Yuta Ota and Taisuke Otsu

Published 22 October 2025

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This paper proposes a Hausman type statistic to test specification of a parametric binary choice model by comparing the maximum likelihood estimator and maximum score estimator. Although the convergence rates are different, it is still meaningful to compare these estimators to detect misspecification of parametric models. A simulation illustrates that the proposed test is powerful against common forms of misspecification, such as heteroskedasticity and heavy-tailed distributions, while also maintaining reasonable power in distinguishing between closely related distributions, such as the normal and logistic.