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.
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 (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.
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. Applied Mathematics, 6, 1902-1912. doi: 10.4236/am.2015.611167.
References
[1] Schmidt, J.S. (2005) Econometrics. McGraw-Hill International Edition. [2] Koutsoyainnis, A. (1977) Theory of Econometrics. 2nd Edition, Palgrave Publishers Ltd., New York. [3] Odunta, E.A. (2004) A Monte Carlo Study of the Problem of Multicollinearity in a Simultaneous Equation Model. Unpulished Ph.D. Thesis, Department of Statistics University of Ibadan, Ibadan. [4] Kmenta, J. and Gilberet, R.F. (1967) Small Sample Properties of Alternative Estimators of Seemingly Unrelated Regression. Journal of the American Statistical Association, 63, 1180-1200.
http://dx.doi.org/10.1080/01621459.1968.10480919 [5] Chatterjee, S. and Ali, S.H. (2012) Regression Analysis by Example. 5th Edition, John Wiley and Sons, Hoboken. [6] Johnson, T.L., Ayinde, K. and Oyejola, B.A. (2010) Effect of Correlations and Equation Identification Status on Estimators of a System of Simultaneous Equation Model. Electronic Journal of Applied Statistical Analysis EJASA, 3, 115-125.
http://siba-ese.unile.it/index.php/ejasa/index [7] Ayinde, K., Johnson, T.L. and Oyejola, B.A. (2011) Effect of Equation Identification Status and Correlation between Error Terms on Estimators of System of a Simultaneous Equation Model. American Journal of Scientific and Industrial Research, 2, 184-190.
http://dx.doi.org/10.5251/ajsir.2011.2.2.184.190 [8] Ayinde, K. (2007) Equation to Generate Normal Variates with Desired Intercorrelations Matrix. International Journal of Statistics and System, 2, 99-111. [9] Schumann, E. (2009) Generating Correlated Uniform Variates.
http://comisef.wikidot.com/tutorial:correlated
[1] Schmidt, J.S. (2005) Econometrics. McGraw-Hill International Edition. [2] Koutsoyainnis, A. (1977) Theory of Econometrics. 2nd Edition, Palgrave Publishers Ltd., New York. [3] Odunta, E.A. (2004) A Monte Carlo Study of the Problem of Multicollinearity in a Simultaneous Equation Model. Unpulished Ph.D. Thesis, Department of Statistics University of Ibadan, Ibadan. [4] Kmenta, J. and Gilberet, R.F. (1967) Small Sample Properties of Alternative Estimators of Seemingly Unrelated Regression. Journal of the American Statistical Association, 63, 1180-1200.
http://dx.doi.org/10.1080/01621459.1968.10480919 [5] Chatterjee, S. and Ali, S.H. (2012) Regression Analysis by Example. 5th Edition, John Wiley and Sons, Hoboken. [6] Johnson, T.L., Ayinde, K. and Oyejola, B.A. (2010) Effect of Correlations and Equation Identification Status on Estimators of a System of Simultaneous Equation Model. Electronic Journal of Applied Statistical Analysis EJASA, 3, 115-125.
http://siba-ese.unile.it/index.php/ejasa/index [7] Ayinde, K., Johnson, T.L. and Oyejola, B.A. (2011) Effect of Equation Identification Status and Correlation between Error Terms on Estimators of System of a Simultaneous Equation Model. American Journal of Scientific and Industrial Research, 2, 184-190.
http://dx.doi.org/10.5251/ajsir.2011.2.2.184.190 [8] Ayinde, K. (2007) Equation to Generate Normal Variates with Desired Intercorrelations Matrix. International Journal of Statistics and System, 2, 99-111. [9] Schumann, E. (2009) Generating Correlated Uniform Variates.
http://comisef.wikidot.com/tutorial:correlated