Robust Estimation in Simultaneous Equation Models: Addressing Multicollinearity and Heteroscedasticity through Adaptive Penalized GMM Techniques

This study develops and evaluates robust estimation techniques for simultaneous equation models (SEMs) under conditions that violate the classical linear regression assumptions specifically multicollinearity, and heteroscedasticity. Building on limitations identified in conventional estimators such as Two-Stage Least Squares (2SLS), Three-Stage Least Squares (3SLS), and Full Information Maximum Likelihood (FIML), we propose five novel estimators: Adaptive Ridge IV (ARIV), Generalized Two-Stage Adaptive Elastic-Net (G2SAE), Elastic-Net IV (ENIV), Heteroscedasticity-Consistent Generalized Method of Moments (HCGMM), and Three-Stage Adaptive Elastic-Net (3SAEN). The performance of these estimators were assessed using extensive Monte Carlo simulations across varying degrees of multicollinearity, heteroscedasticity, and sample sizes (n = 30, 50, 100, 200), with 2,000 replications for each scenario. Evaluation metrics include Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Bias. The results reveal that the proposed estimators consistently outperform traditional methods, especially under severe assumption violations. HCGMM emerges as the most robust and efficient estimator, exhibiting the lowest RMSE and bias across nearly all conditions, including small sample sizes. G2SAE and 3SAEN also demonstrate strong asymptotic properties and adaptability to complex data structures. In contrast, traditional estimators particularly 2SLS and 3SLS exhibit significant performance deterioration in the presence of heteroscedasticity and multicollinearity. A comparative analysis further highlights a trade-off between computational efficiency and estimation accuracy, with the proposed methods offering a favorable balance. These findings have practical implications for econometric modeling in applied research, particularly in fields where data irregularities are prevalent. The study underscores the need for methodological reform and adoption of robust estimation techniques to improve the reliability of policy-relevant empirical analysis.