Moment Approximation for Least Squares Estimators in Dynamic Regression Models with a Unit Root

Paper number: 99/09

Paper date: February 1999

Year: 1999

Paper Category: Discussion Paper

Authors

Jan F Kiviet*
University of Amsterdam

and

Garry DA Phillips**
University of Exeter

Abstract

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. For this purpose such expansions are shown to be useful only when the autoregressive model contains at least one non-redundant exogenous explanatory variable. It is found that large sample and small disturbance asymptotic techniques give closely related results in this model, which is not the case in stable dynamic regression models. The results are specialised to the random walk with drift model, where it is seen that the ratio of the standard deviation of the disturbance tot he drift term plays a crucial role. The random walk to the model with drift plus a linear trend is also examined. The accuracy of the approximations are checked in the context of these models making use of a set of Monte Carlo experiments to estimate the true moments.

JEL Classification Nos: C13, C22
Keywords: Asymptotic expansions, dynamic regression, finite sample bias, moment approximations, unit root

Corresponding Author: Garry D.A. Phillips, School of Business and Economics, University of Exeter, Streatham Court, Rennes Drive, Exeter, EX4 4PU, UK, tel: (44) 1392 263341, fax (44) 1392 263242, email: G.D.A.Phillips@exeter.ac.uk

 


* Tinbergen Institute & Faculty of Economics and Econometrics, University of Amsterdam, Roeterstraat 11, 1018 WB Amsterdam, The Netherlands (JFK@FEE.UnA.NL).

** School of Business and Economics, University of Exeter, Streatham Court, Rennes Drive, Exeter, EX4 4PU, UK