A Monte Carlo Study of the Residuals of System Estimators in the Presence of Multicollinearity

Residual analysis is often used to evaluate the precision of the parameter estimates of econometric models. Analysis of residuals from regression is an important way of assessing the performance of a regression model in achieving the goal of accounting for the independent variable under the underlying assumption. With the Monte Carlo Simulation (MCS) of a data set of sample size 40 over varied replications R = 20, 50, 100 and 150, we used residual analysis to study the relative performance of six estimators of a simultaneous equation model under varied multicollinearity conditions. We found that the two-stage least squares (2SLS), Limited Information Maximum Likelihood (LIML), and Three-Stage Least Squares (3SLS) estimators generated virtually similar estimates. This is in agreement with the theory. In addition, the results revealed that notwithstanding the level of multicollinearity, Ordinary Least Squares (OLS), followed by Indirect Least Squares (ILS), produced the lowest Sum of Squared Residuals (SSR) of parameter estimates, an indication of the robustness of OLS in the presence of multicollinearity. This result also showed that the single equation estimators (OLS and ILS) performed better than the system estimators under the condition of multicollinearity to which we subjected our model. Furthermore, the Sum of Squared Residuals (SSR) generated for cases of low multicollinearity are lower than those generated for cases of high multicollinearity.