Evaluation of Instrumental Variable Estimators in the Presence of Weak Instruments and Heteroskedastic Errors in Panel Data Models

Abstract

Instrumental variable (IV) estimation is widely used technique in econometric analysis, especially for tackling problems of endogeneity that can compromise the validity of regression results. When explanatory variables are correlated with the error term, traditional methods such as ordinary least squares (OLS) produce biased and inconsistent parameter estimates.  This paper provides a comprehensive evaluation of various instrumental variable estimators when applied to panel data models characterized by weak instruments and heteroskedastic error structures. We examine the finite sample properties of two-stage least squares, limited information maximum likelihood, and generalized method of moments estimators through extensive Monte Carlo simulations. Our analysis reveals that the performance of these estimators deteriorates significantly when instruments are weak, with the degree of deterioration being approximately 15\% to 30\% higher in the presence of heteroskedasticity compared to homoskedastic settings. We develop a robust testing framework for instrument strength that accounts for both cross-sectional and time-series heteroskedasticity patterns commonly observed in panel data. The proposed methodology demonstrates superior finite sample performance, reducing mean squared error by up to 25\% compared to conventional approaches. Additionally, we establish theoretical bounds for the bias and variance of these estimators under weak instrument asymptotics. Our findings suggest that practitioners should exercise considerable caution when employing instrumental variable techniques in panel data contexts, particularly when instrument strength is questionable and error structures exhibit heteroskedastic patterns.