Solving Sample Selection Bias in Credit Scoring: The Reject Inference

Published: March 2010
Credit Technology, Number 71
By Gabriele Sabato
Share:LinkedIn Logo


Nonrandom samples may present a significant problem in credit scoring. In general, the developer of a credit scoring system possesses only the behavioural information of accepted applicants. However, the scoring model is to be used to evaluate applicants who are drawn, arguable randomly, from the entire population. Assuming that accepted applicants were qualitatively different from individuals whose application were rejected, developing a scoring model on a sample that includes only accepted applicants may introduce sample selection bias and lead to inferior classification results (see Hand (1998) and Greene (1998)). Methods for coping with this problem are known as reject inference techniques.

Some statisticians argue that reject inference can solve the nonrandom sample selection problem (e.g. Copas and Li (1997), Joanes (1994), Donald (1995) and Green (1998)). In particular, reject inference techniques attempt to get additional data for rejected applicants or try to infer the missing performance (good/bad) information. The most common methods explored in the literature are: enlargement, reweighting and extrapolation (see Ash and Meester (2002), Banasik et al. (2003), Crook and Banasik (2004) and Parnitzke (2005)). However, some authors (e.g. Hand and Henley (1993)) demonstrate that the reject inference methods typically employed in the industry are often not sound and rest on very tenuous assumptions. They point out that reliable reject inference is impossible and that the only robust approach to reject inference is to accept a sample of rejected applications and observe their behaviour.

In this paper, we analyze the reasons to use reject inference and we assess the different proposed solutions from a statistical and business related point of view. However, in contrast with most of the available literature, we consider the business perspective more relevant than the statistical one in the financial industry context. As such, we conclude that increasing the prediction accuracy of scoring models should not be regarded as the main goal of reject inference techniques. The possibility of including rejects in the development sample should be considered, instead, as an opportunity to replicate the experience and the decision taken by underwriters, credit analysts or branch managers when assessing applicants’ creditworthiness.

Aligning a new scoring model to underwriters’ risk assessment will help them to better understand the way the model works and takes the accept/reject decision. This will likely facilitate the introduction of an automated decision system for a product that was previously manually underwritten and will lower the number of requests to override the system decision increasing the efficiency of the acquisition process.

With regards to reject inference methodologies, most of the literature focuses on how to infer the missing performance of the rejected clients without considering the significant value of the accept/reject information. Although the most common approaches to reject inference (e.g. Hand (2002), Ash and Meester (2002) and Crook and Banasik (2004)) are extremely valuable from the statistical point of view, we believe that financial institutions should follow a more practical method when developing their application models in order to guarantee the successful implementation of their systems. We are convinced that scoring models should not be judged only looking at their performance metrics (e.g. discriminatory power, accuracy, stability), but also based on their comprehensibility, simplicity, level of implementation efforts required and level of overrides that would generate.

Finally, we propose a practical approach that allows to make use of the rejected applicants when developing a new scoring model. First, we develop a model to predict the probability of default using only accepted clients and we apply it on the entire sample (accepted and rejected clients). Then, we use the reject rate (RR) to “correct” the observed good/bad odds (O-G/B odds) and find out what would have been the rejected good/bad odds (I-G/B odds). Ultimately, we combine the O-G/B odds and the I-G/B odds in order to derive the real good/bad odds (R-G/B odds), similar to the one that we would have observed if rejected clients would have been accepted.

The remainder of the article is structured as follows. In Section 2, we review some of the most relevant research related to reject inference methodologies for credit scoring. In Section 3, we extensively analyze the proposed methodology from both a theoretical and an empirical point of view. Data from an unsecured personal loans portfolio of a Brazilian bank is used to test the proposed technique. In Section 4, we submit our conclusions.

Unlocked Padlocked Icon

Unlock the rest of this paper by providing your email address below

You will receive an email with a link to download the paper.

Your request has been registered. Please check your email inbox for a link to the research paper. There is a possibility it may end up in your junk folder so please check there.

Other articles you might enjoy

Credit Risk Scoring Models

Abstract Credit scoring models play a fundamental role in the risk…

Read more

Assessing the Credit Worthiness of Italian SMEs and Mini-bond Issuers

Abstract A number of innovations have been introduced in the last five…

Read more

Does Industry-wide Distress Affect Defaulted Firms? - Evidence from Creditor Recoveries

Abstract Using data on defaulted firms in the United States over the…

Read more

Like these pieces? Register for our newsletter to get updates, learn when we publish more, and recieve the latest news from Wiserfunding straight to your inbox.

Thank you for subscribing to our newsletter you should receive an email shortly. Please check you junk folder if you cannot find it.

Join our newsletter and receive quarterly updates about Wiserfunding and our progress.

Wiserfunding logo

Wiserfunding Ltd
1-15 Clere Street


Thank you for subscribing to our newsletter you should receive an email shortly. Please check you junk folder if you cannot find it.
Send Icon

Join our newsletter to stay up to date on features and releases

Linkedin Logo
Linkedin Logo
Twitter logo
Twitter logo
Facebook Logo
Facebook Logo