A Simple and Powerful Diagnostic Test for Binary Choice Models

Ting Ji, Laura Liu, Yulong Wang and Jiahe Xing

Papers from arXiv.org

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.

Date: 2026-03, Revised 2026-09
New Economics Papers: this item is included in nep-dcm and nep-ecm
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