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— For my stochastic model, the gênerai interest is not only to produce the "best" possible estimator of the régression parameter but also to use it to make inference, The finite sample distribution of the estimator on which the inference can be based7i is usually unknown, but Us asymptotic distribution is known. It has been a common practice in Econometrics to use an estimated asymptotic distribution to make inference in small sample. Obviou$lyt this will give misleadïng inference unless the estimated asymptotic distribution can wett approximate the exact finite sample distribution, Gîven the present practice of making inference in the absence of our knowledge of the finite sample distribution of an estimator, if we have to choose an estimator from a set of estimators^ it seems one shouid choose the one for which the estimated asymptotic distribution is closest to its exact distribution, This can be contrasted with the well known criterion ofchoice such as the mean squared error (MSE). Though it may be possible, it does not seem likely that these two criteria wil produce the same choice. We examine the five most used estimators of the régression coefficients of the régression model with the error foliowing the first-order autoregressive process, namely Ordinary Least Squares (OLS), Cochrane-Orcutt (CO% Cochrane-Orcutt modified by Frais and Winston (FW% Durbin and Maximum Likelihood (ML) estimators. Adopting the well known measure of distance between two distributions by Kolmogorov and Smimov as a measure of closeness of the two distributions* we compute the distance between the asymptotic distribution and its small sample estimate for each of these estimators. Due to analytical complexity* we resort to Monte Carlo study. General conclusion that can be drawn from our study is that OLS shouid never be preferred, and even though all other estimators are comparable over the entire range of the autocorrélation parameter, PW seems to be préférable, This can be contrasted to the well known conclusion using MSE as the criterion that OLS may be preferred when the order of the autocorrélation coefficient does not exceed .30 and for larger values of this coefficient, all other estimaros are comparable, but possibly the ML estimator may be prefered.

The Kolmogorov-Smirnov distance as criterion of choice of estimators with application to the first order auto-regressive case : a Monte Carlo study