Many analyses of rationing in credit markets have focused upon the role of imperfect information: lenders may not know whether borrowers are honest or what they will do with the proceeds of a loan once it has been granted. It seems plausible that under such conditions borrowers will be able to borrow less than they wish to. Models of credit rationing tend to be based on an analogy with commodity rationing, taking the actual interest rate as a reference point and asking whether at this rate borrowers would wish to borrow more or less.
In Discussion Paper No. 261, Anindya Banerjee and Research Fellow Timothy Besley consider instead the concept of `credit restriction', using a simple two-period model of credit contracts with two agents, a lender and a borrower. In the first period, a loan is made. The borrower undertakes a project which has two possible outcomes: a `good' one yielding a positive return, and a `bad' one yielding nothing. The borrower chooses how the loan is used and controls the probability of `success'. This approach highlights two kinds of credit market imperfections: a `bad' outcome may lead to default, and the agent may take risks without the lender's knowledge.
Banerjee and Besley therefore focus on the phenomena of limited liability and imperfect information. Limited liability arises since it is assumed that lenders do not go bankrupt if the loan they grant to the borrower is not repaid. Hence the issue is one of differential liability for the failure of the project. Imperfect information is introduced into the model by assuming that the project to which the proceeds of the loan are applied by the borrower cannot be observed by the lender like the moral hazard problem analysed in the insurance literature.
Even with full information concerning the probability of success, can the possibility of default by itself lead to restriction or rationing of credit? The authors test for credit rationing by using as a reference the depositors' interest rate, i.e. the rate which borrowers would face if, instead of demanding a loan from the lender, they deposited savings with him; they find that if the consumer were able to borrow at the depositors' interest rate, he would always do so credit is rationed.
Rationing arises under full information because the first-best outcome (in an Arrow-Debreu sense) is unattainable as the bad outcome is not insured against. Hence the credit market is still imperfect, since it is in effect assumed that the borrower but not the lender has limited liability. The lender, who still pays depositors when the project fails, does not set the marginal rate of substitution between the good and bad states equal to the deposit rate. This is a `limited liability effect'. Although Banerjee and Besley draw unambiguous conclusions about credit restriction in their model, they find that credit rationing does not always occur. In one case, if the lender is risk-neutral, over-consumption of credit occurs

Moral Hazard and Limited Liability in the Market for Loans: Credit Restriction Versus Credit Rationing Anindya Banerjee and Timothy Besley

Discussion Paper No. 261, August 1988 (ATE)