Alternative bias approximations in first-order dynamic reduced form models

Abstract

Abstract The small sample bias of the least squares estimator is examined in the context of a first-order dynamic reduced form model with normally distributed white noise disturbances and an arbitrary number of exogenous regressors. Bias approximations are derived based on small disturbance ( σ →0) and large sample ( T →∞) asymptotics which are both used to construct bias corrected estimators. The performance of the two bias corrected estimators is compared in a number of Monte Carlo experiments which show that, whereas both estimators are often approximately unbiased, the small disturbance procedure may sometimes yield poor results. However, this does not occur with the large sample procedure which yields almost unbiased estimators in a variety of experimental situations with a mean square error comparable to (though slightly larger than) that of the least squares estimator.