Nonlinear relationships in a logistic model of default for a high-default installment portfolio

Christian Lohmann and Thorsten Ohliger

Journal of Credit Risk

Abstract: This study uses data on consumer credit provided by a German retail and trading company along with generalized additive models to analyze nonlinear relationships and their effect on predicting the probability of default in the context of consumer credit scoring. In particular, this study examines which aspects of the contract and which characteristics of the debtor are nonlinearly related to the probability that specific debtors will default on the loans they are seeking to obtain. The findings of our analysis provide clear empirical evidence that certain contract and debtor characteristics have nonlinear and nonmonotonic effects on the probability that a specific debtor will default on their consumer credit. The results of our analysis and the forms that these nonlinear relationships take are interpreted with regard to their economic relevance. Specifically, the study shows that the nonlinear relationships identified are economically relevant because they take into account the costs of a range of misclassification errors. On the basis of this evidence, the study recommends that analysts include nonlinear relationships in the models they design to predict consumer default, although including such relationships increases the complexity of the models that are applied for this purpose.

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