Comparison of Instrumental Variable Approaches in Addressing Endogeneity within Linear Panel Data Models

Abstract

Endogeneity presents one of the most persistent challenges in empirical econometric analysis, particularly when researchers attempt to establish causal relationships from observational data in panel settings. This paper provides a comprehensive comparative analysis of instrumental variable approaches specifically designed to address endogeneity issues within linear panel data models. We examine the theoretical foundations and practical implementation of fixed effects instrumental variables, random effects instrumental variables, difference-in-differences instrumental variables, and system generalized method of moments estimators. Through detailed mathematical exposition, we demonstrate how each approach handles different sources of endogeneity including omitted variable bias, simultaneity, and measurement error. The analysis reveals that the choice of instrumental variable strategy critically depends on the underlying data generating process, the nature of unobserved heterogeneity, and the availability of valid instruments. Our findings indicate that system GMM estimators perform particularly well when lagged values serve as valid instruments, while fixed effects IV approaches excel in controlling for time-invariant unobserved heterogeneity. The paper contributes to the literature by establishing a unified framework for comparing these methodologies and providing practical guidance for empirical researchers facing endogeneity concerns in panel data analysis.