Effect of correlations and equation identification status on estimators of a system of simultaneous equation model

Abstract

In simultaneous equations model, multicollinearity and status of identification of the equations have been observed to influence estimation of the model parameters. The error terms of each equation in the model are also expected to be correlated with each other. This study therefore examined the effect of multicollinearity, correlation between error terms and status of identification of equations on six methods of parameter estimation in a simultaneous equations model using Monte Carlo approach. A two equation model, with one equation exactly identified and the other over identified, was considered. The levels of multicollinearity among the exogeneous variables were specified as r = 0.3, 0.6, 0.8, 0.9 and 0.99 and that of correlation between error terms as l = 0.3, 0.6, and 0.9. A Monte Carlo experiment of 250 trials was carried out at three sample sizes (20, 50 and 100). The six estimation methods; Ordinary Least Squares (OLS), Indirect Least Squares (ILS), Limited Information Maximum Likelihood (LIML), Two Stage Least Squares (2SLS), Full Information Maximum Likelihood (FIML) and Three Stage Least Squares (3SLS); were ranked according to their performances. Finite properties of estimators’ criteria namely bias, absolute bias, variance and mean squared error were used for comparing the methods. An estimator is best at a specified level of multicollinearity, correlation between error terms and sample size if it has minimum total rank over the model parameters and the criteria. Results show that the OLS estimator is best in estimating the parameters of the exactly identified equation at severe level of multicollinearity (r®1) at all sample sizes. At other levels of multicollinearity, the best estimator is FIML or 3SLS except when the correlation between error terms is low (l = 0.3). At this instance, the best estimators are LIML and 2SLS. The parameters of over identification model are best estimated with FIML or 3SLS at all levels of multicollinearity, correlation between error terms and at all sample sizes.