Scoring by usage

This paper aims to discover whether the predictive accuracy of a new applicant scoring model for a credit card can be improved by estimating separate scoring models for applicants who are predicted to have high or low usage of the card. Two models are estimated. First we estimate a model to explain the desired usage of a card, and second we estimate separately two further scoring models, one for those applicants whose usage is predicted to be high, and one for those for whom it is predicted to be low. The desired usage model is a two-stage Heckman model to take into account the fact that the observed usage of accepted applicants is constrained by their credit limit. Thus a model of the determinants of the credit limit, and one of usage, are both estimated using Heckman's ML estimator. We find a large number of variables to be correlated with desired usage. We also find that the two stage scoring methodology gives only very marginal improvements over a single stage scoring model, that we are able to predict a greater percentage of bad payers for low users than for high users and a greater percentage of good payers for high users than for low users

Sample selection bias in credit scoring models

One of the aims of credit scoring models is to predict the probability of repayment of any applicant and yet such models are usually parameterised using a sample of accepted applicants only. This may lead to biased estimates of the parameters. In this paper we examine two issues. First, we compare the classification accuracy of a model based only on accepted applicants, relative to one based on a sample of all applicants. We find only a minimal difference, given the cutoff scores for the old model used by the data supplier. Using a simulated model we examine the predictive performance of models estimated from bands of applicants, ranked by predicted creditworthiness. We find that the lower the risk band of the training sample, the less accurate the predictions for all applicants. We also find that the lower the risk band of the training sample, the greater the overestimate of the true performance of the model, when tested on a sample of applicants within the same risk band ¾ as a financial institution would do. The overestimation may be very large. Second, we examine the predictive accuracy of a bivariate probit model with selection (BVP). This parameterises the accept-reject model allowing for (unknown) omitted variables to be correlated with those of the original good-bad model. The BVP model may improve accuracy if the loan officer has overridden a scoring rule. We find that a small improvement when using the BVP model is sometimes possible

Recalibrating scorecards

Many credit scoring systems depend on scorecards which order applicants by credit risk. However the scorecards may also have other properties with certain scores reflecting certain good:bad odds or differences in scores having the same property throughout the score range. Other properties like positivity of attribute points may be required for palatability or internal marketing reasons. The paper outlines the results of a small survey of what properties scorecard builders require of their scorecards. It then discusses how these properties can be obtained and describes a linear programming formulation which recalibrates scorecards so as to produce the best approximate scorecard with the properties required

Does scoring a subpopulation make a difference?

SIGLEAvailable from British Library Document Supply Centre- DSC:9350.10705(EU-DBS-WP--95/20) / BLDSC - British Library Document Supply CentreGBUnited Kingdo