Credit scoring models based on accepted applications may be biased and their consequences can have a statistical and economic impact. Reject inference is the process of attempting to infer the creditworthiness status of the rejected applications. In this research, we use deep generative models to develop two new semi-supervised Bayesian models for reject inference in credit scoring, in which we model the data generating process to be dependent on a Gaussian mixture. The goal is to improve the classification accuracy in credit scoring models by adding reject applications. Our proposed models infer the unknown creditworthiness of the rejected applications by exact enumeration of the two possible outcomes of the loan (default or non-default). The efficient stochastic gradient optimization technique used in deep generative models makes our models suitable for large data sets. Finally, the experiments in this research show that our proposed models perform better than classical and alternative machine learning models for reject inference in credit scoring.
A simple approach for reject inference is augmentation @cite_44 . In this approach, the accepted applications are re-weighted to represent the entire population. The common way to find these weights is using the accept reject probability. For example if a given application has a probability of being rejected of 0.80, then all similar applications would be weighted up @math times @cite_2 . None of the empirical research using augmentation shows significant improvements in either correcting the selection bias or improving model performance, see @cite_2 @cite_34 @cite_43 @cite_0 @cite_27 @cite_41 @cite_14 . The augmentation technique assumes that the default probability is independent of whether the loan is accepted or rejected @cite_38 . However, @cite_6 shows empirically that this assumption is wrong.
@cite_38 @cite_14 @cite_41 @cite_6 @cite_44 @cite_43 @cite_0 @cite_27 @cite_2 @cite_34
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This article seeks to gain insight into the influence of sample bias in a consumer credit scoring model. In earlier research, sample bias has been suggested to pose a sizeable threat to predictive performance and profitability due to its implications on either population drainage or biased estimates. Contrary to previous – mainly theoretical – research on sample bias, the unique features of the dataset used in this study provide the opportunity to investigate the issue in an empirical setting. Based on the data of a mail-order company offering short term consumer credit to their consumers, we show that (i) given a certain sample size, sample bias has a significant effect on consumer credit-scoring performance and profitability, (ii) its effect is composed of the inclusion of rejected orders in the scoring model, and the inclusion of these orders into the variable-selection process, and (iii) the impact of the effect of sample bias on consumer credit scoring performance and profitability is modest. Abstract The parameters of application scorecards are usually estimated using a sample that excludes rejected applicants which may prove biased when applied to all applicants. This paper uses a rare sample that includes those who would normally be rejected to examine the extent to which (1) the exclusion of rejected applicants undermines the predictive performance of a scorecard based only on accepted applicants, and (2) reject inference techniques can remedy the influence of this exclusion. AbstractTechnology evaluation has become a critical part of technology investment, and accurate evaluation can lead more funds to the companies that have innovative technology. However, existing processes have a weakness in that it considers only accepted applicants at the application stage. We analyse the effectiveness of technology evaluation model that encompasses both accepted and rejected applicants and compare its performance with the original accept-only model. Also, we include the analysis of reject inference technique, bivariate probit model, in order to see if the reject inference technique is of use against the accept-only model. The results show that sample selection bias of the accept-only model exists and the reject inference technique improves the accept-only model. However, the reject inference technique does not completely resolve the problem of sample selection bias. Many researchers see the need for reject inference in credit scoring models to come from a sample selection problem whereby a missing variable results in omitted variable bias. Alternatively, practitioners often see the problem as one of missing data where the relationship in the new model is biased because the behaviour of the omitted cases differs from that of those who make up the sample for a new model. To attempt to correct for this, differential weights are applied to the new cases. The aim of this paper is to see if the use of both a Heckman style sample selection model and the use of sampling weights, together, will improve predictive performance compared with either technique used alone. This paper will use a sample of applicants in which virtually every applicant was accepted. This allows us to compare the actual performance of each model with the performance of models which are based only on accepted cases. 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 — 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. We generalize an empirical likelihood approach to deal with missing data to a model of consumer credit scoring. An application to recent consumer credit data shows that our procedure yields parameter estimates which are significantly different (both statistically and economically) from the case where customers who were refused credit are ignored. This has obvious implications for commercial banks as it shows that refused customers should not be ignored when developing scorecards for the retail business. We also show that forecasts of defaults derived from the method proposed in this paper improve upon the standard ones when refused customers do not enter the estimation data set. The Credit Scoring Toolkit provides an all-encompassing view of the use of statistical models to assess retail credit risk and provide automated decisions. In eight modules, the book provides frameworks for both theory and practice. It first explores the economic justification and history of Credit Scoring, risk linkages and decision science, statistical and mathematical tools, the assessment of business enterprises, and regulatory issues ranging from data privacy to Basel II. It then provides a practical how-to-guide for scorecard development, including data collection, scorecard implementation, and use within the credit risk management cycle. Including numerous real-life examples and an extensive glossary and bibliography, the text assumes little prior knowledge making it an indispensable desktop reference for graduate students in statistics, business, economics and finance, MBA students, credit risk and financial practitioners. If a credit scoring model is built using only applicants who have been previously accepted for credit such a non-random sample selection may produce bias in the estimated model parameters and accordingly the model's predictions of repayment performance may not be optimal. Previous empirical research suggests that omission of rejected applicants has a detrimental impact on model estimation and prediction. This paper explores the extent to which, given the previous cutoff score applied to decide on accepted applicants, the number of included variables influences the efficacy of a commonly used reject inference technique, reweighting. The analysis benefits from the availability of a rare sample, where virtually no applicant was denied credit. The general indication is that the efficacy of reject inference is little influenced by either model leanness or interaction between model leanness and the rejection rate that determined the sample. However, there remains some hint that very lean models may benefit from reject inference where modelling is conducted on data characterized by a very high rate of applicant rejection.