Asymptotic expansions are employed in a dynamic regression model with a unit root in order to find approximations for the bias, the variance and for the mean squared error of the least-squares estimator of all coefficients. It is found that in this particular context such expansions exist only when the autoregressive model contains at least one non-redundant exogenous explanatory variable and that local to zero asymptotic approaches are here without avail. Surprisingly the large sample and small disturbance asymptotic techniques give closely related results, which is not the case in stable dynamic regression models. The expressions for moment approximations are specialized to the random walk with (trend in) drift model and their accuracy is examined in Monte Carlo experiments.
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