In linear regression models in which the disturbances are autocorrelated, it is often assumed that these are given by a Markov process. This article investigates the loss of efficiency of estimators of the regression parameters when there are certain types of specification bias concerning the disturbances. Specifically, it points out that the loss of efficiency can be serious if the initial conditions of the process which are assumed to be true are in fact not true. In particular, if the process is incorrectly assumed to be stationary, then although the estimation procedure which is presumed to yield the best linear unbiased estimators will produce unbiased estimators, their joint efficiency may nevertheless be close to zero.