Evaluating Efficiency of Hybrid Estimators in Exact and Over – Identified Simultaneous Equations

Multicollinearity poses a significant threat to the reliability of classical estimators in Simultaneous Equation Models (SEMs). This problem leads to inflated variances and unstable coefficient estimates. Conventional SEM estimators such as Two-Stage Least Squares (2SLS), Three–Stage Least Squares (3SLS), Full Information Maximum Likelihood (FIML), Indirect Least Squares (ILS) and Limited Information Maximum Likelihood (LIML) do not inherently address collinearity among regressors. This study develops and evaluates hybrid estimators that integrate Principal Component Analysis (PCA) with classical SEM estimators (PCR-2SLS, PCR-3SLS, PCR-FIML, PCR-ILS, PCR-LIML) to mitigate multicollinearity. A Monte Carlo simulation is conducted under varying sample sizes and multicollinearity levels. Performance is assessed using the Mean Squared Error (MSE) criterion. Results demonstrate that for over–identified equations, the FIML-PCR estimator consistently outperforms all competitors across all sample sizes and collinearity levels. For exact identified equations, 3SLS-PCR and FIML-PCR are generally preferred. The study concludes that hybrid PCR–SEM estimators, particularly FIML-PCR, offer substantial improvements in estimation efficiency under multicollinearity and are recommended for applied econometric modelling.