The Bias of the 2SLS Variance Estimator

Paper number: 99/04

Paper date: December 1998

Year: 1999

Paper Category: Discussion Paper


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


Garry D.A. Phillips


In simultaneous equation models the two stage least squares (2SLS) estimator of the coefficients, though consistent, is biased in general and the nature of this bias has given rise to a good deal of research. However, little if any attention has been given to the bias that arises when an estimate of the asymptotic variance is used to approximate the small sample variance. In this paper we use asymptotic expansions to show that, in general, the asymptotic variance estimator has an upwards bias.

JEL Classification Nos: C13, C22
Keywords: 2SLS estimation, Nagar expansions, asymptotic variance, variance estimation bias

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: