Specification testing for binary choice model via maximum score

This paper proposes a Hausman-type statistic to the test specification of a parametric binary choice model by comparing the maximum likelihood estimator and the 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 study illustrates that the proposed test offers better size properties than the conventional information matrix test, and exhibits reasonable power against common forms of misspecification, such as heavy-tailed distributions and heteroskedasticity.