Reject Inference Methods in Credit Scoring

International audience; The granting process of all credit institutions is based on the probability that the applicant will refund his/her loan given his/her characteristics. This probability also called score is learnt based on a dataset in which rejected applicants are de facto excluded. This implies that the population on which the score is used will be different from the learning population. Thus, this biased learning can have consequences on the scorecard's relevance. Many methods dubbed "reject inference" have been developed in order to try to exploit the data available from the rejected applicants to build the score. However most of these methods are considered from an empirical point of view, and there is some lack of formalization of the assumptions that are really made, and of the theoretical properties that can be expected. In order to propose a formalization of such usually hidden assumptions for some of the most common reject inference methods, we rely on the general missing data modelling paradigm. It reveals that hidden modelling is mostly incomplete, thus prohibiting to compare existing methods within the general model selection mechanism (except by financing "non-fundable" applicants, which is rarely performed in practice). So, we are reduced to empirically assess performance of the methods in some controlled situations involving both some simulated data and some real data (from Crédit Agricole Consumer Finance (CACF), a major European loan issuer). Unsurprisingly, no method seems uniformly dominant. Both these theoretical and empirical results not only reinforce the idea to carefully use the classical reject inference methods but also to invest in future research works for designing model-based reject inference methods, which allow rigorous selection methods (without financing "non-fundable" applicants).