EFFECT OF EQUATION IDENTIFICATION STATUS ON ESIMATORS OF A SYSTEM OF SIMULTANEOUS EQUATIONS MODEL

Title of Publication: EFFECT OF EQUATION IDENTIFICATION STATUS ON ESIMATORS OF A SYSTEM OF SIMULTANEOUS EQUATIONS MODEL
Author(s): T. L. Johnson, B.A. Oyejola, Kayode Ayinde
Year of Publication: 2009
ABSTRACT
Equation identification is one of the problems often encountered in a system of simultaneous equations model. While some equations are exactly identified others may be over identified. This inevitably influences the estimation methods of the model parameters. In this paper, effort is made to investigate the effect of this problem on the parameter estimation of a system of simultaneous equation model using a Monte Carlo approach. A two equation model with one exactly identified equation and the other over identified was considered. A Monte Carlo experiment of 250 trials was carried out at three sample sizes (n = 20, 50 and 100). 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 using the finite properties of estimators’ criteria which are bias, absolute bias, variance and mean squared error. An estimator is best at a specified sample size if it has minimum total rank over the parameters of the equation and the criteria. Results show that the parameters of an exactly identified equation are best estimated with the OLS estimator if the small sample size is small (n = 20) and with LIML or 2SLS with moderate sample size (n = 50). For large sample size (n = 100), the FIML or 3SLS is best. The parameters of an over identified equation are best estimated with FIML or 3SLS at all the sample sizes.    
Keywords:     Equation Identification Status, Exactly identified equation, Over Identified         equation, Estimators.
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