On the Estimation of a Linear Time Trend Regression with a One- Way Error Component Model in the Presence of Serially Correlated Errors

In this paper, we study the limiting distributions for the ordinary least squares (OLS), the fixed effects (FE), first difference (FD), and the generalized least squares (GLS) estimators in a linear time trend regression with a one-way error component model in the presence of serially correlated errors. We show that when the error term is I(0), the FE is asymptotically equivalent to GLS. However, when the error term is I(1), the GLS could be less efficient than FD or FE estimators and FD is the most efficient estimator. However, when the intercept is included in the model and the error term is I(0), the OLS, FE, and GLS are asymptotically equivalent. The limiting distribution of the GLS depends on the initial condition significantly when the error term is I(1) and an intercept is included in the regression. Monte Carlo experiments are employed to compare the performance of these estimators in finite samples. The main findings are: (1) the two-steps GLS estimators perform well if the variance component is small and close to zero when autocorrelation coefficient is less than one, (2) the FD estimator dominates the other estimators when autocorrelation coefficient equals to one for all values of variance component and (3) the FE estimator is recommended in practice since it performs pretty well for all values of the autocorrelation coefficient and variance component.