Estimating Deterministic Trends In The Presence Of Serially Correlated Errors

Eugene Canjels and Mark Watson

The Review of Economics and Statistics, 1997, vol. 79, issue 2, 184-200

Abstract: This paper studies the problems of estimation and inference in the linear trend model y t = α + βt + u t , where u t follows an autoregressive process with largest root ρ and β is the parameter of interest. We contrast asymptotic results for the cases |ρ| < 1 and ρ = 1 and argue that the most useful asymptotic approximations obtain from modeling ρ as local to unity. Asymptotic distributions are derived for the OLS, first-difference, infeasible GLS, and three feasible GLS estimators. These distributions depend on the local-to-unity parameter and a parameter that governs the variance of the initial error term κ. The feasible Cochrane-Orcutt estimator has poor properties, and the feasible Prais-Winsten estimator is the preferred estimator unless the researcher has sharp a priori knowledge about ρ and κ. The paper develops methods for constructing confidence intervals for β that account for uncertainty in ρ and κ. We use these results to estimate growth rates for real per-capita GDP in 128 countries. © 1997 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology

Date: 1997
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Related works:
Working Paper: Estimating deterministic trends in the presence of serially correlated errors (1994)
Working Paper: Estimating Deterministic Trends in the Presence of Serially Correlated Errors (1994)
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