The Finite Sample Moments of OLS in Dynamic Models when Disturbances are Small

Abstract

For many years, econometric researchers have been using Least Squares methods (LS) to estimate the coefficients in dynamic single equation econometric models. These methods are usually justified by citing research that proves LS estimators have desirable asymptotic properties when the errors are assumed to be independent and identically distributed. Seminal articles by Mann and Wald (1943), White (1958) and Anderson (1959) are among those cited. These articles prove that under the assumption of independent and identically distributed errors, LS is asymptotically unbiased, asymptotically efficient and consistent in the context of dynamic econometric models. However, in small samples typical of econometric research involving time series data, the distribution of the LS estimator in dynamic models is much less certain and is difficult to obtain. As a result, researchers who ignore these finite sample problems may sacrifice the accuracy of their conclusions.