.718 2  Jinx, + 0.183 Jinx, + 3 4  -0.014inx and the Cobb-Douglas g (CD) = x 2  and  2  £nx^ +  2  >  0.030(£nx^) /2)  and s i m p l e sum forms are  exp(0.693 Jinx  0.032(£nx- ) /2 3  + 0.220 £nx^)  2  178  -  g2(sum) = x-, +  -  + x^.  The mean time d e p o s i t q u a n t i t y , i n m i l l i o n s i s 112.9, and the g e o m e t r i c sample mean i s 0 . 8 3 .  On a b a s i s of u n i t y at the g e o m e t r i c  mean f o r cash and the i n d i c e s , and g2(sum) = 2.376887.  1978  (trans)  Again,  = 2.357688, g-,(CD) = 2.355375  the s i m p l e sum y i e l d s an upward b i a s  of  about 1 p e r c e n t . In an e r a of i n c r e a s i n g 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 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 g e o m e t r i c mean.  year  The o b t a i n e d  r e s u l t s are s i m i l a r t o the M1 c a s e . In terms o f s e l e c t i n g between M1 and M2 as the a p p r o p r i a t e money supply, monetary  the r e s u l t s are i n c o n c l u s i v e . index i s r e j e c t e d .  the n u l l h y p o t h e s i s  In both cases the t e s t o f a  U s i n g the p r o b - v a l u e , or p r o b a b i l i t y t h a t  cannot be r e j e c t e d , the r e s u l t s l e a n s l i g h t l y  f a v o r 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 t h a t  i s p o s s i b l e t o develop a t e s t a b l e model on the money s u p p l y , constituent 7.5  in  and  it  its  components.  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 r a n s f o r m a t i o n are r e p o r t e d i n Table  Those f o r m a t e r i a l s are o b t a i n e d r e s i d u a l l y , u s i n g  7.7.  the c o n s t r a i n t s  that  the r e l a t i v e e x p e n d i t u r e s sum t o one, and t h a t the e l a s t i c i t i e s weighted by r e l a t i v e e x p e n d i t u r e s sum to z e r o . For the geometric mean d a t a p o i n t , the e l a s t i c i t i e s are d e f i n e d  1  +  e  ii  1  +  B  ij^ i j  /  c  t  a  i  2  a  "  1  /  a  i  1  =  j  i*j  i  ,  J  =  1  ,..., 6  (7.11)  -  Table 7.7  179 -  Estimates of E l a s t 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:  E l a s t i c i t i e s of transformation are 1  ^  +  3  ii  /  a  i  "  1 + i3 /o o l j  1  1  j  /  a  i  i = j  „  i,j=l,...,6  i*j  and r e l a t i v e expenditures are X^U^/TT  =  i=l,...,6, with and  > 0 for an output, a  < 0 for an input.  - 180 -  w i t h m a t e r i a l s beinq the s i x t h good.  A l l the e s t i m a t e s  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 . i s made by p e r f o r m i n g the  B  n  + ctj  u  i r  This determination  substitution  = a] ( l - D  3.. = c . a . ( n  are s i g n i f i -  1)  i=j  i,j=1,...,6  (7.12)  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 .  This highly  non-linear  system i s e s t i m a t e d u s i n g the Newton method. The e l a s t i c i t i e s of t r a n s f o r m a t i o n are r e p o r t e d on the upper p a n e l of Table 7.7.  Along the p r i n c i p a l d i a g o n a 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 t h a t t h e s e be n o n - n e g a t i v e .  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 complem e n t a r i t y between i n p u t s and o u t p u t s . relative It  In the lowe»* p a n e l are the  expenditures. i s noted t h a t whether two goods are s u b s t i t u t e s or  cannot be determined s o l e l y by t h e s i g n o f n . ^ , i n p u t s are i n the c o n f i g u r a t i o n .  complements  s i n c e both o u t p u t s  and  For cost f u n c t i o n e s t i m a t i o n , with  output exogenous, a n e g a t i v e o f f - d i a g o n a l element i n the  substitution  matrix i m p l i e s complementarity. The e l a s t i c i t i e s of supply and demand are r e p o r t e d i n Table 7.8. These are a . + B../a. - 1 1  0).  1  1  i=,J  i,j=1,...,6.  1  .  a.  +  i  0../a.  i j  i*j  J  On the p r i n c i p a l d i a g o n a l are the own e l a s t i c i t i e s o f supply  and  (7.13)  -  181 -  T a b l e 7.8 E s t i m a t e s 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)  Cash  Demand Deposits  Time Deposits  0.3351  1.3571  0.7296  0.5212  -0.0772  -1.3519  -0.1407  -0.0622  0.2933  0.9942  0.0810  0.5253  0.3875  0.7404  Time D e p o s 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  Materials  -0.0957  -0.5552  -0.1516  -0.0893  -0.0660  -1 .0871  Loans Loans  Cash  Demand D e p o s i t s  Mote:  Labor 1.1509  Materials 1.1609  -0.0478 = ^0.3838  to.. = n . . e . where n . . i s the t r a n s f o r m a t i o n e l a s t i c i t y and e. r e l a t i v e expenditure,  i,j=1,...,6  -  demand.  182  -  Since loans and demand deposits are outputs,  ties are p o s i t i v e .  In the case of loans, a 1 percent  the own  elastici-  increase i n the  user cost of loans increases the loan supply by 0.3351 percent, a relatively  inelastic  implying  supply.  For demand deposits, the supply e l a s t i c i t y i s 0.0810 also revealing an i n e l a s t i c 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  ii  =  a  i  ( a )  ii "  ! )  "  a  i  i.J-l,...,6  i = j  (7.14) B  = a.(co. . - a.)  and re-estimation.  i*j  The non-linear system, again estimated by the Newton  method, indicates that a l l diagonal elements are s i g n i f i c a n t l y from unity at the 5 percent  different  level.  Demand for cash by banks i s r e l a t i v e l y  elastic.  The own  elasticity  i s -1.3519 with respect to i t s user cost, e s s e n t i a l l y the interest f o r e gone by holding cash. again s i g n i f i c a n t l y  For time deposits, the e l a s t i c i t y i s -0.5044,  different from unity.  For physical inputs, the technology i s r e l a t i v e l y more f l e x i b l e . The demand for both labor and raw materials i s e l a s t i c , with the labor demand e l a s t i c i t y -1.2360, and that for materials -1.0871.  Off the  p r i n c i p a l diagonal, i t i s possible to c l a s s i f y 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 price e l a s t i c i t y indicates complements.  cross  - 183 -  It i s possible to c l a s s i f y pairs of goods as substitutes or complements, whether inputs or outputs. being two outputs, Consider  There are three combinations,  two inputs, and one input and one output.  f i r s t the two output case.  for output i , 3x^/3Uj < 0.  If output j i s a substitute  The supply of output i decreases as the  price of substitute output j increases.  implies the Hessian  2 element 3 T T / 3 U ^ 3 U J  Since  <  =  3TT/3U^,  3x^/3u^ < 0  0 i f i and j are s u b s t i t u t e s .  The reverse condition obtains for complements. Now consider the two input case. input i , 3x^/3u. > 0.  If input j i s a substitute for  That i s 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 . x^ i s an input  = -Sir/Su^, then 3x /3u^ i  If  > 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 t h i r d case obtains for one input and one output.  If good j i s  an output and good i an input, 3x^/3u^ > 0 i f these are complements. increase i s the price of output e l i c i t s an increase i n quantity supplied, and i n the quantity demanded of an input which i s complementary.  Symmetrically,  i f the input price u  increases, i t s  An  - 184 -  quantity declines, and i f x^. i s a complement, x. must decrease.  Since  2 3x^/9uj = 3 TT/3U^3U_., the Hessian element i s positive i f goods i and j are complements and negative  i f they are substitutes.  This indicates a general c l a s s i f i c a t i o n 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 / 3 U ^ 3 U J  ^>  0.  The  procedure can be applied to any pair of goods, and not only two inputs, as i n the cost function approach.  The procedure generalizes the  d e f i n i t i o n of substitutes and complements to the p r o f i t function.  The  c l a s s i f i c a t i o n for the bank, data i s indicated i n Table 7.9 using the Hessian matrix of the variable p r o f i t function, Table 7.4. The cross price e l a s t i c i t y i s 3x^/3u^ • u^ /x^, or the Hessian element times u_./x^. e l a s t i c i t y i s opposite negatively.  If x^ i s an input then the sign of the cross price to that of the Hessian since inputs are measured  If x^ i s an output then the cross price e l a s t i c i t y has the  same sign as that i n the Hessian matrix.  So i t i s also possible to use  Table 7.8 to c l a s s i f y pairs. On the output side, i f the cross price e l a s t i c i t y between any two outputs i s p o s i t i v e , they are complements.  An increase i n the return to  loans raises i t s supply, and also the supply of demand deposits.  This  implies that the bank produces j o i n t services i n demand deposits and  -  Table 7.9  Classification  185 -  of P a i r s ,  S u b s t i t u t e s 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 i s indicated the direction of quantity response of an input or output when the user cost of another changes. by reading down each column of Table 7.8.  This i s obtained  For example, -0.0772 i s 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 i n the user cost of cash reduces the supply of  loans. This permits an examination input and one output. and outputs.  of the response i n pairs containing one  A l l pairs indicate s u b s t i t u t a b i l t y between input  In the case of loans, supply i s decreasing i n the user  cost of a l l inputs.  A l l effects are r e l a t i v e l y i n e l a s t i c , i n that they  are less than unity. costs, at -0.3738.  The largest magnitude i s with respect to labor  The remaining responses are reported i n 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 f i n a n c i a l goods.  Barnett [1981, Appendix E]  obtains many e l a s t i c i t i e s close to zero.  Of 23 estimates presented f o r  substitution between passbook savings, small time and negotiable deposits at various i n s t i t u t i o n s , only two exceed unity.  The results  are reported with the exception of the two cases just described, s u b s t i t u t a b i l i t y between f i n a n c i a l assets has remained very low. E a r l i e r published studies of s u b s t i t u t a b i l i t y between monetary assets have a l l indicated very low s u b s t i t u t a b i l i t y between monetary assets (Barnett [1981], p. 218). The comments pertain to the demand side, and the construction of aggregate money demand.  187  -  The c r o s s ' p r i c e e l a s t i c i t i e s o f s u p p l y , demand d e p o s i t s time d e p o s i t s ,  i n the f i r s t and t h i r d columns,  of the c r o s s p r i c e e l a s t i c i t i e s are l e s s  three.  These are the demands  user c o s t of l o a n s changes. loans  results.  u n d e r l y i n g user c o s t s ,  less  on the part o f the  As the user c o s t o f l o a n s  banks.  increases,  f o r cash and l a b o r t o  R e l a t i v e l y l a r g e changes i n the p r i c e in interest rates, deposit  i n the supply of l o a n s  banks.  again  than u n i t y except f o r  insurance  wage r a t e s and m a t e r i a l p r i c e s , are r e q u i r e d to induce shifts  than u n i t y ,  f o r l a b o r and m a t e r i a l s and cash when the  are s u p p l i e d , and a d d i t i o n a l demands  these loans  and demand, f o r c a s h ,  l a b o r and m a t e r i a l s , are g e n e r a l l y  suggesting a r e l a t i v e l y i n f l e x i b l e technology All  i n the case o f l o a n s and  and demand d e p o s i t s ,  more service  variables charges,  substantial  and i n p u t demands  by  T h 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 t e s should be the o b j e c t of c e n t r a l bank c o n t r o l i n monetary policy.  7.6 Rate of Return on Capital T h e . f i n a l item i n the e s t i m a t i o n i s of r e t u r n on c a p i t a l ex p o s t .  the d e t e r m i n a t i o n of the r a t e  In p r o f i t f u n c t i o n e s t i m a t i o n w i t h o u t 7  demand or supply  equations,  r a t e of r e t u r n on c a p i t a l i s r e t u r n , and s h o r t requires  3TT  3 T T ( U , X  )/3x  Also,  > 0 under the same c o n d i t i o n s ,  to i d e n t i f y .  31nTr(u,x )/31nx K  must be c o v e r e d . K  =  p r o v i d e d q u a s i - r e n t s n are  For the v a r i a b l e p r o f i t f u n c t i o n as  The  and f o r a p o s i t i v e r a t e of  run o p e r a t i o n , some q u a s i - r e n t s  (u,x >/3x^ > 0. K  t h i s has proved d i f f i c u l t  specified  This  (c)-a(u,x^)/C)X^)X^/T!  positive.  K  i=1  and 3TT  _ 9£,nTf  _  3xj^ "  U  K " '3Anx  TT__ IT  x~  K  =  ^  \  .\  +  B  1=1  iK  £  n  U  i  +  w i t h 3TT/3X^ t h e ex post shadow user c o s t of c a p i t a l . measured a n a l o g o u s l y f i t t e d values 0  i K  ,  t o o t h e r user c o s t s .  This  KK  £  N  X  It i s  (7.16)  K  thus  i s the ex post r e t u r n i f  are used f o r TT and 3£nir/3Jtnx , and e s t i m a t e s f o r a  and  1=1 , . . . , 5 and B ^ . At the g e o m e t r i c mean of the sample, 3TT/3X  ct^ =  0  U ^ X ^ / T T ,  constant  = a ir/x^, = u .  the v a l u e of c a p i t a l s e r v i c e s d i v i d e d by p r o f i t s .  r e t u r n s t o s c a l e and c o m p e t i t i v e markets  Hence Under  f o r o u t p u t s and  i n p u t s , product e x h a u s t i o n o b t a i n s 'and c a p i t a l s e r v i c e e x p e n d i t u r e s 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 test for  = 1  and B j ^ = 0 , i = 1 , . . . , 5 w i t h 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 .  hypothesis  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  at the 0.01 l e v e l , w i t h a x  2  2 t e s t s t a t i s t i c f o r x /7 o f 8 . 7 5 .  Hence the c a p i t a l parameters accepted by the d a t a are those o f T a b l e 7.2 w i t h a  = 0.840, i n d i c a t i n g t h a t c o m p e t i t i v e l y p r i c e d 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.  Locational rent,  m a n a g e r i a l p r o d u c t i v i t y not measured i n l a b o r i n p u t , and u n c o m p e t i t i v e market phenomena are o t h e r p o s s i b l e e x p l a n a t i o n s . The r e t u r n u i s measured a n a l o g o u s l y t o the user c o s t s . The r e t u r n i s thus t h e premium  - 189  -  earned on c a p i t a l above that earned on low r i s k then the bank does not engage i n p r o d u c t i o n . measure of the a d d i t i o n a l r e t u r n t o c a p i t a l The measure u^ i s financial costs,  forms.  namely  investments.  in discounted  IL. < 0  The e x t e n t of u^ > 0 i s a in  banking.  the user c o s t of c a p i t a l i n p h y s i c a l  T h i s i s measured  If  i n the same u n i t s  and  as the o t h e r  user  form.  The mean v a r i a b l e p r o f i t s a t t a i n e d are $6,098 m i l l i o n .  The  value  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 . 2 6 8 . M u l t i p l y i n g by a 0.225.  = 0.84  the ex post  is  T h i s i m p l i e s t h a t the r a t e of r e t u r n on c a p i t a l i s 22.5  before  percent  tax.  The m a r g i n a l i s 0.48.  So  r a t e of c o r p o r a t e income tax p a i d by the banks,  TT(1-T)/X  k  = 0.268*0.52 or 0 . 1 3 9 .  r e t u r n on c a p i t a l i s 11.6 opportunity costs  percent.  P o l i c y Implications;  7.7.1  The a f t e r t a x r a t e o f  T h i s r e t u r n covers  depreciation,  and the c a p i t a l i z e d l o c a t i o n a l , m a n a g e r i a l  c o m p e t i t i v e or u n c o m p e t i t i v e a s p e c t s  7.7.  r e a l i z e d r e t u r n on c a p i t a l  of bank  and  behavior.  Monetary P o l i c y and Bank Behavior  Introduction The e m p i r i c a l r e s u l t s  by an i n e l a s t i c supply  suggest that bank technology  for outputs,  characterized  and r e l a t i v e l y e l a s t i c demand  inputs.  Both loans  than 0.5  at the geometric mean of the d a t a .  monetary  policy,  respect  is  and demand d e p o s i t s  have supply  f o r the o f f e r i n g of loans  t o changes i n user c o s t components  elasticities  for less  T h i s has i m p l i c a t i o n s is r e l a t i v e l y rigid such as i n t e r e s t  with  rates.  for  -  190 -  On t h e i n p u t s i d e , the bank i s a net demander of c a s h , deposits,  l a b o r and m a t e r i a l s .  time  From Table 7.8 the r e s p e c t i v e  elastici-  t i e s o f demand f o r a bank having sample g e o m e t r i c mean c h a r a c t e r i s t i c s are - 1 . 3 5 1 9 , - 0 . 5 0 4 4 , -1.2360 and - 1 . 0 8 7 1 . than u n i t y .  Three of these are g r e a t e r  However, f o r time d e p o s i t s , the demand i s r e l a t i v e l y  inelastic. I n t h e f i n a n c i a l s e c t o r of bank o p e r a t i o n s , a p i c t u r e of a r i g i d technology a r i s e s . h i r i n g processing  While banks are r e l a t i v e l y r e s p o n s i v e  to prices i n  and m a n a g e r i a l employees, or i n p u r c h a s i n g  copy o r o f f i c e s u p p l i e s ,  advertising  they are l e s s r e s p o n s i v e t o i n t e r e s t r a t e s or  o t h e r monetary p o l i c y r e g u l a t i o n s .  To examine the b e h a v i o r of banks  r e g a r d i n g monetary p o l i c y , some p o l i c y e x p e r i m e n t s are p e r f o r m e d . first,  corresponding  t o the subsequent  d e r e g u l a t i o n of deposit  The  interest  r a t e s i n 1980, p e r m i t s an i n c r e a s e i n the maximum i n t e r e s t r a t e p a y a b l e on time d e p o s i t s o f one h a l f o f one p e r c e n t . r e s e r v e r e q u i r e m e n t s on demand d e p o s i t s . s t r u c t u r e ofchanges  i n FDIC premiums.  The second e l i m i n a t e s t h e  The t h i r d examines t h e  I t i s assumed t h a t t h e r e i s no  change i n c o v e r a g e .  7.7.2. Interest  Rate C e i l i n g D e r e g u l a t i o n  The user c o s t o f time d e p o s i t s  is  U, = -1 + (1 + r + b + Rk TD TD TD where r  TD  Tl  i s the i n t e r e s t r a t e paid on time d e p o s i t s , b  i n s u r a n c e premium, R the d i s c o u n t s e r v i c e charge revenue. i s 1.1565 p e r c e n t .  (7.17)  s J/(1+R)  r a t e , k. TD  TD  the d e p o s i t  the r e s e r v e requirement and  In 1978, t h e mean time d e p o s i t user  cost  -  191  S i n c e 3uy /8 r-^ D  deposit  = 1/0+R),  an i n c r e a s e of 0.5 p e r c e n t i n time  r a t e s r a i s e s user c o s t s by 0.5/O+R) p e r c e n t .  r a t e p a i d on such d e p o s i t s percent r a i s e s  i n 1978 i s 5.037 p e r c e n t .  The mean i n t e r e s t An i n c r e a s e o f 0.5  the average i n t e r e s t r a t e by 9.9 p e r c e n t .  This  is  a p p r o x i m a t e l y the same as the e f f e c t on t h e user c o s t , because the discount  f a c t o r i s close to u n i t y .  Barro and Santomero  [1972]  have  shown t h a t the c e i l i n g r a t e c o n s t r a i n t i s b i n d i n g , and Santomero and Siegel  [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 a c t u a l d e p o s i t c e i l i n g d e r e g u l a t i o n i m p l i e s an a p p r o x i m a t e 10 p e r c e n t i n c r e a s e i n user  costs.  From T a b l e 7 . 8 , the own e l a s t i c i t y o f demand f o r time d e p o s i t s  is  Q  -0.07.  This  deposits. mean.  i m p l i e s a 7 percent d e c l i n e i n the q u a n t i t y of time  Bank p r o f i t s are a f f e c t e d by 3£mr/3£nu^ =  at the sample  From T a b l e 7.2 t h i s i s - . 2 0 , so the e f f e c t i s t o lower bank  p r o f i t s by 2.0 p e r c e n t , by o b l i g i n g the bank t o pay a h i g h e r r a t e t o depositors. An argument  a g a i n s t d e p o s i t r a t e c e i l i n g removal i s t h a t banks  on t h e lower i n t e r e s t r a t e s as reduced c o s t s t o b o r r o w e r s .  Apart  pass  from  the e f f i c i e n c y and e q u i t y 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 t o examine the degree t o which t h i s a l l e g e d c r o s s place.  subsidization  takes  The c r o s s p r i c e e l a s t i c i t y of loan supply w i t h r e s p e c t t o time  d e p o s i t user c o s t s  i s -0.08,  q u a n t i t i e s by 0.8 p e r c e n t .  so a 10 percent i n c r e a s e reduces  loan  The e l a s t i c i t y i t s e l f i s c l o s e t o z e r o  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 r e q u i r e d on whether a r e d u c t i o n i n l o a n volume of 0.8 percent i s l a r g e or s m a l l .  9  192  -  -  On d e p o s i t s w i t c h i n g , the evidence i s a l s o of s l u g g i s h As i n t e r e s t r a t e s r i s e on time d e p o s i t s , time d e p o s i t s .  holders s h i f t  response.  from demand to  T h i s has the e f f e c t of i n c r e a s i n g the average c o s t  d e p o s i t s to the bank.  of  The c r o s s p r i c e e l a s t i c i t y of demand d e p o s i t  s u p p l y w i t h r e s p e c t to the user cost of time d e p o s i t s d e c l i n e i n the d o l l a r q u a n t i t y of demand d e p o s i t s  i s -0.21,  i s 2.1  the  percent.  In c o n c l u s i o n , d e p o s i t r a t e c e i l i n g d e r e g u l a t i o n has s m a l l n u m e r i c a l e f f e c t s on the c o m p o s i t i o n of loans and d e p o s i t s .  Hence the c o n s e -  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 C o s t s Reserve r e q u i r e m e n t s e n t e r the user c o s t s of d e p o s i t s These r e q u i r e m e n t s act as taxes on the f i n a n c i a l f i r m .  explicitly.  The second  p o l i c y experiment i n v o l v e s a b o l i s h i n g the r e s e r v e requirement on demand deposits.  As r e s e r v e reguirements  c o s t s of d e p o s i t s . U  2  The user cost of demand d e p o s i t s  = -1 + (1 + r  analogously  i n c r e a s e , banks f a c e h i g h e r  D n  to (7.17).  + b  Q D  + Rk  Here r p  n o  - s )/(1+R)  (7.18)  DD  The d e p o s i t  bpp, and the r e s e r v e requirement cost Rk^p.  If  is  i s p o s i t i v e o n l y i n 1978, where NOW  n  accounts are i n c l u d e d as of November.  p e n a l t i e s are  user  insurance  S e r v i c e charges  premium and  s^.  r e s e r v e r e q u i r e m e n t s were e l i m i n a t e d , then Rk^p = 0.  As an  o p p o s i t e p o l a r c a s e , the I r v i n g F i s h e r [1935] "100 percent money" implies k ^  = 1, and Rkpp = R.  demand d e p o s i t s  is  i s -4.07  In 1978 the mean user c o s t  percent.  The n e g a t i v e user c o s t  policy  of implies that  -  193 -  demand d e p o s i t s y i e l d net revenue to the banks, or are o u t p u t s .  The  r e s e r v e requirement e f f e c t Rk^p i s 0.475 p e r c e n t , on a v e r a g e .  Now  Su^/Skpp = R/(1+R), the e f f e c t on demand d e p o s i t user c o s t s of  changing  reserve requirements.  If  k^  = 0, the e f f e c t on  Rkpp/M+R) term or 0.0456 p e r c e n t . f o r demand d e p o s i t s to -4.53  1 0  i s to e l i m i n a t e the  T h i s reduces user  percent.  The r e s e r v e  costs  requirement  e l i m i n a t i o n would reduce user c o s t s by 11.3 percent f o r the mean bank. The own p r i c e e l a s t i c i t y of supply f o r demand d e p o s i t s  i s 0.08,  so  an i n c r e a s e i n net revenue per d o l l a r s e r v i c e d i n such an account per year i n c r e a s e s d e p o s i t s by 0.9 p e r c e n t . s u p p l y demand d e p o s i t s are e l i m i n a t e d . e l a s t i c i t y of  The banks are more w i l l i n g t o  i f the t a x e s imposed by the r e s e r v e  requirement  The e f f e c t i s s m a l l , because of the low own p r i c e  supply.  The e f f e c t on p r o f i t s i s ^ m r / a ^ n u ^ =  at the q e o m e t r i c 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 c o s t demand d e p o s i t s Table 7.2  r e s p e c t i v e l y n o r m a l i z e d by the p r i c e of m a t e r i a l s .  t h i s i s 0.84,  unit deposit  of From  or an 11 percent i n c r e a s e i n net revenue per  i n c r e a s e s 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 l o a n s and p h y s i c a l i n p u t s , the c r o s s e f f e c t s are l a r g e s t  for cash.  As the demand d e p o s i t revenue  increases,  banks i n c r e a s e employment of a l l f o u r v a r i a b l e i n p u t s , and expand also.  Cash h o l d i n g s  i n c r e a s e by over 12 p e r c e n t , and employment  l a b o r i n c r e a s e s by 0 . 3 9 * 0 . 1 1 , or by 4.3 p e r c e n t .  The r e s u l t s  loans of  indicate  -  194 -  t h a t the r e s e r v e requirement imposes c o s t s on bank o p e r a t i o n s , and reduces output and employment  f o r those i n the banking s e c t o r .  c o n c l u s i o n r e s t s on the view of r e s e r v e r e q u i r e m e n t s as pure While normative c o n c l u s i o n s  This  taxes.  depend on the weights p o l i c y makers  a s c r i b e t o 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 benef i t s o f the r e g u l a t i o n s , measures.  i t i s p o s s i b l e to compare the two p o l i c y  The i n t e r e s t r a t e d e r e g u l a t i o n i n the f i r s t  p e r m i t s i n c r e a s e s of 0.5 percent per y e a r . requirement on demand d e p o s i t s identical  figure.  simulation,  The c o s t of the r e s e r v e  i s 0.475 percent per y e a r , an almost  Yet a d e r e g u l a t i o n on demand d e p o s i t s ,  the l a t t e r  c a s e , i n c r e a s e s 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 t e d e r e g u l a t i o n on time d e p o s i t s , and has g r e a t e r e f f e c t s on output and employment i n the banks.  7.7.4. Deposit  I n s u r a n c e - FDIC R e g u l a t i o n  The f i n a l c o m p a r a t i v e s t a t i c i s on changes i n the FDIC premium. The c o m p a r a t i v e s t a t i c s of the premium are examined. and exogenous d u r i n g t h e p e r i o d .  Capital is  fixed  I t may be p o s s i b l e t o model c a p i t a l  adequacy, or r e g u l a t i o n s on s h a r e h o l d e r s '  equity.  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 v a r y i n g e f f e c t s dependent on whether a s s e t s or l i a b i l i t i e s Another i s s u e  are a l t e r e d as a conseguence.  i s the coverage of the FDIC premium, or t h r e s h o l d  d e p o s i t l e v e l up t o which the d e p o s i t o r i s e l i g i b l e f o r reimbursement. T h i s i n c r e a s e d d u r i n g the p e r i o d , i m p l y i n g a g r e a t e r i n s u r a n c e r e t u r n to the bank per d o l l a r o f premium p a i d . obtained.  A d d i t i o n a l d e p o s i t s may be  S i n c e i n d i v i d u a l d e p o s 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 a d j u s t e d f o r , but i s  -  recognized.  R e l a t e d 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 , shareholders'  equity.  on r e g u l a t e d  There may be u l t i m a t e l y a r e g u l a t o r y  tradeoff  between the FDIC premium and the degree of d e b t - e q u i t y r e g u l a t i o n .  A  complete a n a l y s i s would i n c l u d e a v a r i e t y of r e q u l a t o r y t r a d e o f f s . Q u a n t i f i a b l e c o s t s of d e p o s i t  insurance  a b l e o n l y f o r the premium p a i d t o FDIC. supervision, as B u s e r ,  asset  r e g u l a t i o n are r e a d i l y  Indirect  r e g u l a t i o n , in  avail-  solvency  and l i a b i l i t y c o v e r a g e , and i n s p e c t i o n may a l s o o b t a i n ,  Chen and Kane [1981] have p o i n t e d o u t .  Further, risk  pooling  and c r o s s s u b s i d i z a t i o n may make the premium lower than t h a t which would have o b t a i n e d had a p r i v a t e agency been the i n s u r e r .  It  remains the case  t h a t FDIC coverage i s mandatory f o r the banks i n the sample. The r e g u l a t i o n s over the sample p e r i o d 1973-1978 p r o v i d e t h a t a premium o f 1/12 o f one p e r c e n t of d e p o s i t s be l e v i e d .  This  is  t o an e f f e c t i v e premium o f 1/30 of one percent a p p r o x i m a t e l y .  rebated If  no  r e b a t e i s made, the e f f e c t i v e premium i n c r e a s e s 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 r e b a t e i s examined.  For demand d e p o s i t s , the average FDIC premium r a t e as c a l c u l a t e d on t h e average d o l l a r Is 0.0392 percent i n 1 9 7 8 . the premium r a t e becomes 0.098 p e r c e n t .  1 0  Applying t h i s  The FDIC premium i s a l r e a d y 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 . sample mean v a l u e s i n Table (5.13) i n percent r  b  D D  = 0.0006  DD =  Rk s  D 0  D D =  0  '  0  3  9  factor,  2  0.4750  = 0.7167  Using  the  - 196 -  w i t h the s e r v i c e charge and p e n a l t y r a t e of 0.7167 p e r c e n t y i e l d i n g s u f f i c i e n t t o exceed the o t h e r components. the change i n FDIC premium i s 0.059 p e r c e n t .  Now ^ . , / 3 b ^ = l/(1+R), and F u r t h e r , 0.059/O+R)  0.056 p e r c e n t , the change i n the user cost of demand d e p o s i t s . mean demand d e p o s i t user cost of -4.07  From the  p e r c e n t , the FDIC r e b a t e a b o l i -  t i o n reduces the net revenue per u n i t of demand d e p o s i t s p e r c e n t , or 1.5  is  to  4.01  percent.  T h i s e f f e c t of 1.5 percent compares w i t h the 9 p e r c e n t e f f e c t of e l i m i n a t i n g the r e s e r v e r e q u i r e m e n t , so the impact i s p r o p o r t i o n a t e l y smaller. on o u t p u t .  Hence the e l i m i n a t i o n of the premium r e b a t e has a s m a l l e f f e c t Demand d e p o s i t s i n c r e a s e by 0.6 of 1 p e r c e n t , and l o a n s by  0.4 of one p e r c e n t .  These are the d i r e c t e s t i m a t e s .  If  the d e p o s i t o r s  p e r c e i v e h i g h e r premium r a t e s as an i n d i c a t i o n of s a f e r banks,  deposits  may i n c r e a s e 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 t h a t a user c o s t f o r m u l a t i o n of l o a n s  d e p o s i t s can be a p p l i e d t o d a t a on the banking s y s t e m .  and  Arbitrary  c l a s s i f i c a t i o n o f i n p u t s and o u t p u t s can be d i s p e n s e d w i t h , f o r the procedure determines t h i s .  The e s t i m a t i o n c o n f i r m s a w e l l - b e h a v e d  p r o d u c t i o n t e c h n o l o g y , e x h i b i t i n g c o n v e x i t y and m o n o t o n i c i t y . A wide range of p o l i c i e s can be a n a l y z e d , because the user i n c l u d e reserve requirements, deposit  costs  i n s u r a n c e and i n t e r e s t r a t e s .  bank t e c h n o l o g y on the supply of l o a n s and demand d e p o s i t s has shown t o be i n f l e x i b l e , w i t h low e l a s t i c i t i e s of s u p p l y .  The  The  been analysis  - 197 -  o f money demand has been e x t e n s i v e , but l e s s a t t e n t i o n has been p a i d to the p r o c e s s by which money i s s u p p l i e d . an a n a l y s i s i s p o s s i b l e .  The r e s u l t s i n d i c a t e t h a t such  - 198  -  NOTES lhis i s result (6.A.5) in the Appendix to Chapter 6 and i s derived there. 1  For the general case, with an arbitrary variable p r o f i t = n..e.  OK. i j  i J  ]  u. = e. 1 + e J. e . J  3e.  9u.'  1  3u.  j  1  function  J  TT  u.x. 1  J  1  3u. 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 U  ii  = ii i= n  e  i  8  i  e  i  e  1^  ~  1  = ± + 3Jtne /3£nu - 1 e  i  i  i=1,...,5  where Slne./SlnUj i s the e l a s t i c i t y of the r e l a t i v e expenditure with respect to i t s own user cost. 3u^/3u^ = 0 and i * j  "ii  =  n  ij j- = j e  e  =  For the cross price e l a s t i c i t i e s ,  1 + e  i j e  3  u  j  + 3£ne^/3)lnuj  i,j=1  5  where 31ne./31nu^ i s the cross r e l a t i v e expenditure e l a s t i c i t y 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 m u l t i p l i e r form involves imposing the r e s t r i c t i o n s as constraints on the likelihood function. See Berndt and Savin [1977] for an e x p l i c i t derivation. ^The convexity i s also tested at each data point in the sample, following the appendix to Chapter 6. It obtains for a l l observations. To determine the s e n s i t i v i t y of results to the point of normalization, the entire model was re-estimated at the data point corresponding to a l l 1973 observations on bank 1. The results did not d i f f e r s u b s t a n t i a l l y . To examine the global properties of the translog, renormalization at every every sample point would be necessary. 5  - 199 -  D  T h e MQ money supply  i s a degenerate c a s e , s i n c e an  aggregate  c o n t a i n i n g one good can be o b t a i n e d by the i m p l i c i t f u n c t i o n theorem. F u r t h e r , a l l c o n s i d e r e d money aggregates c o n t a i n at l e a s t c a s h . 7  The e l a s t i c i t y used i n t h i s and i n the remaining s i m u l t a t i o n s i s that o b t a i n i n g at the sample mean. For use w i t h data i n 1978, t h i s i s not s t r i c t l y a p p r o p r i a t e , as another e l a s t i c i t y m a t r i x i s r e q u i r e d f o r the 1978 d a t a . However, the m a t r i c e s are s i m i l a r i n s t r u c t u r e . Q  As the d e p o s i t base f a l l s , may a l s o be a f f e c t e d .  the c a p a c i t y to make f u r t h e r  loans  g  The d i s c o u n t r a t e R, used as the minimum i n t e r e s t r a t e p a i d by any sample bank on time d e p o s i t s , i s 4.03 p e r c e n t . The average FDIC premium r a t e i n c l u d e s i n the denominator accounts w i t h p o r t i o n s over the i n s u r a n c e l i m i t . 1 0  - 200  -  CHAPTER 8 IMPERFECT COMPETITION AND 8.1  THE FINANCIAL FIRM  Introduction The objective i s to develop a model of f i n a n c i a l firms which can  be estimated  empirically.  T y p i c a l l y , estimation of firm technologies  assumes that the firm i s a price taker in output and input markets. F i n a n c i a l firms such as banks, whether in loans or deposits markets, or in the markets for physical labor or materials, are assumed to exert noncompetitive presence. supply  no  It i s assumed they face perfectly e l a s t i c  schedules in input markets and perfect e l a s t i c demand schedules  in output markets. Making such price taking assumptions testable In both output and input markets has implications for regulatory p o l i c y . monetary policy may  The effect of  d i f f e r i f price taking i s imposed on a structure  where t h i s i s not the case. Section 2 develops the i n s t i t u t i o n a l context of It i s shown that  imperfect  competition  in the banking industry.  competition  can exist at both regional and national levels in the  product markets relevant for f i n a n c i a l firms.  imperfect  In Section 3 a model i s  developed which allows s t a t i s t i c a l testing of competitive both input and output markets.  behavior in  An implementable s p e c i f i c a t i o n i s  developed in section 4, and empirical results are in section 5.  Section  6 analyzes the implications for monetary p o l i c y . The data used are 1973-1978 observations on eighteen banks in the New  York Federal Reserve D i s t r i c t .  The banks supply loans and demand  - 201 -  deposits to customers with inputs labor, time deposits and cash.  Price  taking behavior i s accepted as a hypothesis, only i n the labor market.  The analysis of the effects of monetary policy must take account  of t h i s . 8.2  Noncompetitive Banking Behavior: The fundamental  The Context  case for a policy of stimulating competition i n  the f i n a n c i a l system must rest on ensuring that credit i s allocated to i t s most valuable uses at the minimum average cost.  Competition also  ensures that a broad range of f i n a n c i a l instruments i s made available to asset holders, offering the most favorable combinations of r i s k , l i q u i d i t y and expected  yield.  1  F i n a n c i a l firms produce several outputs.  The products include  services, such as demand deposits and d i f f e r e n t kinds of loans.  Each  product constitutes a separate market i n which the f i n a n c i a l firm operates.  In these product markets, the firm, such as a bank, faces  competition i n 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, t y p i c a l l y savings deposits, labor, materials and c a p i t a l . geographic markets. i t was  Financial firms also operate in d i f f e r e n t  In a survey conducted by the Federal Reserve System  found that the bank market for large business loans i s national  while that for small business loans i s l o c a l . There appear to be at least two i n s t i t u t i o n a l reasons that contribute potentially to imperfect competition i n the f i n a n c i a l sector.  The f i r s t i s the regulatory structure.  Laws and regulations  - 202  -  d e a l i n g w i t h c o n d i t i o n s of e n t r y , b r a n c h i n g , and h o l d i n g  company  e x p a n s i o n have not always acted to maximize c o m p e t i t i o n among f i n a n c i a l firms. bank.  In many r u r a l markets i n the U n i t e d S t a t e s Also regulations  t h e r e i s o n l y one  r e s t r i c t i n g unsound c o m p e t i t i o n , 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 d e p o s i t s , may r e s u l t i n c r e a s e d market power f o r i n d i v i d u a l banks.  in  Second, t h e r e may be  economies of s c a 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 .  Prices, interest  rates  and user c o s t s are t y p i c a l l y u n c e r t a i n , as are r e g u l a t o r y changes by t h e F e d e r a l Reserve System and the FDIC. hedge more s u c c e s s f u l l y a g a i n s t t e n d e n c i e s can a r i s e .  If  l a r g e r i n s t i t u t i o n s are a b l e t o  these u n c e r t a i n t i e s , then m o n o p o l i s t i c  As examples, forward c o n t r a c t s and f u t u r e s markets  may r e q u i r e l a r g e minimum c o n t r a c t purchases,  and average b r o k e r a g e  l e g a l f e e s may d e c l i n e w i t h the amount of funds  involved.  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 . a r e charged t o d i f f e r e n t customers.  and  Different prices  T h i s may be i n d i c a t i v e of  imperfectly competitive behavior. The t r a d i t i o n a l approach to measuring m o n o p o l i s t i c power i n an i n d u s t r y i s t o use c o n c e n t r a t i o n r a t i o s .  These are s u b j e c t t o  serious  m i s i n t e r p r e t a t i o n u n l e s s supplemented w i t h o t h e r 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 n d u s t r y i s i n d e f i n i n g t h e a p p r o p r i a t e market, both product and g e o g r a p h i c .  Concentration r a t i o s  i n banking are u s u a l l y measured i n terms of d e p o s i t s f o r t h r e e s e p a r a t e g e o g r a p h i c m a r k e t s , n a t i o n a l , s t a t e and m e t r o p o l i t a n a r e a . C o n c e n t r a t i o n i n the n a t i o n a l market i s r e l a t i v e l y low compared w i t h many o t h e r American i n d u s t r i e s .  States permitting statewide  b r a n c h i n g are more h e a v i l y c o n c e n t r a t e d than s t a t e s w i t h u n i t  banking,  - 203 -  although  the i n c r e a s e i n the number of branch o f f i c e s has  s u b s t a n t i a l l y g r e a t e r i n s t a t e s w i t h branch b a n k i n g .  been  At the l o c a l  market l e v e l c o n c e n t r a t i o n appears h i g h , and becomes h i g h e r the s m a l l e r the m e t r o p o l i t a n a r e a . ratios  S t a t e s w i t h branch banking have u n i f o r m l y  than those l o c a t e d w i t h u n i t b a n k i n g .  l i m i t e d branch banking f a l l  Ratios  f o r areas  i n between the o t h e r two.  In the  higher  having average  l o c a l banking market i n 1977 t h e r e were the e q u i v a l e n t of o n l y 2.3 on a s i z e - w e i g h t e d b a s i s , 0.44.  banks  i m p l y i n g the average H e r f i n d a h l index was  W h i l e a high degree of c o n c e n t r a t i o n i s i n i m i c a l t o a c t i v e p r i c e  4  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 a c k of such c o m p e t i t i o n .  K l e i n [1971] argues t h a t although government  s e c u r i t i e s can be  s a i d t o be i n p e r f e c t l y e l a s t i c supply t o the i n d i v i d u a l bank, not t h e case f o r p r i v a t e s e c u r i t i e s or l o a n s . bank wishes  to increase i t s loan/asset  i n the m a r g i n a l r e t u r n on l o a n s .  5  is  if a  r a t i o i t must accept a r e d u c t i o n  Hence these l o a n s are i n i m p e r f e c t l y  e l a s t i c supply t o the i n d i v i d u a l bank, competition.  Ceteris paribus,  this  i m p l y i n g some form of i m p e r f e c t  Elsewhere K l e i n [1972] argues t h a t f a i l u r e t o  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  recognize  in traditional portfolio  t h e o r e t i c models and i s r e p o n s i b l e f o r the almost n o n e x i s t e n t use of such models i n a p p l i e d banking Sealey  research.  [1980] argues t h a t d e p o s 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 t e r m e d i a r i e s set r a t e s and f a c e deposit l e v e l s . is usually  It  random  i s f u r t h e r argued t h a t because p e r f e c t c o m p e t i t i o n  assumed i n d e p o s i t m a r k e t s , l i q u i d i t y c o n s i d e r a t i o n s  are  ignored. In e s t i m a t i n g a p r o f i t f u n c t i o n , M u l l i n e a u x [1978] r e s u l t s which do not conform t o a p r i o r i e x p e c t a t i o n s .  obtains  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 e v i d e n c e of monopoly power f o r banks i n  his  sample. If  i t i s assumed t h a t p e r f e c t c o m p e t i t i o n e x i s t s when monopoly  power i s p r e s e n t , e s t i m a t e s of s u b s t i t u t i o n and t r a n s f o r m a t i o n p o s s i b i l i t i e s between o u t p u t s and i n p u t s may be b i a s e d .  It  is  t o know the e l a s t i c i t y of demand f a c i n g the f i n a n c i a l f i r m f o r  important its  p r o d u c t s i n o r d e r to o b t a i n the f i n a l change i n output when t h e r e i s a change i n i t s p r i c e . necessary.  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 n p u t s  are  T h i s i s e s p e c i a l l y t r u e s i n c e many monetary p o l i c y changes  a f f e c t the components o f user c o s t s or p r i c e s , f o r the p r o d u c t s o f t h e financial firm.  Monetary p o l i c y r e s u l t s d i f f e r depending on whether  p e r f e c t c o m p e t i t i o n i s assumed or n o t . It  i s d e s i r a b l e t o be a b l e t o t e s t s t a t i s t i c a l l y f o r c o m p e t i t i v e  b e h a v i o r 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 t h e o r y which can be extended t o s e v e r a l monopolistically supplied outputs.  6  However, t h i s method i s based on  t h e c o s t f u n c t i o n and hence must assume i n p u t 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 i n p u t and output markets may be noncompetitive.  A model i s developed which a l l o w s s t a t i s t i c a l t e s t i n g  of c o m p e t i t i v e b e h a v i o r i n both i n p u t and output m a r k e t s .  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 o u t p u t , m u l t i p l e i n p u t e n t i t y .  The  - d i m e n s i o n a l v e c t o r z denotes q u a n t i t i e s of o u t p u t s , and the N^-  d i m e n s i o n a l v e c t o 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 .  Physical  c a p i t a l i n equipment, s t r u c t u r e s and i n v e n t o r y , x^ i s f i x e d i n t h e  - 205  d e c i s i o n making p e r i o d . transformation  The p r o d u c t i o n p o s s i b i l i t y set y i e l d s  f u n c t i o n between o u t p u t s and i n p u t s T ( z , x , x ^ )  By the i m p l i c i t be e x p r e s s e d  -  the  = 0.  f u n c t i o n theorem, the t r a n s f o r m a t i o n f u n c t i o n can  i n terms of one of the arguments.  S e l e c t i n g the  first  i n p u t , we have the p r o d u c t i o n f u n c t i o n , x  1  = F(z,x ,...,x ) 2  (8.1)  K  7  where both o u t p u t s and i n p u t s are measured p o s i t i v e l y  (z > 0 , x > 0 ) .  M o n o t o n i c i t y of the f u n c t i o n i m p l i e s 3F/9z^ > 0, i=1 , . . . 0,  and 9F/9x^ <  i=2,...,N^. For the v a r i a b l e goods t h e r e are user c o s t s , or p r i c e s per u n i t  service.  The u s e r c o s t s f o r o u t p u t s are n e g a t i v e , and we denote  p r i c e s by v = ( v ^ , . . . , v ^ ) = ( - u ^ , . . . - u ^ )  goods by w =  output  where u^ are the u s e r  c o s t s o f o u t p u t s , t y p i c a l l y o f l o a n and d e p o s i t s e r v i c e s . p o s i t i v e user c o s t s .  of  Inputs  have  We denote i n p u t 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  ^....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 t h e i n v e r s e , demand f u n c t i o n v  i  =  D  i  (  z  i  1=1  )  where 9D^(z^) / 3z^ _< 0 . downward s l o p i n g .  This  Demands by consumers  N  for f i n a n c i a l services  s p e c i f i c a t i o n accomodates  behavior of f i n a n c i a l f i r m s .  If ^ ( Z j )  (8.2)  1  non-competitive  i s constant,  independent of  t h e n the f i n a n c i a l f i r m i s a p r i c e t a k e r i n the i t h output m a r k e t . F u r t h e r , the D , ( z ) f  are  s p e c i f i c a t i o n can account f o r q u a n t i t y r e l a t e d  z.,  - 206  pricing,  -  such as lower loan i n t e r e s t r a t e s on l a r g e r l o a n  sizes.  3  Supply of i n p u t s to the f i n a n c i a l f i r m i s determined by analogous i n v e r s e supply  functions.  These  are  w. = S . ( x . ) J  J  j=1  J  J  (8.3)  ,...,N,. >  >  2  This permits t e s t i n g for p r i c e taking in input markets.  Under complete  price taking, S.(x.) is a constant, J J  is  independent of q u a n t i t y s u p p l i e d .  and the observed w. J  The requirement o f minimum d e p o s i t  b a l a n c e s , w i t h d i f f e r e n t i n t e r e s t r a t e s p a i d above and below the t h r e s h o l d l e v e l , exemplifies non-price taking behavior f o r f i n a n c i a l goods.  For p h y s i c a l goods, q u a n t i t y d i s c o u n t s  wage r a t e s are a l s o  on purchases  and o v e r t i m e  examples.  The f i n a n c i a l f i r m i s assumed to choose the  input-output  c o m b i n a t i o n which maximizes p r o f i t d u r i n g the p r o d u c t i o n p e r i o d . V a r i a b l e p r o f i t f o r the f i n a n c i a l f i r m i s t o t a l revenue l e s s v a r i a b l e c o s t o r z»D(z)  constraint,  : x^ = F ( z , x , . . . , x z>0  financial  product.  function  or  TT = max {v.»z - w x z,x  Substituting  total  - x * S ( x ) w i t h the dot d e n o t i n g an i n n e r  V a r i a b l e p r o f i t s are maximized s u b j e c t t o the p r o d u c t i o n  1 0  (8.2)  and (8.3)  x > 0, x  (8.4)  )}  > 0 .  i n t o (8.4), v a r i a b l e p r o f i t s o f the  f i r m are TT = max{D(z)*z - S ( x ) * x : x ^ = F(z,\^ z,x  , . . . ,x^)}.  Now l e t ~x denote the v e c t o r of v a r i a b l e i n p u t s i n t h e p r o d u c t i o n  (8.5)  - 207  function, x = x.,,...,x^  .  S = S _ ( x _ ) , . . . , S.. (x.. ). 2 2 N N 2  x.^ = F ( z , x", x ^ ) .  -  The c o r r e s p o n d i n g  supply  The p r o d u c t i o n f u n c t i o n can then be  Substituting  expressed  f o r x^  The term S ^ ( F ( z , x , x ^ ) ) F ( z , x , x ^ ) i n p u t , x^ .  are  2  TT = max{D(z)*z - S^ ( F ( z , x , x ^ ) ) F ( z , x , x ^ ) z,x  first  functions  - S(x)«x}  .  (8.6)  i s the v a r i a b l e c o s t a s s o c i a t e d w i t h the  V a r i a b l e c o s t f o r o t h e r i n p u t s i s r e p r e s e n t e d by  S(x)»x. The f i r s t o r d e r c o n d i t i o n s f o r p r o f i t m a x i m i z a t i o n are o b t a i n e d 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 t h r e s p e c t t o the c h o i c e o f the model, namely output and i n p u t q u a n t i t i e s . zero simultaneously.  variables  These are set e q u a l t o  The f i r s t o r d e r c o n d i t i o n s w i t h r e s p e c t to output  q u a n t i t i e s are, 3 IT  9  9771 =  2  =  i  -  n  317i  i  °i "  +  i i Tl\ 3  Z  D  ^."'V  .  3F . i " 17^ 1  D  +  D  .  1 3F 3x7 3zT 1 i  3F  3S  c  F  < »*»*|C>  3xj  Z  0  S  3S +  S  n  ' 1 317 1=  i=1,...,N  < ]  1  =  0  .  (8.7)  F i r s t order c o n d i t i o n s w i t h r e s p e c t t o i n p u t q u a n t i t i e s i l - _ ! ! l. 3x.j ' j 3xj x  3  S  S  j  i  - F ( z x" x ) - ^ i ^ '*>\> z  3F  •*) 3 X " i " f . 1  S  [  — 3 x  ^  - ^s IE^  -  S  1  +  F(  3 x  3S  1  *'*» K> 3 ^ X  j=2,...,N  2  -  -  u  are,  0  = °  ]  .  (8.8)  - 208 -  By rearranging (8.7) and (8.8) and r e c a l l i n g the inverse demand functions for  outputs, v  for  inputs  = ^i^ i^ z  i=  j  =  =  3F  <  " i 3i7 Z  +  3S W  * ^"'" * * ' ^ l  o r  anc  * ' t  ^  ie  n v e r s e  supply functions  = S .(x^) for 1=1,...,^ the following results are obtained,  3 D  V  ^  " j X  JT^l  +  F  (  Z  9^. 1 3 [S  j  X  l  ' V ^  _  3 F  9^7"  '  dS  -  +  F ( Z  3S  ' ' K 3 7 X  X  )  1  (8.10)  J= »---' 2 2  1  X  N  1  3S  The term in square brackets i s equal to w^+ x^  3  price of F(z,x,x^) = x^ .  (8.9)  1-1.....N,  x  1_ which i s the shadow l  Equation (8.9) states that the firm  produces  output z^ u n t i l the observed output price v^ i s equal to the marginal 3F product of output z^,  , expressed i n value terms less the imperfect  competition term z^3D^/3z^.  Now  3F/3z^ > 0 for an output, and i f price  taking obtains i n the i t h output market, as well as for the f i r s t input, v^ = (3F/3z^) w^.  If the f i n a n c i a l firm i s 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. supply, Wj • In  If the f i n a n c i a l firm faces a perfectly e l a s t i c input  3SJ/3XJ =  (3F/3Xj) w^.  0, and i f the f i r s t  input has a similar condition,  The factor payment i s equal to the marginal product.  a case where SS^/Sx^ > 0,  -XJ3SJ/3XJ  i s negative, so the factor  payment exceeds the marginal product. Multiplying both sides of (8.9) by  z /x ±  l  - 209  v.z. 11  =  x.j  2 -z. 1  -  3D. 3S 1 3£nF nt — \ i " 5 — + T » — IS. + F ( z , x , x . J - — J 3z. 3£nz. 1 ' K 3x^ c  1 1  r c  5  x^  i=1,...N  (8.11)  1  and m u l t i p l y i n g both s i d e s of (8.10) by j/*-] x  w.x. —  -x. = —  x^  x^  2  3S.  ~,  IT ax.  " l i ^  1  ,1  j  3S. LS  j=2,...,N  2  F(Z,7,X„) ^-1 ]  K  1 +  3x^  .  (8.12)  E q u a t i o n (8.11) s t a t e s t h a t the output e l a s t i c i t y i s l e s s than t h e r e l a t i v e e x p e n d i t u r e share v.z.fx. r  arises.  1  i f 3D./3z. < 0 or i f non p r i c e t a k i n g 1  I  1  1  For the i n p u t m a r k e t s , -3£nF/3£nXj, the i n p u t  elasticity  i s p o s i t i v e , hence monopsony  power a r i s e s  e x p e n d i t u r e i s l e s s than the i n p u t e l a s t i c i t y .  i f the r e l a t i v e  T h i s o c c u r s i f 3S./3x.  J  is  3  positive. If  the f i r s t i n p u t market has been s e l e c t e d t o be one where  p e r f e c t c o m p e t i t i o n o b t a i n s , then 3S^/3x^ i s z e r o . are measured r e l a t i v e t o x^ , the f i r s t i n p u t .  u n i t y . Then S . + F ( z , x , x )  3S  1 /  3x  v.z.  2 -z.  x.j  x^  1 1  1  1 = 1.  Equations  The p r i c e s v^ and w^  1 1  Hence w^ i s equal t o  (8.11) and (8.12) become  1  — 3£n F(z,x,x..) 1 ' K + 3z^ 3£nz^ 3D.  i=1,...N.  1  (8.13)  - 210 -  w.x.  J J _  -x.  3S.  3Jln F ( z , x , x . . )  x.  3x .  3£nx .  J  J  1  *  (8.14)  j=2,...N.  J  • J  respectively. Suppose t h a t i n v e r s e demand f u n c t i o n s f o r o u t p u t s adequately  approximated by the f o l l o w i n g  D(z.) l over  1 = 1 ,...N 1 I n v e r s e supply  over the r e l e v a n t x^ range by the  J  J  J  If  (8.15)  f u n c t i o n s are  approximated  functions, J=2,...,N.  = c . + d . Jinx. J  where the v e c t o r s a^,b^, parameters.  functions:  = a . + b.Jlnz. l i i  the r e l e v a n t z ^ range.  S(x.)  z^ can be  (8.16)  i = 1 , . . . , N ^ and c ^ , d j , j = 2 , . . . ,N_, are  b^ < 0 then the demand f u n c t i o n i s downward s l o p i n g  output i and i f d . > 0 f o r i n p u t j the supply  i s upward  for  sloping.  J  S u b s t i t u t i o n of  v  i i z  z  (8.15) and (8.16) i n t o (8.13) and (8.14)  i i b  3  £  N  F V Z  » » K^ X  X  3£nz. l  w.x.  -x.d  "1  1  J J  4  J J  G i v e n the o b s e r v a b l e  3£n  F(z,x,x ) K  3Jlnx.  1=1,...,ii.  (8.17)  j=2,...,N.  (8.18)  J  p r i c e and g u a n t i t y v a r i a b l e s  and z , the system of e q u a t i o n s  f a c i n g the f i r m ,  (8.17) and (8.18) can be j o i n t l y  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 f o r the function F(z,x,x  ).  yields  estimated  production  Note t h a t i f b. = 0 i n (8.17) the producer  v,w,x  is  - 211  -  behaving c o m p e t i t i v e l y , s e l l i n g output such t h a t the output e l a s t i c i t y e q u a l s the r e l a t i v e e x p e n d i t u r e s h a r e .  I f b^< 0 then the f i r m  i s not a p r i c e t a k e r i n output market i and faces a downard demand c u r v e . competitively.  If  d j = 0 i n (8.18) the producer i s again  sloping  behaving  But i f d. > 0 then he i s behaving l i k e a monopsonist  i n p u t market j .  F i n a l l y , Zlnz^/Zln  demand f o r output z . .  If  v^= v ^ / b j i s the p r i c e e l a s t i c i t y o f  the a b s o l u t e v a l u e of v . / b . < 1 then the f i r m i  l  i  o p e r a t e s i n the i n e l a s t i c r e g i o n of the demand c u r v e .  For  supply,  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 r m  J  J  J J  behaving as a c l a s s i c a l  in  is  monopsonist.  8.* Specification The s t r u c t u r e i s a p p l i e d t o the bank t e c h n o l o g y , c o n t a i n i n g v a r i a b l e goods l o a n s , demand d e p o s i t s , c a s h , time d e p o s i t s , materials.  l a b o r and  User c o s t s per u n i t of s e r v i c e are c o n s t r u c t e d f o r  s i x , but t h e r e i s no p r i o r d e t e r m i n a t i o n t h a t the user c o s t  as  these  is  inde-  pendent o f the l e v e l of the q u a n t i t y of s e r v i c e . For the d a t a on 18 banks i n the New York F e d e r a l Reserve D i s t r i c t , 1973-1978, l o a n s and demand d e p o s i t s are c l a s s i f i e d as o u t p u t s , net revenue e a r n e r s  f o r the banks, w h i l e time d e p o s i t s , c a s h ,  m a t e r i a l s and c a p i t a l are i n p u t s .  Output z = ( z ^ , z ^ )  r e f e r r i n g t o l o a n s and demand d e p o s i t s .  labor,  respectively  I n p u t s 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 t o raw m a t e r i a l s , c a s h , time d e p o s i t s , capital.  being  l a b o r and  - 212  The p r o d u c t i o n f u n c t i o n i s x  = F(z  -  , x ^ , x ^ , x ^ ,x^)  1  between  i n p u t s and o u t p u t s , w i t h 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 a n 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 0 i i i l i=1 i=2 i=1 j=1 5 + 1/2 E i=2  5 E j=2  2 5 6. .Jinx. Jinx. + 1/2 E E i=1 j=2 1 J  1  J  B. .Jlnz. inz. ij l j  (8.20)  9 . . Jlnz . Jinx . 1 J  1  J  and the e l a s t i c i t y o f the aggregate F w i t h r e s p e c t t o each good y i e l d s * dlnz 3  = ct. + E i j  n F  =  i  f o r the outputs, 4T^3*nx  i  1  6..inz. + E ij j j _  1  5 9..Jlnz. + E ij J j  2  6..Jinx. ij j  1=1,2  6..Jinx. ij J  1=2,... ,4  (8.21)  and  2 = Y. + E i j =  =  2  (8.22)  p  for inputs.  S i n c e 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 w i t h r e s p e c t  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 o n l y be s u b s t i t u t e d i n t o t h e  p r i c e d e t e r m i n a t i o n e q u a t i o n s f o r i n p u t s and o u t p u t s t o y i e l d v-z b z 2 5 -^-i = — — + a . + E B..Jlnz. + E 9 . . £ n x . i=1,2 (8.23) 1 1 j=1 ^ j=2 J where the v^, output user c o s t s , are measured r e l a t i v e t o the p r i c e o f x  materials.  x  1  l  J  1  J  The dependent v a r i a b l e i s the r a t i o o f output revenue t o  e x p e n d i t u r e 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  the r a t i o o f output t o m a t e r i a l s q u a n t i t y , a c o n s t a n t and the of o t h e r q u a n t i t i e s . F o r i n p u t s , the analogous f u n c t i o n s are  are  logarithms  - 213  w.x. - i - ^ 1 X  d.x. = — 1  -  2 5 + Y . + E 9..£nz. + Z 6 . . i n x . j=1 j=2  X  1  1 J  J  i  J  i=2,...,4  (8.24)  J  w i t h the dependent v a r i a b l e being the r a t i o of i n p u t e x p e n d i t u r e s on good i t o those on m a t e r i a l s .  If  b.= 0 f o r an output market, the f i r m  s e l l s output i n a p e r f e c t l y c o m p e t i t i v e market.  Whatever output  i s produced can be s o l d at a g i v e n user c o s t v ^ .  For b^ = 0 ,  level an  u n l i m i t e d q u a n 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 t e s and o t h e r components o f user If sloping.  costs.  b^ < 0 then the demand f a c i n g the f i n a n c i a l f i r m i s  downward  A change i n q u a n t i t y s u p p l i e d i n c r e a s e s p r o f i t s by l e s s  the user c o s t .  Input markets can be examined a n a l o g o u s l y .  If  than  d^ = 0  t h e f i r m f a c e s a p e r f e c t l y e l a s t i c s u p p l y , and an u n l i m i t e d q u a n t i t y o f i n p u t 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 r m i s not p e r f e c t l y e l a s t i c .  d  L  It  i s upward s l o p i n g  for  > 0. The d a t a are as b e f o r e , c o n t a i n i n g pooled time s e r i e s and c r o s s  s e c t i o n o b s e r v a t i o n s on e i g h t e e n banks i n the New York F e d e r a l R e s e r v e District  1973-1978.  There are two output e q u a t i o n s and t h r e e i n p u t  demand e q u a t i o n s , o r f i v e i n t o t a l .  The dependent v a r i a b l e o f r e l a t i v e  e x p e n d i t u r e s i s y = ( v ^ z ^ / x ^ , \^z^lx^, independent v a r i a b l e s i n the system are £ n x , £nx^, £ n x ) 3  first  5  and  = (z^x^  w ^ x ^ / x ^ w^x^/x^, w^x^/x^).  The  = ( 1 , Anz^ , fcnz^, Inx^ , Jinx.,,  ^ / x , , , x^/*^, x / x , X ^ / x ^ . ?  1  The  b l o c k o f v a r i a b l e s e n t e r s a l l e s t i m a t i n g e q u a t i o n s , w h i l e o n l y one  - 214 -  If X = (X^,X.,),  variable from the second block enters each equation. then *nt = n t X  F  +  nt  e  n=1,...,18  (8.25)  t=1973,...,1978 and there are NT observations. in X . 2  There are eight variables in X^ and  Hence Y i s 13 by 5, or a 68 by unity column vector.  five  Rearranging  t h i s as a matrix with 13 rows and 5 columns, the parameters to be estimated are  l l  B  a  2  T  B  9  21  8  31  2  ^3  1 2  e  "tl  bl  0  0  b  0  0  d  35  0  0  0  •• U5  0  0  0  • »  6  .  9  • ••  •  25 6  6  15  25  6  2  0  0  0  0  0  0  0  0  2  °3  0  0 df  Restrictions can be applied to this T matrix. In addition, there may pooled data.  Unbiased  be systematic bank e f f e c t s , arising from the  estimates of T are obtained by 'within'  estimation (Mundlak [1978]).  In practice, this i s achieved by a system  whose t y p i c a l element i s y .- y = (X . - X ) r + e n t 'n' nt n* nt J r  7  dot notation indicates the sample mean for each bank. bank dummy variables can be introduced as  Where the  Alternatively,  with parameter 0.  l a t t e r permits s t a t i s t i c a l testing on bank e f f e c t s . bank e f f e c t s .  e n«  The  If 0=0 there are no  - 215  8.5  Empirical  Results  Hypothesis  8.5.1  T e s t i n g on C o m p e t i t i v e  P r i o r to examining markets  -  Behavior  i m p e r f e c t c o m p e t i t i o n i n the i n p u t and  f o r banks, some r e g u l a r i t y c o n d i t i o n s  are v e r i f i e d .  T e s t s of bank e f f e c t s w i t h f i v e dummy v a r i a b l e groups performed.  In the u n r e s t r i c t e d c a s e , x 175 i s 3 . 7 1 .  i s not a c c e p t e d , s i n c e the c r i t i c a l v a l u e i s 1.79 significance effects, If  are  With f i v e dummy v a r i a b l e s , t h e r e are 25 degrees  f o r the t e s t .  level.  and symmetry  output  of  The  freedom hypothesis  at a 1 p e r c e n t  Subsequent t e s t s are a p p l i e d t o a model w i t h bank imposed.  bank e f f e c t s are e x c l u d e d when they should be i n c l u d e d , the  e s t i m a t e s o f r are b i a s e d .  Parameter e s t i m a t e s w i t h and w i t h o u t bank  e f f e c t s are i n d i c a t e d i n Table 8.1. unadjusted'  The columns  l a b e l l e d 'bank e f f e c t s  e x c l u d e them.  The r e s u l t s  i n d i c a t e t h a t the markets f o r o u t p u t s and  suggest some n o n - p r i c e t a k i n g b e h a v i o r by banks. t h e b^ c o e f f i c i e n t o f z.j/x.j i s -8.97  Including  inputs bank e f f e c t s  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  zero.  The v a r i a b l e y^ /x^ i s e n t e r e d p o s i t i v e l y  result  o f b^ < 0 i n d i c a t e s a downward s l o p i n g demand curve f o r  Analogously,  the demand by customers  w i t h c o e f f i c i e n t b^ of - 3 . 0 6 .  deposits  and l a b o r , the c o e f f i c i e n t s of x^/x^,  p o s i t i v e , s u g g e s t i n g upward s l o p i n g  i n e s t i m a t i o n - , so the  f o r demand d e p o s i t s  sloping,  from  is  loans.  downward  For the i n p u t s o f c a s h ,  time  1=2,...,4 are a l l  supply c u r v e s .  In the case of  t h e 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 z e r o .  labor  - 216 -  T a b l e 8.1  Loans (-vizi/xx)  Intercept Inzi £nz2 in\2 inx inx^ inx zi/xi 3  5  Cash (w X2/x!) 2  Intercept £nzi Jlnz 2 Jinx *nx Jlnx^ inx 2  3  5  X  2  / X !  Labor (W4XI+/X1)  Intercept inz\ inz 2 Jinx 2 *nx Jlnxi, inx 3  s  Xl+/Xl  Note:  Parameter E s t i m a t e s , Bank Supply and Demand F u n c t i o n s (asymptotic standard e r r o r s i n parenthesis) Bank Effects Adjusted  -3.62 -5.52 4.74 -1.03 1.45 0.68 -0.51 -8.97  (1.10) (4.19) (0.68) (0.27) (2.40) (0.51) (0.70) (0.79)  Bank Effects Unadjusted  Demand Deposits (-V Z /X!) 2  2  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)  Intercept *nz! inz 2 inx 2 inx inxi+ *nx Z2/xi  Bank Effects Unadjusted  Time Deposits (w x /x!)  -  Bank Effects Adjusted  3  5  3  3  0.30 (0.07) 0.29(0.05) I n t e r c e p t - 1 . 0 3 (0.27) - 0.92(0.28) inz 1 0.31 (0.13) 0.38(0.13) inz 2 0.24 (0.05) 0.27(0.05) £ n x 0.55 (0.16) 0.55(0.17) * n x -0.20 (0.05) - 0.34(0.05) Jlnx^ 0.13 (0.06) 0.10(0.06) Jinx 5 0.44 (0.04) 0.48(0.04) * 3 / * l 2  3  (0.31) (0.51) (0.28) (0.05) (0.24) (0.36) (0.24) (0.29)  -2.28 4.74 -4.12 0.31 -1.69 0.95 0.36 -3.06  (0.51) (1.59) (0.79) (0.13) (0.91) (0.28) (0.34) (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) Bank Effects Unadjusted  Bank Effects Adjusted  1.06 (0.42) 0.66 1.72 1.45 (2.40) - 1 . 6 9 (0.91) -1.91 0.55 (0.16) 0.55 0.35 (1.42) 0.24 -0.44 (0.24) -0.67 0.37 (0.29) 0.32 1.03 1.10 (0.29)  Bank Effects Unadjusted  Bank Effects Adjusted 3.63 0.68 0.95 -0.20 -0.44 -1.08 -1 .05 0.37  Bank Effects Unadjusted  Bank Effects Adjusted  -  4.34(0.16) 1.08(0.54) 1.67(0.26) 0.34(0.05) 0.67(0.24) 1.24(0.35) 0.92(0.25) 0.51(0.13)  Output q u a n t i t i e s a r e : z i l o a n s , z demand d e p o s i t s . q u a n t i t i e s are x i m a t e r i a l s and s u p p l i e s , X2 c a s h , x d e p o s i t s , xit l a b o r , X5 c a p i t a l . 2  3  Input time  (0.29) (2.47) (0.92) (0.17) (1.45) (0.24) (0.29) (0.27)  - 217 -  Tests for imperfectly competitive behavior are performed sequent i a l l y and separately on each market and are reported in Table 8.2. loans, the logarithm of the likelihood function i s -375.23.  For  The  logarithm of the likelihood function under the bank effects model i s -349.12, so the resulting x freedom.  2  s t a t i s t i c i s 52.22 with one degree of  The hypothesis of price taking behavior  test s t a t i s t i c s are reported in Table 8.3.  i s not accepted.  The  There i s one parameter  r e s t r i c t i o n in each case. For the labor market, the x c r i t i c a l value of x  2  of 7.88,  2  test s t a t i s t i c i s 7.22  against a  so the hypothesis of price taking behavior  in the labor market i s not rejected.  It cannot be rejected that banks  face perfectly e l a s t i c supplies of labor. F i n a l l y , the test of competitive behavior in a l l markets y i e l d s the results of Table 8.4.  This hypothesis i s not accepted.  The conclusion  i s 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 d i r e c t l y applicable to the banks i s the  bank e f f e c t s adjusted group for d^ = 0, or competitive labour markets in Table 8.2. v^/b^.  On the consumer demand for loans, the price e l a s t i c i t y i s  Sample s t a t i 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 sample means.  This includes the variables z./x^, i=1,2  geometric  and x^/x^, x^  =2,...,4, whose c o e f f i c i e n t s 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 Loans Intercept Jtnzi £nz2 £nx £nx Jlnx^ £nx 2  3  5  -13.26(0.71) -14.95(4.11) - 1.13(0.27) 9.10(1.54) 6.22(2.36) 1.93(0.50) - 1.74(0.69) 0  Cash 0.31(0.07) Intercept - 1.13(0.27) fcnzi 0.25(0.05) £nz 0.33(0.13) £nx £nx 0.57(0.16) Anx^ - 0.17(0.05) *nx 0.16(0.06) X /X! 0.44(0.04) 2  2  b2 = 0 only d2 = 0 only  -  -  3  -  5  2  Demand Deposits Intercept - 1.91(0.51) Jtnz! 9.10(1.54) 0.33(0.13) £nz £nx - 5.44(0.78) £nx - 3.96(0.89) Anxit 0.54(0.28) £nx - 0.07(0.34) - 3.45(0.32) z /xi 2  2  3  -  5  2  -  3.60(1.10) 2.58(4.19) 0.82(0.27) 4.17(1.59) 0.65(2.39) 0.44(0.51) 0.71(0.70) 8.82(0.79)  -2.85 0.14 -1.26 3.21 -1 .75 0.11 -0.75 -9.77  0.78(0.06) 0.52 0.82(0.27) -1 .26 0.71(0.03) 0.46 0.07(0.13) 0.23 0.25(0.16) 0.60 0.22(0.05) -0.19 0.18(0.06) 0.18 0.24 0  (1.10) (4.15) (0.28) (1.58) (2.38) (0.50) (0.70) (0.78)  d  3  = 0 only  -4.83 -9.68 -1.05 6.45 3.63 0.93 -0.47 -7.78  (1 .05) (4.05) (0.27) (1.52) (2.33) (0.50) (0.70) (0.72)  di+ = 0 only  -3.79 -5.31 -1 .08 5.00 1.59 0.03 -0.61 -8.94  (1.10) (4.19) (0.27) (1.59) (2.40) (0.47) (0.70) (0.79)  (0.07) 0.32 (0.07) 0.30 (0.07) (0.27) -1.05 (0.27) -1 .08 (0.27) (0.04) 0.26 (0.05) 0.24 (0.05) (0.13) 0.30 (0.13) 0.31 (0.13) (0.16) 0.56 (0.16) 0.57 (0.16) (0.05) -0.20 (0.05) -0.17 (0.05) (0.06) 0.13 (0.06) 0.14 (0.06) (0.03) 0.43 (0.03) 0.44 (0.04)  4.80(0.47) -5.43 (0.39) -1.78 (0.49) -2.34 4.17(1.59) 3.21 (1.58) 6.45 (1.52) 5.00 0.07(0.13) 0.23 (0.13) 0.30 (0.13) 0.31 4.64(0.79) -4.84 (0.79) -4.38 (0.79) -4.07 0.77(0.91) 0.12 (0.89) -2.92 (0.86) -1 .72 1.43(0.28) 1.44 (0.28) 0.79 (0.28) 0.65 0.31(0.34) 0.28 (0.34) 0.29 (0.34) 0.30 0.65(0.26) 0 -3.54 (0.29) -3.05  (0.51) (1.59) (0.13) (0.79) (0.91) (0.27) (0.34) (0.32)  Time Deposits 2.43(0.40) Intercept £nzi 6.22(2.36) 0.57(0.16) £nz2 - 3.96(0.89) £nx £nx - 1.52(1.41) Anxit - 0.87(0.23) £nx 0.14(0.29) X /Xi - 0.21(0.26) 2  -  3  -  5  3  Labor Intercept inzi lr\Z2 ^nx2 *nx Irxx^ £nx 3  5  XI+/X!  AnL  -  3.77(0.31) 1.93(0.50) 0.17(0.05) 0.54(0.28) 0.87(0.23) 1.10(0.36) 1.35(0.24) 0.39(0.12) -375.23  -  1.46(0.42) 0.01 (0.41) 2.22 (0.29) 1.21 (0.42) 0.65(2.39) -1.75 (2.38) 3.63 (2.33) 1.59 (2.40) 0.25(0.16) 0.60 (0.16) 0.56 (0.16) 0.57 (0.16) 0.77(0.91) 0.12 (0.89) -2.92 (0.86) -1.72 (0.91) 1.68(1.42) 1.50 (1.42) -0.33 (1.41) 0.38 (1 .42) 0.45(0.24) -0.24 (0.24) -0.70 (0.23) -0.55 (0.23) 0.55(0.29) 0.43 (0.29) 0.36 (0.29) 0.34 (0.29) 0.72(0.29) 2.18 (0.26) 0 0.97 (0.29) 3.70(0.31) 0.44(0.51) 0.22(0.05) 1.43(0.28) 0.45(0.24) 1.21(0.36) 1.07(0.24) 0.45(0.12) -393.96  3.78 0.11 -0.19 1.44 -0.24 -1.10 -1.06 0.40  (0.31) (0.50) (0.05) (0.28) (0.24) (0.36) (0.24) (0.12)  -374.17  3.72 0.93 -0.20 0.79 -0.70 -0.93 -1.01 0.35  (0.31) (0.50) (0.05) (0.28) (0.23) (0.36) (0.24) (0.12)  -354.36  4.21 0.03 -0.17 0.65 -0.55 -0.14 -0.78  (0.26) (0.47) (0.05) (0.27) (0.23) (0.22) (0.22) 0  -352.73  Note: Dependent variables are identical to those indicated i n parentheses in Table 8.1  - Sa-  l a b l e 8.3  Test S t a t i s t i c s , C o m p e t i t i v e B e h a v i o r i n Output and Input Markets (X /DF) 2  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 V a l u e ( 0 . 0 0 5 ) , DF  Loans  52.22  7.88,1  Demand D e p o s i t s  89.68  7.88,1  Cash  50.10  7.88,1  Time D e p o s i t s  10.48  7.88,1  7.22  7.88,1  26.23  2.57,5  Labor All  Markets  - 220 -  T a b l e 8.4 Parameter E s t i m a t e s , T e s t s of C o m p e t i t i v e Rank B e h a v i o r , A l l Markets ( a s y m p t o t i c s t a n d a r d e r r o r s i n p a r e n t h e s e s and bank e f f e c t s  Loans Intercept £nz £nx  2 2  £nx3  Jlnxit £nx zi/*l z /xi 5  -13.32 - 9.49 - 1.13 8.14 3.07 0.82 - 2.16 0  (0.71) (4.01) (0.26) (1.50) (2.31) (0.45) (0.69)  Cash  2  2  3  £nx  5  X2/X1 X3/xi  0.79 -1.13 0.71 0.01 0.37 -0.16 0.22 0  (0.06) (0.26) (0.03) (0.13) (0.16) (0.05) (0.06)  Intercept £nzi £nz2 £nx2  £nx  3  £nxi+ £nx5 XLJ/X!  £nL  4.51 0.82 -0.16 0.85 -0.88 -0.25 -1.12 0 -414.70  (0.39) (1.50) (0.13) (0.77) (0.84) (0.26) (0.34)  Time Deposits 2.28 3.07 0.37 -2.31 0.12 -0.88 0.26 0  Labor .  -5.56 8.14 0.01 -6.17 -2.31 0.85 -0.21 0  2  Intercept £nzj, £nz &nx £nx  Demand Deposits  (0.26) (0.45) (0.05) (0.26) (0.22) (0.22) (0.22)  (0.29) (2.31) (0.16) (0.84) (1.40) (0.22) (0.29)  adjusted)  - 221  ( z ^ f z )/(x^fx  -  ) where z^ and x^ are the r e s p e c t i v e l y g e o m e t r i c sample  means f o r loans and m a t e r i a l s .  The dependent v a r i a b l e  remains  e x p e n d i t u r e on a g i v e n good d i v i d e d by t h a t on m a t e r i a l s , or v . z . / x ^ for outputs.  In a c t u a l e s t i m a t i o n , the p r i c e and g u a n t i t y of output  _ __ are r e s p e c t i v e l y (v^z^/x^)  * _ _ = v^ and (z^/x^) • (x.Jz^)  i  » = 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 g e o m e t r i c mean i n Table 8 . 5 .  Both l o a n s and demand d e p o s 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 . w i t h r e s p e c t t o own user c o s t s e n s i t i v e i n responding  is -1.72.  The e l a s t i c i t y of l o a n demand  Consumers are even more p r i c e  to demand d e p o s i t user c o s t s .  e l a s t i c i t y of demand i s - 2 . 2 5 .  Interest  The p r i c e  payments on c h e c k i n g  such as NOW a c c o u n t s , e l i c i t a l a r g e response  in deposit  increases.  On the supply s i d e , i n c o n f o r m i t y w i t h the h y p o t h e s i s the l a b o r market i s c o m p e t i t i v e .  testing,  P e r f e c t l y c o m p e t i t i v e l a b o r markets  imply t h a t the e l a s t i c i t y o f 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 i m e d e p o s i t s , both s u p p l i e d by customers, unity.  accounts,  are a l s o g r e a t e r  Consumers thus appear t o 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 8.6.1  than  Policy  Implications  Costs of Noncompetitive 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 n p u t s are g r e a t e r than u n i t y .  A l t h o u g h the t e s t of p r i c e t a k i n g  b e h a v i o r i n a l l markets i s not a c c e p t e d , the r e l a t i v e l y e l a s t i c  - 222 -  Table 8 . 5 Price E l a s t i c i t i e s of Demand for Outputs and Supply for Inputs (eighteen New York/New Jersey banks 1 9 7 3 - 1 9 7 8 ) User Cost (Unsealed)  Scaling Factor  User Cost Index  Price E l a s t i c i t y of  (2)  (3) =(D*(2)  Demand(Supply)  (1) 0.0376  Demand Deposits v  0.0451  z /xi  0.0520  x / 2  X l  16.38  0.0082  x /  X l  237.94  1.1872  X1+/X!  Cash  Time Deposits  Labor  v  2  151.87  *  15.41  *. . vi/bi  6.85  * v /b  * w  0.85  *, w /d  * 3  1.95  * w /d  * w  5.77  Wi^d^  v  2  2  2  -1.72  -2.25  2  w  2  w  A  409.94  l  Loans  3  2  w  2  3  2  3  1.93  2.01  3  4.86  4  *  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. e l a s t i c i t i e s are negative, supply e l a s t i c i t i e s p o s i t i v e .  Demand  - 223  -  e s t i m a t e s may suggest the c o s t s of imposing p e r f e c t c o m p e t i t i o n are low. Considering e f f e c t s adjusted -v z /x 1  1  1  the loan market, the e s t i m a t e d e q u a t i o n w i t h bank is  = -3.79  -5.3Unz  -1 . 0 8 £ n z  ]  -0.03£nx^ - 0 . 6 U n x  +5.0(Hnx  2  -8.94z /x  5  1  + 1 .59fcnx  2  (8.27)  1  the n e g a t i v e s i g n on v^ a r i s i n g because user c o s t s of loans expressed  n e g a t i v e l y , as net revenues.  If  are  perfect competition is  imposed  on a l l m a r k e t s , the loan e q u a t i o n i s , again w i t h bank e f f e c t s a d j u s t e d -v z /x l  1  1  = -13.32 - 9 . 4 9 J l n z  -1.13£nz  1  -0.82£nx^ -2.16£nx  2  +8.14£nx  2  +3.07£nx  3  (8.28)  5  The mean 1975 o b s e r v a t i o n , w i t h d a t a measured as d e v i a t i o n s from the g e o m e t r i c mean i s f o r the e n t i r e sample £nz  1  0.035  £nz  2  0.017  *nx  2  0.038  £nx  3  0.117  so - v z / x 1  -12.53,  1  1  = -12.74 i n ( 8 . 2 7 ) .  irxx^ 0.198 z 1  /  Inx^  0.052  1.017  x 1  With z / x 1  under n o n - p r i c e t a k i n g b e h a v i o r .  1  If  = 1.017, the v  1  index  perfect competition  imposed, from (8.28) the same v a l u e i s - 1 5 . 0 4 , or a user c o s t -14.79.  User c o s t s of output are n e g a t i v e .  c a s e , -v.j = 14.79, or v^ = - 1 4 . 7 9 .  is is  index of  Here, i n the c o m p e t i t i v e  Smaller negative values  imply  r e t u r n s , which o b t a i n i n the i m p e r f e c t l y c o m p e t i t i v e model.  higher  The net  r e t u r n from l o a n s i s u n d e r s t a t e d by about 15 p e r c e n t . The r e s u l t s c o n f i r m t h a t i m p e r f e c t c o m p e t i t i o n r e s u l t s prices.  The a c t u a l d i f f e r e n t i a l  i s 15.2  percent.  in  higher  This i m p l i e s that  if  p e r f e c t c o m p e t i t i o n i s imposed and e s t i m a t e d , and t h i s does not o b t a i n ,  - 224  l o a n revenues Further, user  for a given  loan l e v e l are u n d e r s t a t e d  the loan demand i s not i n s e n s i t i v e  c o s t components.  loans,  -  deposits  by 15.2  to i n t e r e s t  percent.  r a t e s and o t h e r  The response i s performed f o r the same l e v e l  of  and o t h e r 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 competition.  For  p o l i c y purposes, e s t i m a t e s based on imposed p r i c e t a k i n g may lead to errors.  If  o t h e r components  of loan user c o s t s  t h a t l o a n i n t e r e s t r a t e s are h i g h e r  8.6.2  Monetary  policy.  As an example, c o n s i d e r  for  a Federal  Suppose t h e r e i s a ten percent r e d u c t i o n i n cash or e x c e s s quantity.  In the loans e q u a t i o n  the dependent  (8.27) w i t h a c o e f f i c i e n t  v a r i a b l e changes by +0.19.  monetary  policy is  Regarding  substantially  time d e p o s i t s ,  the c o e f f i c i e n t of x^ i n l o g a r i t h m s  The c o e f f i c i e n t on demand d e p o s i t s  t a k i n g model, and -9.49 conclusions  are s i m i l a r .  c o n s i d e r e d , monetary  so the e f f e c t of  greater.  i n the non p r i c e t a k i n g e q u a t i o n , and 3.07  equation.  of  In the p e r f e c t  c o m p e t i t i o n imposed model the c o e f f i c i e n t i s 8.14,  1.59  assumptions.  a c t i o n t o change the q u a n t i t y of money as r e f l e c t e d i n x.,,  reserve 5.00,  implies  i s s u e examined i s the i m p l i c a t i o n of these r e s u l t s  t h e conduct of monetary  cash.  than under c o m p e t i t i v e  it  Policy  The second  Reserve  are c o n s t a n t ,  i n the p r i c e  i s -5.31  i n the p r i c e t a k i n g model.  is  taking  i n the non p r i c e  In a l l cases the  R e g a r d l e s s of the type of monetary  good  p o l i c y e f f e c t s on the loan market are o v e r s t a t e d  p e r f e c t l y c o m p e t i t i v e markets are i n c o r r e c t l y assumed. amount of l o a n response,  g i v e n user c o s t s ,  The p r e d i c t e d  i s only about 60 percent  of  if  - 225  -  t h e magnitude p r e d i c t e d i f time d e p o s i t b a l a n c e s  change.  On the i n p u t s i d e , the demand by hanks f o r time d e p o s i t s , p r i c e t a k i n g i s not imposed w w /x 3  3  1  = 1.21  is  + 1.59Jlnz  1  + 0.57J>nz  - 0.55Jlnx^ + 0 . 3 4 £ n x  and the c o r r e s p o n d i n g  where  2  - 0.72Jlnx  - 0.97x /x  5  3  eguation with p r i c e taking  +  2  0.38£nx  3  (8.29)  1  imposed  i n a l l markets  is w w /x 3  3  1  = 2.28 + 3 . 0 7 £ n z  1  + 0.37£nz  - O.SSJlnx^ - 0 . 2 6 £ n x  2  8.7  o f 1.72  Concluding  2  + 0.12Jlnx  3  (8.30)  t o monetary p o l i c y .  reduces time d e p o s i t s  t h e model w i t h p r i c e t a k i n g imposed. a response  - 2.3Unx  5  A g a i n , t h e r e are d i f f e r e n c e s i n response i n cash of one percent from x  2  by 2.31  An  increase  percent  The non p r i c e t a k i n g model  p e r c e n t , or about 30 percent  in  involves  smaller.  Remarks  The r e s u l t s i n d i c a t e t h a t i t i s p o s s i b l e t o d e v e l o p and t e s t a model o f non p r i c e t a k i n g i n b a n k i n g .  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 t a k i n g i s not r e j e c t e d o n l y i n the l a b o r market.  The  parameter e s t i m a t e s o b t a i n e d by imposing p r i c e t a k i n g when i t i s not t h e c a s e are s i m i l a r i n some c a s e s , The a n a l y s i s  but d i s s i m i l a r i n  others.  of monetary p o l i c y u l t i m a t e l y r e q u i r e s a complete  model o f the microeconomics of f i n a n c i a l f i r m s .  If  these f i r m s are not  p e r f e c t c o m p e t i t o r s , t h i s must be r e c o g n i z e d i n the model b u i l d i n g .  - 226  -  NOTES  ^ e e Bond and Shearer 2  S e e L u c k e t t [1976, p.  [1972, p.  315].  72-92].  3  There are two a l t e r n a t i v e procedures f o r measuring concentrations. The market snare h e l d by a s p e c i f i c number of f i r m s and t h e H e r f i n d a h l index which i s the sum of the squares of the s h a r e s . Hence, t h r e e banks of equal s i z e would have a H e r f i n d a h l index v a l u e o f ( 1 / 3 ) + ( 1 / 3 ) + (1/3) = 3/9 = 0 . 3 3 . During the sample p e r i o d 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 s w i t c h to the l a t t e r measure was made i n 1982. 2  2  '•See Mingo 5  [1977].  K l e i n [1971,  p.  207].  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 t h e r e i s m o n o p o l i s t i c b e h a v i o r on the p a r t of p r o d u c e r s . Two drawbacks t o L a u ' s method are t h a t ( i ) i t cannot be t e s t e d 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 e s t i m a t e d e q u a t i o n s can not be used to p r e d i c t output q u a n t i t y or s e l l i n g p r i c e separately. D i e w e r t ' s approach r e q u i r e s the assumption of a convex t e c h n o l o g y and a l o c a l knowledge of the demand and supply c u r v e s t h a t t h e f i r m i s e x p l o i t i n g so t h a t a p p r o p r i a t e shadow p r i c e s can be calculated. See Diewert [1982, pp. 584-590] f o r more i n f o r m a t i o n . 6  See C h r i s t e n s e n , Jorgenson and Lau [ 1 9 7 3 ] , where l a b o r i n p u t used as t h e 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 .  is  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, p e r s o n a l c h a r a c t e r i s t i c s and p r i c e s of o t h e r goods. These have the e f f e c t o f s h i f t i n g t h e r e c i p r o c a l demand f u n c t i o n . Hence the D^ can be s c a l e d by s h i f t e f f e c t s t o account f o r t h e s e f a c t o r s .  See Diewert [ 1 9 8 2 ] ,  p.  585.  q  P r i c e - t a k i n g b e h a v i o r on output markets has been t e s t e d by Appelbaum [1979] f o r the U.S. petroleum i n d u s t r y and Appelbaum and K o h l i [1979] f o r Canadian aggregate o u t p u t . T h e assumption of p r o f i t m a x i m i z i n g b e h a v i o r u n d e r l i e s t h e models o f Pesek [ 1 9 7 0 ] , Towey [ 1 9 7 4 ] , Adar, Agmon and O r g l e r [ 1 9 7 5 ] , Greenbaum,. A l i , and M e r r i s [ 1 9 7 7 ] , Sealey and L i n d l e y [ 1 9 7 7 ] , Mingo and W o l k o w i t z [1977] and M u l l i n e a u x [ 1 9 7 8 ] . l 0  i s p a r a m e t r i c i t may s t i l l be not 1 p o s s i b l e t o i d e n t i f y t h i s , and a n o r m a l i z a t i o n 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 t o view the r e m a i n i n g i m p e r f e c t c o m p e t i t i o n e f f e c t s as o c c u r r i n g r e l a t i v e t o the f i r s t input market. 1 1  In  e s t i m a t i o n , although  - 227 -  CHAPTER 9  CONCLUDING REMARKS T h i s r e s e a r c h has i n v e s t i g a t e d t h e s h o r t technology  run p r o d u c t i o n  and the e f f e c t s of r e g u l a t i o n on f i n a n c i a l f i r m s .  tions considered and d e p o s i t  include reserve reguirements,  Regula-  interest rate  ceilings,  insurance.  User c o s t s per u n i t o f s e r v i c e have been d e r i v e d f o 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 n c l u d e t h e e f f e c t s o f r e s e r v e  ments, c a p i t a l g a i n s o r l o s s e s , service charges.  deposit  insurance,  i n t e r e s t r a t e s , and  Items g e n e r a t i n g more e x p e n d i t u r e than revenue f o r t h e  f i r m have p o s i t i v e user c o s t s ,  and are d e f i n e d t o be i n p u t s .  n e g a t i v e u s e r c o s t s are d e f i n e d as o u t p u t s .  i m p o r t a n t t h a t p r i c e s ( o r user c o s t s )  user c o s t s profit  Those w i t h  Though i t i s not i m p o r t a n t  which f i n a n c i a l goods are i n p u t s and which a r e o u t p u t s is  require-  to the f i r m , i t  be a s s i g n e d t o each good.  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  function.  The  of the  Comparative s t a t i c s on p r o f i t s , s u p p l i e s o f output and  demands f o r i n p u t a r e d e r i v e d f o r i n t e r e s t r a t e s and monetary regulations. A s p e c i f i c a t i o n has been d e r i v e d f o r t h e v a r i a b l e p r o f i t f u n c t i o n , and t h e 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 m o n o t o n i c i t y and c o n v e x i t y .  A t e s t f o r t h e e x i s t e n c e o f a producer based money  supply,  as a subset  imposes  no p r i o r r e s t r i c t i o n on t h e form of t h e money Symmetry  o f f i n a n c i a l goods has been d e v e l o p e d .  i s imposed on t h e e s t i m a t i n g system.  The t e s t  supply. Given t h i s ,  both  m o n o t o n i c i t y and c o n v e x i t y h o l d f o r t h e g e o m e t r i c mean and at a l l d a t a points.  - 228  -  The m a t r i x of e l a s t i c i t i e s of t r a n s f o r m a t i o n i s w e l l All  p r i n c i p a l d i a g o n a l elements are p o s i t i v e .  supply,  f o r l o a n s and demand d e p o s i t s ,  behaved.  The e l a s t i c i t i e s of  are both l e s s than u n i t y .  On t h e  demand s i d e , e l a s t i c i t i e s f o r c a s h , l a b o 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 s e t o u n i t y , w h i l e t h a t f o r time d e p o s i t s than one.  This  suggests an i n f l e x i b l e t e c h n o l o g y  is  less  for f i n a n c i a l inputs  and o u t p u t s , w h 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 physical  inputs.  R e l a t i v e l y l a r g e changes costs,  i n the p r i c e v a r i a b l e s u n d e r l y i n g  i n i n t e r e s t r a t e s , deposit insurance charges,  user  wage r a t e s and  m a t e r i a l p r i c e s , are r e q u i r e d t o induce s u b s t a n t i a l s h i f t s  i n the  of l o a n s and demand d e p o s i t s ,  This  and input demands by banks.  supply  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 t e s s h o u l d be the o b j e c t o f c e n t r a l bank c o n t r o l i n monetary p o l i c y . T e s t s on t h e e x i s t e n c e of a producer based monetary are p e r f o r m e d .  subaggregate  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 t h a t the r e l a t i v e u s e r  c o s t f o r any p a i r o f f i n a n c i a l commodities w i t h i n the subaggregate independent of t h e q u a n t i t i t y of any commodity o u t s i d e i t . performed on whether the monetary subaggregate  Tests  c o n t a i n s cash o n l y ,  is are cash  and demand d e p o s i t s , or c a s h , demand d e p o s i t s and time d e p o s i t s . The proposed a g g r e g a t i n g  s t r u c t u r e does not r e q u i r e the money  s u p p l y t o 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  money subaggregates  the  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 s u p p l y i s always p r e f e r a b l e to the Cobb-Douglas logarithmic)  aggregate.  (linear  The r e s u l t s suggest t h a t 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 l a c k e r b y , Primont and R u s s e l l  [1977] may be  substantial. Some c o m p a r a t i v e s t a t i c s on changes i n r e g u l a t i o n s u s i n g the e s t i m a t e d t e c h n o l o g y . deposit  S p e c i f i c a l l y , interest rate  i n s u r a n c e and r e s e r v e requirements are The t h e o r y i s extended to account  financial firms. elastic,  are  performed ceilings,  changed.  f o r market i m p e r f e c t i o n s  facing  The demand f o r output i s p e r m i t t e d not to be p e r f e c t l y  and s i m i l a r f l e x i b i l i t y  i s p e r m i t t e d on the supply  of  inputs.  P r e v i o u s models do not permit non p r i c e t a k i n g i n output and markets.  Also,  the e l a s t i c i t i e s are a l l e s t i m a t e d , and do not r e q u i r e a  p r i o r i information.  The model developed commences from the  production  f u n c t i o n , and i s not s t r i c t l y comparable t o the v a r i a b l e p r o f i t model.  input  function  T h i s i s because a t r a n s l o g s p e c i f i c a t i o n i s used, and the form  is  not s e l f - d u a l . T e s t s are developed s e p a r a t e l y f o r p r i c e t a k i n g i n l o a n s , demand d e p o s i t s ,  time d e p o s i t s and l a b o r .  cash,  In the e m p i r i c a l r e s u l t s  for  t h e e i g h t e e n New York and New 3ersey banks 1973-1978, p r i c e t a k i n g a c c e p t e d i n the l a b o r market, but not accepted i n the r e m a i n i n g markets. introduces  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 .  is  four  This  the i s s u e o f the c o s t of imposing p r i c e t a k i n g when i t i s  not  the case. P r i c e t a k i n g i s imposed i n a l l m a r k e t s , and the e s t i m a t e s w i t h those when p r i c e t a k i n g i s not imposed. are c a l c u l a t e d f o r h o l d i n g s In some c a s e s ,  Monetary  of c a s h , demand d e p o s i t s ,  policy and time  compared  responses deposits.  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 , w h i l e i n o t h e r s  e r r o r can be as l a r g e as 20 p e r c e n t .  the  - 230 BIBLIOGRAPHY A d a r , Z., T. Agmon, and Y . E . O r g l e r [ 1 9 7 5 ] , "Output Mix and J o i n t n e s s i n P r o d u c t i o n i n the Banking F i r m , " J o u r n a l o f Money C r e d i t and B a n k i n g , 7 , 235-243. A l h a d e f f , D.A. [ 1 9 5 4 ] , Monopoly and C o m p e t i t i o n i n B a n k i n g , B e r k e l e y , California: U n i v e r s i t y of C a l i f o r n i a P r e s s . A i g n e r , D . J . 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