Handling selection bias when choosing actions in retail credit applications

In many situations one needs to know which action one should take with a customer to yield the greatest response. Typically, estimates of the response functions of different actions will be based on the responses of customers previously assigned to each action. Often, however, the previous assignments will not have been random, so that estimates of the response functions will be biased. We examine the case of two possible actions. We look at the error arising from using the simple OLS estimate ignoring the selection bias, and also explore the possibility of using the Heckman model to allow for the sample selectivity. The performance of Heckman’s model is then compared with the simple OLS through simulation.