Sample selection bias in non-traditional lending: A copula-based approach for imbalanced data

Abstract

Credit scoring models for non-traditional lending channels, such as peer-to-peer (P2P) lending platforms, are usually estimated only on the sample of accepted applicants. This may lead to biased estimates of the risk drivers. This issue can be addressed using a reject inference technique that includes the characteristics of rejected applicants in the model. Due to the low numbers of accepted applicants and default records, credit scoring models usually face a class imbalance problem. However, previous literature on sample selection models for credit scoring does not address the class imbalance issue. To fill this gap, we extend the Generalised Extreme Value (GEV) regression model for binary data to the sample selection framework. We consider the quantile function of the GEV distribution as a link function in both the selection and outcome equations. We use the copula function to model the dependence structure between the two equations for its flexibility. This proposal is called the Sample Selection Generalised Extreme Value (SSGEV) model and it is implemented in the R package BivGEV. We apply this model to a comprehensive dataset provided by Lending Club, and we show that parameter estimates obtained only on accepted P2P applicants are biased and coherently with the literature. The SSGEV model achieves a higher predictive accuracy than those obtained using univariate approaches or a sample selection probit model. Our proposal also provides more conservative estimates of the Value-at-Risk and the Expected Shortfall.