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.
Highlights
IntroductionA simultaneous equation system is a regression equation system where two types of variables (the endogenous, the predetermined or exogenous variable) appear with disturbance terms. [1] defined simultaneous equation as the process of modeling more than one equation at a time; a multi-equation modeling
A simultaneous equation system is a regression equation system where two types of variables appear with disturbance terms. [1] defined simultaneous equation as the process of modeling more than one equation at a time; a multi-equation modeling
The preferred estimators are slightly affected by the two exogenous variables
Summary
A simultaneous equation system is a regression equation system where two types of variables (the endogenous, the predetermined or exogenous variable) appear with disturbance terms. [1] defined simultaneous equation as the process of modeling more than one equation at a time; a multi-equation modeling. The X variable appears as the explanatory variable in the equations This creates problems of equation identification, multicollinearity and choice of estimation techniques among others. Correlation between the pairs of exogenous or independent variables is an important problem in econometrics especially in single equation estimation. This study examines the performances of four (4) common estimation techniques namely; Ordinary Least squares (OLS), Two-stage Least squares (2SLS), Three-stage Least squares (3SLS) and Full Information Maximum Likelihood Estimators under both normally and uniformly distributed exogenous variables for different equation identification status. Various works done in the recent time especially on correlation studies on simultaneous equation model have being with normally distributed exogenous variables, exhibiting both positive and negative values [6] [7]
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