Testing the assumptions of credit-scoring models

Abstract

This paper discusses a number of issues that are relevant when setting up a credit-scoring model and tests the assumptions used in accounting-based credit-scoring models. A nonstandard comparison of two hazard models with differently specified hazard functions is made: one with a logit specification and the other with a probit specification. The specification of the credit-scoring model as a hazard model allows us to include information leading up to financial distress. The logistic distribution is similar to the normal, except in the tails, and so the logit and the probit model tend to give similar probabilities, except in the tails. The tails of the logistic distribution are considerably heavier than the tails of the normal distribution, i.e. in the tails of the logistic distribution, the probabilities are larger compared to the normal distribution. The comparison of the two distributions is relevant, as the properties at the tails of the distributions are at focus here. The logit and the probit specification are formally tested against each other using two tests, which are probably used for the first time within the credit-scoring iterature. The estimations assume that if two firms have identical values of the covariates, they also have identical hazard functions, that is, unobserved heterogeneity is assumed away. The presence of unobserved heterogeneity can cause several problems, therefore, as a specification check, the hazard functions are extended to also include unobserved heterogeneity. In addition to investigating the various specifications of the hazard function, the paper discusses the treatment in the literature of different types of exits. There are recent examples of studies within the credit-scoring and the industrial organization literature, which still do not distinguish between exit types. As the extensive data set allows comparisons of different specifications, the paper explores the consequences of setting up 1) a hazard model where the event financial distress is modelled and where firms that exit for other reasons than financial distress are treated as censored or no longer observed and 2) a hazard model where the general exit event is modelled (i.e. not split up on exit type). To the best of our knowledge no other paper has provided results from such estimations. The conclusions in the article are the following: Firstly, there does not seem to be any major difference between the logit and the probit specification. Secondly, unobserved heterogeneity seems to be unimportant, probably because a number of proxies are used for inherently unobservable variables. Thirdly, the results differ depending on the event, which is modelled (financial distress versus pooled exits). This is the case for the estimated parameters as well as the predictive abilities of the models, no matter whether the specification for the hazard functions is the logit or the probit specification. The practical implication of the paper is that it is important to think careful about the specification of credit-scoring models. It is crucial to understand that the results depend on the portfolio under consideration, and hence, that every model builder has to think about the issues.