Higher-order Asymptotic Expansions of the Least-squares Estimation Bias in First-order Dynamic Regression Models

Paper number: 99/03

Paper date: October 1998

Year: 1999

Paper Category: Discussion Paper


Jan F. Kiviet
Tinbergen Institute & Faculty of Economics and Econometrics
University of Amsterdam


Garry D.A. Phillips


An approximation to order T-2 is obtained for the bias of the least-squares estimator in the stationary ARX model which yields generalisations of Kendall's and White's classic results for particular variants of AR(1) models. The accuracy of the various approximations is compared for particular parametrisations of AR(1) and ARX(1) models. The results show that generally the second-order approximation is considerably better than its first-order counterpart in ARX models. This is also largely true for AR(1) models except that in such models second-order approximations may be vulnerable in the near unit root case.

JEL Classification Nos: C13, C22
Keywords: ARX model, first-order dynamics, lagged dependent variables bias, large sample asymptotics, Nagar expansions

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