Effects of Multicollinearity on Ols, 2sls and 3sls in a Simultaneous Equation Model Framework

This research investigates the effect of multicollinearity on Ordinary Least Squares (OLS), Two Stage Least Squares (2SLS) and Three Stage Least Squares (3SLS) in a simultaneous equation model framework. The research systematically examines how varying degrees of multicollinearity affect estimator performance across different sample sizes within a simultaneous equation framework. The investigation employs four distinct sample sizes (n = 10, 20, 50 and 100) and four multicollinearity levels (ρ = 0, 0.1, 0.5 and 0.9) to capture scenarios ranging from no multicollinearity to severe multicollinearity. Performance evaluation is conducted using multiple diagnostic measures such as Mean Squared Error (MSE), Adjusted R2, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC). Results indicate that while OLS demonstrates notable robustness against multicollinearity, both 2SLS and 3SLS estimators suffer significant performance degradation under severe multicollinearity, especially in small samples. These findings underscore the trade-off between theoretical consistency and practical reliability, offering valuable guidance for researchers navigating simultaneous equation modeling in multicollinear environments. Based on these findings, the study recommends that researchers prioritize OLS when endogeneity is minimal and multicollinearity is high, while reserving 2SLS and 3SLS for contexts with sufficient sample size and validated instrumental variables. These insights offer practical guidance for estimator selection and model specification in applied econometrics.