A Simple and Powerful Diagnostic Test for Binary Choice Models

2026-03-29

AI Summary

This study addresses the challenge of testing distributional assumptions—particularly tail behavior—of error terms in binary choice models by proposing a nonparametric diagnostic method rooted in extreme value theory. The approach infers the tail index of unobservable error terms through that of observable covariates, obviating the need for model estimation or parametric distributional assumptions. Notably, it formulates the null hypothesis as a zero tail index, thereby encompassing both Probit and Logit models within a unified framework. The resulting test is applicable to both cross-sectional and panel data. Monte Carlo simulations demonstrate excellent size control and high power, and empirical applications in firm export decisions, innovation behavior, and female labor force participation confirm its broad practical relevance.

Abstract

This paper proposes a specification test for the conventional distributional assumptions of error terms in binary choice models, focusing on its tail properties. Based on extreme value theory, we first establish that the tail index of the unobserved error can be recovered by that of the observed covariates. The null hypothesis of the index being zero essentially covers the widely used probit and logit models. We then construct a simple and powerful statistical test for both cross-sectional and panel data, requiring no model estimation and no parametric assumptions. Monte Carlo simulations demonstrate that our test performs well in size and power, and applications to three empirical examples on firm export and innovation decisions and female labor force participation illustrate its general applicability.

Problem

• binary choice models
• specification test
• tail properties
• extreme value theory
• error distribution

Innovation

• specification test
• binary choice models
• extreme value theory
• tail index
• nonparametric