Research Discussion Paper – RDP 8101T Overdrafts and Credit Rationing


A line of credit or overdraft is a common contingent lending contract that is an alternative to a fixed or fully drawn loan. The latter has received much attention in empirical and theoretical analyses while the former has received virtually none. In particular, much effort has been put into investigating credit rationing, which has been defined as occurring when a borrower wants a larger loan than is offered at the ruling interest rate.

The meaning of credit rationing in a line of credit or overdraft regime is the subject of this paper. An overdraft is the right to overdraw an account, up to a specified maximum and over an agreed period after which time credit limits are reviewed. The borrower pays interest on the credit he uses, which is determined by him up to the maximum allowable.

In such a system, the lender faces uncertainty from two sources. First, when the credit limit is established there is uncertainty as to how much credit will actually be used during the life of the credit arrangement. This is significant to the lender because he may have to find cash to cover unexpected fluctuations in realised usage of the credit line. Second, there is uncertainty concerning the borrower's ability to replay the overdraft loan plus interest when the overdraft contracts terminates. This is the default risk issue that is commonly addressed in the context of fixed loans.

There are in effect two distinct demands for credit in an overdraft or line of credit system. First, there is the demand for the credit limit that is available in all contingencies and which is independent of the second demand, which is the actual drawing against the credit limit. This leads quite naturally to two concepts of credit rationing with overdraft, which I shall call ex ante and ex post. Ex ante rationing occurs when a borrower would like a larger credit limit, given his expectations of the interest rate he will be charged, prior to his actual use of the credit limit. That is, the borrower can anticipate the possibility of some situations in which he might face a binding credit constraint. Ex post rationing occurs when the borrower needs more credit than his limit given the interest rate.

This paper is concerned with the existence of ex ante credit rationing in a credit market in which there are no interest rate ceilings on borrowers and lenders, and the credit market is assumed to be competitive in that lenders earn zero expected profit. The result is obtained in a simple two period model in which the borrower requires credit to finance a loan project that is subject to diminishing returns (such as a perfect competitor financing production subject to increasing marginal costs) and faces default risk. A further complication is introduced by assuming that the borrower has a random source of revenue during the life of the credit agreement and this random revenue affects his need for credit from the lender. This model is an abstraction from reality that tries to capture three features of real-life line of credit arrangements:

(i) such facilities are typically available to borrowers who are financing working capital and whose revenue from the sale of output may be randomly spaced during the time the credit facility exists.

(ii) since the borrower's cash flow is irregular, then to the extent that overdraft credit and retained earnings are the only source of working capital to the borrower any fluctuations in cash flow will have an impact on the demand for borrowed credit.

(iii) the credit facility is never established for an indefinite period, but rather is set up subject to review after a finite period. Once established, the limit is not altered until the review date. This abstracts, of course, from any central bank directive concerning limitations on lending rights.

In addition to showing the existence of ex ante credit rationing, the paper also considers the impact of an alternative asset for the borrower to invest in in addition to working capital. As expected, the existence of the asset, by increasing the opportunities to the borrower, leads to a demand for a larger credit limit. The effect of a binding ceiling on lending rate is to raise the average rate of credit utilisation and to increase the degree of credit rationing.