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

2025-08-15

AI Summary

This paper addresses the identification problem in binary-choice logit models with high-dimensional fixed effects—such as individual, time, two-way, or dual effects—under panel and network data. The central challenge is the incidental parameter problem: as the sample size grows, the dimension of fixed effects increases, inducing asymptotic bias. To mitigate this, the paper systematically compares and extends two bias-correction approaches: (i) conditional likelihood based on sufficient statistics, applicable to static models; and (ii) moment-based estimation equations constructed to be invariant to fixed effects, accommodating dynamic specifications and complex dependence structures. Theoretically, the paper establishes a unified framework delineating the identifiability boundaries for various fixed-effect configurations, introduces novel model examples, and proves the consistency and asymptotic efficiency of the proposed estimators. These advances substantially enhance the reliability and applicability of binary-choice models in empirical microeconometrics.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Relational Probabilistic Models
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

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.

Problem

• Analyzing binary choice logit models with fixed effects
• Addressing incidental parameter problem in panel and network data
• Comparing conditional likelihood and moment-based estimation methods

Innovation

• Binary choice logit models with fixed effects
• Conditional likelihood methods for nuisance parameters
• Moment-based methods for fixed-effect-free conditions