Peculiar bias properties of the ols estimator when applied to a dynamic model with autocorrelated disturbances
This study reveals that contrary to the conventional wisdom among econometricians, the bias of the OLS estimator can be quite small when the estimator is applied to a geometrically distributed lag model, yt α + βx t+ λy t-1. + ut, with autocorrelated disturbances, be they AR(1), MA(1), MA(2), AR(2), and ARMA(1,1). This happens when λ is large and xtis smoothly trended (e.g., a real GNP series). In fact, the bias of the OLS estimator becomes zero at one parameter combination, and the OLS estimator performs well over a wide range around this parameter combination. By decomposing the disturbance term into two parts, the paper also explains why OLS shows such an unexpected property. These findings have both pedagogical and practical significance.