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A Theory and Test of Credit Rationing: Comment Georgia State University ScholarWorks @ Georgia State University ECON Publications Department of Economics 1976 A Theory and Test of Credit Rationing: Comment Corry F. Azzi Lawrence University, [email protected] James C. Cox Georgia State University, [email protected] Follow this and additional works at: https://scholarworks.gsu.edu/econ_facpub Part of the Economics Commons Recommended Citation Azzi, Corry F., and James C. Cox. 1976. “A Theory and Test of Credit Rationing: Comment”. The American Economic Review 66 (5): 911–17. This Article is brought to you for free and open access by the Department of Economics at ScholarWorks @ Georgia State University. It has been accepted for inclusion in ECON Publications by an authorized administrator of ScholarWorks @ Georgia State University. For more information, please contact [email protected]. A Theory and Test of CreditRationing: Comment By CORRY F. AzzI AND JAMES C. COX* One frequently encounters the casual em- equity combinations rather than only inter- pirical conclusion that some consumers and est rate offers. firms are not able to borrow as much as they Freimer and Gordon consider the case of a would like at market rates of interest. The risk-neutral lender who faces a certain cost of existence of these rejected offers to pay mar- funds and observe that his supply of credit ket rates of interest is then said to constitute to a borrower may not be an increasing func- "credit rationing." Marshall Freimer and tion of the rate of interest offered by the Myron Gordon, in addition to Dwight Jaffee borrower. They attach significance to this and Franco Modigliani, assume that rejected observation, saying that it raises the possi- market interest rate offers exist and then bility of unstable equilibria and protracted attempt to explain-why lenders might engage excess demand in credit markets; this has in such "credit rationing." been called -"disequilibrium credit ration- Our analysis begins by questioning the ing." In Sections II and III we show that, prevalent identification of credit rationing under various conditions, the supply of credit with rejected offers to pay market rates of to a borrower is an increasing function of the interest. This concept of credit rationing is amounts of collateral and equity offered by apparently derived by analogy with the the borrower. Thus under the conditions as- theory of commodity markets under cer- sumed by Freimer-Gordon, and under more tainty. In that theory, any economic agent general conditions, a borrower will be sup- who makes an effective demand for a com- plied more credit if he offers more collateral modity, that is, who offers to pay its market or equity. price, is subject to nonprice commodity ra- Jaffee and Modigliani's primary concern is tioning if his demand is not supplied. The with "equilibrium credit rationing." They common extension of this conclusion to credit assume that a lender can act as a discrimi- markets is that any economic agent who nating monopolist and conclude that he will offers to pay the market rate of interest on ration some borrowers if he is subject to an some type of loan is subject to credit ration- institutional constraint which requires him to ing if his "demand" for credit is not supplied. charge the same interest rate to borrowers We argue that this concept of credit ration- with different demand curves for credit. In ing is not useful because it is based on an in- Section IV we demonstrate that credit ra- appropriate implicit assumption that an offer tioning is not optimal for any lender unless to pay the market rate of interest on a loan there are effective institutional constraints constitutes an effective demand for credit. In on the collateral and equity terms of loan Section I we show that the distinction be- contracts in addition to an effective con- tween a borrower's wants and demands for straint on interest rates. Therefore, given the credit depends not only on the rate of interest Jaffee and Modigliani assumption of a single offered, but also on the amount of collateral interest rate constraint, their conclusion that offered and on the borrower's equity. There- credit rationing is rational for a monopolistic fore, if one is to have a concept of credit ra- lender is shown to be false. tioning that refers to nonsupplied effective demands for loans, rather than unsatisfied I. Collateral, Equity, and Effective wants, it must involve analysis of lender re- Demand for Loans sponse to offers of interest rate-collateral- We proceed to an analysis of the role of *Assistant professor of economics, Lawrence Uni- equity and collateral in transforming a desire versity, and associate professor of economics, Univer- for into an effective demand for a loan. sity of Massachusetts, respectively. We wish to credit thank Ronald Ehrenberg and Thomas Russell for Assume that a lender has preferences defined helpful comments. over his random terminal wealth x, and that 911 This content downloaded from 131.96.28.172 on Mon, 11 Jan 2016 18:55:05 UTC All use subject to JSTOR Terms and Conditions 912 THE AMERICAN ECONOMIC REVIEW DECEMBER 1976 he prefers more wealth to less. He begins minal wealth x for all values of 0 is given by with some initial wealth w>O and lends an the following function: amount 1, where 0 _ I < w, to a borrower who invests it in an opportunity which yields the (1 + p)w + (0 - p)l + (1 + O)y constant stochastic rate of return 0, where (3) x + (1 +wr)z, for-1 ? 0 <0 0> -1. The lender is assumed to invest the 0 rest of his wealth (w-l) at the constant (1 +p)w+ (r-p)l,for ? stochastic rate of return p, where p_ - 1. If If a loan transaction is to be made, the the loan is repaid, then the lender's terminal ,terms of the transaction must provide the wealth is the sum of the principal and inter- lender with a distribution of terminal wealth est on the loan (1+r)l, and the value of his that he prefers to all other attainable distri- other investment (1+p)(w-1), and can be butions. Unless the borrower has monopoly written as (1+p)w+(r-p)1. control of the probability distribution of 0, The amount the borrower invests is the the lender has the option of investing some sum of the amount of the loan 1, and the of his initial wealth in an opportunity which amount of the borrower's equity y, where yields 0. If the lender can invest in such an y>0. The loan will be in default if 0 is less opportunity, then one of the investment than the default rate of return 0*, which is the options in his feasible choice set is provided lowest rate of return on the borrower's in- by investing the amount (w-l) in an oppor- vestment sufficient to pay the principal and tunity which yields p and an amount I in an interest on the loan. opportunity which yields 0. This provides the terminal wealth function (1) rl-y x= I + y (4) (1+p)(w- 1)+(1+0)1= (l+p)w for all 0 If the borrower provides some collateral, +(O-p)l, the lender can obtain payment of principal If y and z are both zero, then (4) dominates and interest at some rates of return that are (3) and the potential lender will never prefer below the default rate of return on the bor- the loan to making the investment himself. rower's investment. Let the borrower provide Since a desire for credit by a nonmonopolistic as collateral an asset that has value z, where potential borrower who does not supply col- z> O, at the time the loan contract is written. lateral or equity will never be supplied, such The subsequent value of the collateral is the a desire cannot be an effective demand for random variable (1 +lr)z, where 7ris the con- credit. We thus have: stant stochastic rate of return on the col- lateral asset and w ? - 1. The lender will ob- PROPOSITION 1: A nonmonopolistic poten- tain payment of principal and interest on a tial borrowermust providea positive amount of collateralized loan as long as the total re- collateral or equity to transform a desire for turns on the investment (l+O)(l+y), plus credit into demandfor a loan. the value of the collateral (1 +7r) z, exceed the will ever supply a loan to a poten- principal and interest due on the loan (1 + r)1. No lender Thus the lender will collect principal and in- tial borrower who does not provide a positive as as the terest if 0 is not less than the repayment rate amount of collateral or equity long does not have monopoly control of of return 0, where borrower a return distribution. Monopoly control of a (2) ^ rl-y-(1 +ir)z return distribution is a stronger condition = (2) than monopoly control of an investment op- ~~ I + Y portunity. The former requires that the If 0 is less than 0 then the lender's terminal lender be unable, through any combination wealth is the sum of the values of his alterna- of portfolio and direct investment, to dupli- tive investment and the borrower's invest- cate the distribution of returns on the poten- ment and collateral. Thus the lender's ter- tial borrower's investment opportunity. This content downloaded from 131.96.28.172 on Mon, 11 Jan 2016 18:55:05 UTC All use subject to JSTOR Terms and Conditions VOL.
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