Weak Identification in Discrete Choice Models

TL;DR

This paper investigates weak identification in discrete choice models, introduces a new consistent testing method, and demonstrates its effectiveness through simulations and empirical examples.

Contribution

It proposes a novel test for detecting weak identification in discrete choice models, improving upon existing methods and enabling reliable inference.

Findings

The new test outperforms traditional weak identification tests in simulations.

When weak identification is rejected, standard Wald inference remains valid.

Empirical applications illustrate the practical usefulness of the proposed approach.

Abstract

We study the impact of weak identification in discrete choice models, and provide insights into the determinants of identification strength in these models. Using these insights, we propose a novel test that can consistently detect weak identification in commonly applied discrete choice models, such as probit, logit, and many of their extensions. Furthermore, we demonstrate that when the null hypothesis of weak identification is rejected, Wald-based inference can be carried out using standard formulas and critical values. A Monte Carlo study compares our proposed testing approach against commonly applied weak identification tests. The results simultaneously demonstrate the good performance of our approach and the fundamental failure of using conventional weak identification tests for linear models in the discrete choice model context. Furthermore, we compare our approach against those commonly applied in the literature in two empirical examples: married women labor force participation, and US food aid and civil conflicts.