A Monte Carlo Experiment on the Asymptotic Efficiency of System Estimators under Multicollinearity

Classical linear regression model assumes that there is no multicollinearity among the explanatory variables in a regression model. Contrary to this assumption, where multicollinearity is perfect, the regression coefficients of the explanatory variables are indeterminable and their standard errors are infinite. On the other hand, where multicollinearity is less than perfect, the regression coefficients, although determinable, possess large standard errors. This implies that the coefficients cannot be estimated with great precision. Hence multicollinearity problem is a major problem in econometric analysis. Using Monte Carlo Simulation, we evaluated the asymptotic efficiency of six estimators (OLS, ILS,2SLS, 3SLS, LIML and FIML), under different magnitudes of the unintended linear relationship between the exogenous variables. Using the SSR criteria, we found that OLS followed by ILS turned out the best estimates amongst the six estimators under multicollinearity. We also found that with increasing sample size, there is no remarkable asymptotic effect in the performance of the estimators at the levels of multicollinearity.