Overdraft Lending and Aggregating Demands Subject to Constraint

An overdraft is a lending instrument, usually offered by banks, that for a predetermined period allows the borrower to overdraw his account up to a predetermined limit. The timing and size of withdrawals is at the discretion of the borrower except, of course, when the credit limit is reached. Lending by Australian banks is predominantly by overdrafts and some attention has been focussed in the past on explaining the behaviour of overdraft advances. Individual demands for credit can therefore be characterised as censored (that is, subject to an upper limit). In practice there are only aggregate data for advances by overdrafts, which creeates difficulties for estimating the behavioural parameters for the demand for advances by overdraft. This paper develops a theory of aggregation of a group of individual demands that are each censored. A measure of credit rationing can also be derived from the approach. The approach is implemented using Australian data for three classes of business borrowers. The results support the view that the observed aggregate quantity of advances by overdraft is determined by both supply and demand factors. This finding is consistent with earlier work by researchers using Australian data. The significance of the present results lies in the attention paid to aggregation and the implications this has for the specification of the estimating equations. A second benefit of the approach is that it permits direct estimation of the distribution of rationed credit demands. The correctly aggregated equation specifies the observed stock of advances as a weighted average of constrained and unconstrained demands for credit, where the weights are interpreted as the probability that an individual borrower faces a binding credit limit. In that limited sense the probability measure, which varies over time, indicates the likelihood and distribution of credit rationing in the overdraft sector. These estimated probabilities are calculated for the three classes of business borrowers (agriculture, commerce and manufacturing) and are similar to the overdraft utilisation ratios in these sectors, which are independent measure of tightness in credit markets.