On the asymptotic bias of OLS in dynamic regression models with autocorrelated errors

It is well-known that Ordinary Least Squares (OLS) yields inconsistent estimates if applied to a regression equation with lagged dependent variables and correlated errors. Bias expressions which appear in the literature usually assume the exogenous variables to be non-stochastic. Due to this assumption the numerical sizes of these expressions cannot be determined. Further, the analysis is mostly restricted to very simple models. In this paper the problem of calculating the asymptotic bias of OLS is generalized to stationary dynamic regression models, where the errors follow a stationary ARMA process. A general bias expression is derived and a method is introduced by which its actual size can be computed numerically.