COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 802

"Asymptotic Equivalence of OLS and GLS in Regressions
with Integrated Regressors

Peter C.B. Phillips and Joon Y. Park

September 1986

In the multiple regression model y_t = x'_tbeta + u_t where {u_t} is stationary and x_t is an integrated m-vector process it is shown that the asymptotic distributions of the ordinary least squares (OLS) and generalized least squares (GLS) estimators of beta are identical. This generalizes a recent result obtained by Kramer (1986) for simple two variate regression. Our approach makes use of a multivariate invariance principle and yields explicit representations of the asymptotic distributions in terms of fuctionals of vector Brownian motion. Some useful assumption results for hypothesis tests in the model are also provided.

Keywords: Asymptotic efficiency, Integrated regressors, Invariance principle, Multiple regression, Vector Brownian motion