A Simple and Powerful Diagnostic Test for Binary Choice Models

Abstract

Conventional binary choice models, such as probit and logit, impose thin-tailed errors, and that tail determines whether the parameters of a binary choice model can be estimated at the regular rate. We test the restriction on observables, asking whether the conditional choice probability decays at a polynomial rate in a covariate. Identification of tail heaviness requires no independence, no linear index, and no homoskedasticity. The test is simple to implement and attains nearly the point-optimal power envelope among invariant tests. An application to firm innovation decisions rejects the thin tail.