A Simple and Powerful Diagnostic Test for Binary Choice Models

TL;DR

This paper introduces a new, simple diagnostic test for binary choice models that assesses error distribution assumptions using tail properties, applicable to various data types.

Contribution

It develops a non-parametric, model-free test based on extreme value theory to evaluate error tail behavior in binary choice models.

Findings

Test performs well in size and power in simulations.

Applicable to cross-sectional and panel data.

Validated through empirical examples on firm decisions and labor participation.

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.