A Comparative Study of the Performances of the OLS and some GLS Estimators when Stochastic Regressors are both Collinear and Correlated with Error Terms

Kayode Ayinde

doi:10.3844/jmssp.2007.196.200

Abstract

The Classical Linear Regression Model assumes that regressors are non – stochastic, independent and uncorrelated with the error terms. These assumptions are not always tenable especially where regressors are not often assumed fixed in repeated sampling. In this paper, with stochastic regressors, the performances of the Ordinary Least Square (OLS) and some Generalized Least Square (GLS) estimators are investigated and compared under various degree of non – validity of multicollinearity and correlation between regressor and error terms’ assumptions through Monte – Carlo studies at both low and high replications. The mean squared error criterion is used to examine and compare the estimators. Results show that the performances of the estimators improved with increased replication. The ML and MLGD (GLS) estimators compare favorably with the OLS estimator with low replication. However with increased replication, the OLS method is preferred among the estimators in estimating all the parameters of the model in all level of correlations.

Highlights

Regressors are assumed to be non – stochastic, independent and uncorrelated with the error terms in the Classical Linear Regression Model (CLRM)
They noted that if the Ordinary Least Square (OLS) estimator is applied to the CLRM of this form, the estimates are bias but lack property of consistency
Assuming no autocorrelation of the error terms, we examine and compare the performances of some of these Feasible Generalized Least Square (GLS) estimators with that of the OLS

Summary

Introduction

Regressors are assumed to be non – stochastic (fixed in repeated sampling), independent and uncorrelated with the error terms in the Classical Linear Regression Model (CLRM). The ML and MLGD (GLS) estimators compare favorably with the OLS estimator with low replication. The OLS method is preferred among the estimators in estimating all the parameters of the model in all level of correlations.

Results

Conclusion