Binary choice logit models with general fixed effects for panel and network data

TL;DR

This paper reviews and compares identification methods for binary choice logit models with fixed effects in panel and network data, addressing the incidental parameter problem through conditional likelihood and moment-based approaches.

Contribution

It provides a systematic analysis of existing strategies and introduces new examples and results for fixed-effect logit models in complex data settings.

Findings

Conditional likelihood methods effectively eliminate fixed effects.

Moment-based methods offer alternative fixed-effect-free estimators.

The paper summarizes key literature and introduces new model applications.

Abstract

This paper systematically analyzes and reviews identification strategies for binary choice logit models with fixed effects in panel and network data settings. We examine both static and dynamic models with general fixed-effect structures, including individual effects, time trends, and two-way or dyadic effects. A key challenge is the incidental parameter problem, which arises from the increasing number of fixed effects as the sample size grows. We explore two main strategies for eliminating nuisance parameters: conditional likelihood methods, which remove fixed effects by conditioning on sufficient statistics, and moment-based methods, which derive fixed-effect-free moment conditions. We demonstrate how these approaches apply to a variety of models, summarizing key findings from the literature while also presenting new examples and new results.