Bias correction of OLSE in the regression model with lagged dependent variables
It is well known that the ordinary least-squares estimates (OLSE) of autoregressive models are biased in small sample. In this paper, an attempt is made to obtain the unbiased estimates in the sense of median or mean. Using Monte Carlo simulation techniques, we extend the median-unbiased estimator proposed by Andrews (1993, Econometrica 61 (1), 139165) to the higher-order autoregressive processes, the nonnormal error term and inclusion of any exogenous variables. Also, we introduce the mean-unbiased estimator, which is compared with OLSE and the medium-unbiased estimator. Some simulation studies are performed to examine whether the proposed estimation procedure works well or not, where AR(p) for p=1,2,3 models are examined. We obtain the results that it is possible to recover the true parameter values from OLSE and that the proposed procedure gives us the less-biased estimators than OLSE. Finally, using actually obtained data, an empirical example of the median- and mean-unbiased estimators are shown.
olse lagged dependent variable median-unbiased estimator nonnormal error exogenous variables mean-unbiased estimator ar(p) model