Logit versus discriminant analysis: A specification test and application to corporate bankruptcies

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Abstract

Two of the most widely used statistical techniques for analyzing discrete economic phenomena are discriminant analysis (DA) and logit analysis. For purposes of parameter estimation, logit has been shown to be more robust than DA. However, under certain distributional assumptions both procedures yield consistent estimates and the DA estimator is asymptotically efficient. This suggests a natural Hausman specification test of these distributional assumptions by comparing the two estimators. In this paper, such a test is proposed and an empirical example involving corporate bankruptcies is provided. The finite-sample properties of the test statistic are also explored through some sampling experiments.

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This is a revised version of Chapter 4 of my dissertation. I am grateful to Craig MacKinlay, Whitney Newey, and two anonymous referees for many helpful comments. I would like to thank Chris Cavanagh, Jerry Hausman, Daniel McFadden, and Jim Powell for comments on an earlier version of this paper. I also thank Data Resources Inc. for use of their computing facilities and Stephanie Hogue, Gillian Speeth, and Madhavi Vinjamuri for preparing the manuscript. The National Science Foundation and the Alfred P. Sloan Foundation provided much appreciated financial support. Any errors are of course my own.