A lagged dependent variable, autocorrelated disturbances, and unit root tests - peculiar OLS bias properties - a pedagogical note

Abstract

The paper provides applied econometricians with a useful insight into the interaction between lagged dependent variables and autocorrelated disturbances. More specifically, the paper explains heuristically why, how and when the bias of the OLS estimator of the coefficient of a lagged dependent variable can be smaller when the disturbances are autocorrelated than when they are NID. It also explains why and how the powers and sizes of some of the unit root tests are distorted by AR(1) and MA(1) disturbances. The results should be of interest to applied econometricians using vector autoregressive or error-correction models as well.