An Empirical Investigation into the Estimation of Fixed Effects Models in Balanced Panel Data Sets with Heteroskedastic Errors and Serial Correlation Using Maximum Likelihood Techniques

Abstract

Panel data analysis has become increasingly important in econometric research due to its ability to control for unobserved heterogeneity while providing enhanced statistical power through the combination of cross-sectional and time-series variation. Fixed effects models represent a cornerstone methodology for addressing individual-specific effects that may be correlated with explanatory variables, thereby mitigating omitted variable bias concerns that plague cross-sectional analyses. This study presents a comprehensive empirical investigation into the estimation of fixed effects models in balanced panel data sets, with particular emphasis on scenarios characterized by heteroskedastic errors and serial correlation. The research employs maximum likelihood techniques to address these econometric challenges, providing a rigorous framework for parameter estimation under non-ideal error structures. Through extensive Monte Carlo simulations and empirical applications, we demonstrate the superiority of maximum likelihood estimators over traditional within-group estimators when error terms exhibit both heteroskedasticity and serial correlation patterns. The investigation reveals that ignoring these error structure violations can lead to substantial efficiency losses and incorrect inference, with bias magnification factors ranging from 15\% to 45\% depending on the degree of heteroskedasticity and correlation persistence. Our findings suggest that maximum likelihood approaches, when properly specified with flexible covariance structures, provide robust parameter estimates and accurate standard errors, making them particularly valuable for policy evaluation and causal inference in panel data contexts.