Adverse selection and non-take inference with coherent risk and response scoring

Abstract

The authors offer a mathematical model for adverse selection by individual borrowers based on preferences for offers and the default (Bad) or non-default (Good) status of booked accounts. We define the condition for borrower risk and response when there is no adverse selection (NAS). This definition provides us with a direct comparison between the prior and posterior conditional probabilities of default by an individual borrower who Takes an offer; this allows us to obtain estimates of differential response rates for individual borrowers and the Good/Bad odds for Take, Non-Take and Accept sub-populations. Performance of different response-risk segments allows us to compare price-driven risk elasticity and price-driven response elasticity in the presence of Good or Bad adverse selections; a special case applies when the borrower's capacity to repay is not an issue. We offer limited experimental results for selected price-risk segments where action-based risk and response scores are used to estimate borrower preferences. The critical role of Non-Take inference is described.

Keywords:

• adverse selection
• risk and response scoring
• non-take inference
• retail credit
• risk based pricing
• price-risk
• price-response elasticities

Acknowledgements

The authors are indebted to the referees, who made us think carefully about the sources and content of data that influence adverse selection. We are extremely grateful for the careful reading, comments and suggestions by Brian Bloechle, particularly his emphasis on probabilities and Bayes' factors conditioned on data rather than scores.