Hybrid Principal Component-Based Estimators for Multicollinearity in Simultaneous Equation Models

Abstract

This study addresses the problem of multicollinearity in simultaneous equation models (SEMs) by proposing hybrid estimators that integrate Principal Component Analysis (PCA) with conventional estimation techniques. Multicollinearity, characterized by high correlations among explanatory variables, adversely affects the efficiency and stability of estimators such as Two-Stage Least Squares (2SLS), Three-Stage Least Squares (3SLS), and Full Information Maximum Likelihood (FIML). To mitigate this problem, correlated regressors are transformed into orthogonal principal components prior to estimation, leading to the PCR-based SEM estimators. The performance of both classical and hybrid estimators is evaluated through Monte Carlo simulations under varying levels of multicollinearity, sample sizes and error structures. Mean Squared Error (MSE) is used as the evaluation criterion. The results indicate that the hybrid PCR-FIML estimator consistently outperforms competing estimators in most experimental settings. Overall, incorporating PCA into SEM estimation improves predictive accuracy, reduces estimation variance, and enhances robustness in the presence of multicollinearity.