Credit Scoring using Semiparametric Methods

Credit scoring methods aim to assess credit worthiness of potential borrowers to keep the risk of credit loss low and to minimize the costs of failure over risk groups. Standard parametric approaches as logistic discrimination analysis assume that the probability of belonging to the group of ”bad” clients is given by P (Y = 1|X) = F (βX), with Y = 1 indicating a ”bad” client and X denoting the vector of explanatory variables. We consider a semiparametric approach here, that generalizes the linear argument in the probability P (Y = 1|X) to a partial linear argument. This model is a special case of the Generalized Partial Linear Model E(Y |X, T ) = G{βX + m(T )} (GPLM) which allows to model the influence of a part T of the explanatory variables in a nonparametric way. Here, G(•) is a known function, β is an unknown parameter vector, andm(•) is an unknown function. The parametric component β and the nonparametric function m(•) can be estimated by the quasilikelihood method proposed in Severini & Staniswalis (1994). We apply the GPLM estimator mainly as an exploratory tool in a practical credit scoring situation. Credit scoring data usually provide various discrete and continuous explanatory variables which makes the application of a GPLM interesting here. We estimate and compare different variations of the semiparametric model in order to see how the several explanatory variables influence credit worthiness. In contrast to more general nonparametric approaches, the estimated GPLM models allow an easy visualization and interpretation of the results. The estimated curves indicate in which direction the logistic discriminant should be improved to obtain a better separation of ”good” and ”bad” clients.