Assessments of Some Simultaneous Equation Estimation Techniques with Normally and Uniformly Distributed Exogenous Variables

Affiliation(s)

^{1}
Department of Statistics, Federal University of Technology, Akure, Nigeria.

^{2}
Department of Statistics, University of Ilorin, Ilorin, Nigeria.

Abstract

In each equation of simultaneous Equation model, the exogenous variables need to satisfy all the basic assumptions of linear regression model and be non-negative especially in econometric studies. This study examines the performances of the Ordinary Least Square (OLS), Two Stage Least Square (2SLS), Three Stage Least Square (3SLS) and Full Information Maximum Likelihood (FIML) Estimators of simultaneous equation model with both normally and uniformly distributed exogenous variables under different identification status of simultaneous equation model when there is no correlation of any form in the model. Four structural equation models were formed such that the first and third are exact identified while the second and fourth are over identified equations. Monte Carlo experiments conducted 5000 times at different levels of sample size (*n* = 10, 20, 30, 50, 100, 250 and 500) were used as criteria to compare the estimators. Result shows that OLS estimator is best in the exact identified equation except with normally distributed exogenous variables when . At these instances, 2SLS estimator is best. In over identified equations, the 2SLS estimator is best except with normally distributed exogenous variables when the sample size is small and large, and ; and with uniformly distributed exogenous variables when *n* is very large, , the best estimator is either OLS or FIML or 3SLS.

In each equation of simultaneous Equation model, the exogenous variables need to satisfy all the basic assumptions of linear regression model and be non-negative especially in econometric studies. This study examines the performances of the Ordinary Least Square (OLS), Two Stage Least Square (2SLS), Three Stage Least Square (3SLS) and Full Information Maximum Likelihood (FIML) Estimators of simultaneous equation model with both normally and uniformly distributed exogenous variables under different identification status of simultaneous equation model when there is no correlation of any form in the model. Four structural equation models were formed such that the first and third are exact identified while the second and fourth are over identified equations. Monte Carlo experiments conducted 5000 times at different levels of sample size (

Keywords

Normally Distributed Exogenous Variables, Uniformly Distributed Exogenous Variables, Identification Status, Estimators, Exact Identified Equation, Over Identified Equation

Normally Distributed Exogenous Variables, Uniformly Distributed Exogenous Variables, Identification Status, Estimators, Exact Identified Equation, Over Identified Equation

Cite this paper

Alabi, O. and Oyejola, B. (2015) Assessments of Some Simultaneous Equation Estimation Techniques with Normally and Uniformly Distributed Exogenous Variables.*Applied Mathematics*, **6**, 1902-1912. doi: 10.4236/am.2015.611167.

Alabi, O. and Oyejola, B. (2015) Assessments of Some Simultaneous Equation Estimation Techniques with Normally and Uniformly Distributed Exogenous Variables.

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