Finite Sample Efficiency of Ordinary Least Squares in the Linear Regression Model with Autocorrelated Errors

In the standard linear regression model y = X β + u, with errors following a first-order stationary autoregressive process, it is shown that the relative efficiency of the ordinary least squares (OLS) as compared with the Gauss-Markov estimator depends to a great extent on the X matrix observed. In particular, it is seen that the relative efficiency of OLS increases with increasing correlation for certain cases important in practice. Since this seems to run contrary to what one should expect on the basis of previous Monte Carlo studies, some additional sampling experiments are also briefly discussed that keep the X matrix fixed in repeated runs.