In this paper we are concerned with estimation of a classification model using semiparametric and parametric methods. Benefits and limitations of semiparametric models in general, and of Manski's maximum score method in particular, are discussed. The maximum score method yields consistent estimates under very weak distributional assumptions. The maximum score method can very easily be used in situations where it is more serious to make one kind of classification error than another. In this paper, we use a so-called threshold-crossing model to discriminate between credit card holders and nonholders. The estimated parameters of the logit model differ significantly from the estimates of maximum score. Given an asymmetric loss function, maximum score performs better than the logit model.
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