Credit scoring with uncertain class definitions

In credit-granting operations, the definition of what is meant by a ‘good’ customer will depend on economic and commercial factors. Typically the definition has an element of arbitrariness about it: defining profitability is difficult, and various proxy measures are used, such as number of months in arrears, amount over the overdraft limit, current-account turnover, or functions of these and other variables. Moreover, scorecards are often used for long periods of time, so that the level at which behaviour is ‘good’ is likely to change in response to changing external circumstances. To allow for this, one could construct a new scorecard, based on a new definition of what one means by good, but this can be expensive. To overcome this, we propose a new class of credit-scoring models which allows one to choose the definition of ‘good’ when the classification is to be made, and not when the scorecard is constructed. These ‘global’ models are based on estimating the cumulative distribution function of variables which may be partitioned to distinguish between good and bad customers. Moreover, we demonstrate that these global models perform at least as well as purpose-built scorecards obtained by constructing separate scorecards for each new definition of ‘good’. We illustrate with three examples.