Understanding Estimators of Linear Regression Model with AR(1) Error Which are Correlated with Exponential Regressor

Assumptions in the classical normal linear regression model include that of lack of autocorrelation of the error terms and the zero covariance between the explanatory variable and the error terms. This study is channeled towards the estimation of the parameters of the linear regression models when the above two assumptions are violated. The study used the Monte-Carlo method to investigate the performance of five estimators: Ordinary Least Squares (OLS), Cochrane Orcutt (CORC), Hildreth Lu (HILU), Maximum Likelihood (ML) and Maximum Likelihood Grid (MLGRID) in estimating the parameters of a single linear regression model in which` the exponential explanatory variable is also correlated with the autoregressive error terms. The simulation results, under the finite sampling properties of bias, Variance and Root Mean Squared Error (RMSE), show that all estimators are adversely affected as autocorrelation coefficient (ρ) is close to unity. In this regard, the estimators rank as follows in descending order of performance: OLS, MLGRID, ML, CORC and HILU. The estimators conform to the asymptotic properties of estimates considered. This is seen at all levels of autocorrelation and at all significant levels. The estimators rank in decreasing order in conformity with the observed asymptotic behaviour as follows: OLS, ML, MLGRID, HILU and CORC. The results suggest that OLS should be preferred when autocorrelation level is relatively mild (ρ = 0.4) and the exponential regressor is significantly correlated at 5% with the autocorrelated error terms.