Computing a standard error for the Gini coefficient: an application to credit risk model validation

Marius-Cristian Frunza

Abstract

ABSTRACT

Resampling approaches were the first techniques employed to compute a variance for the Gini coefficient. Various authors have demonstrated that estimates of the Gini coefficient can be obtained from a synthetic ordinary linear regression based on the data and their ranks, thereby also providing an exact analytic standard error. We develop these techniques for assessing the quality of credit models and for measuring the confidence interval of Gini coefficients. Special attention is given to data sets that have few defaults and/or are small in size, as well as to low-quality models. In consequence, we develop a new sampling-based method (F -Gini) for measuring the standard error of the Gini coefficient that is better adapted to these situations.