Estimating deterministic trends in the presence of serially correlated errors

Eugene Canjels, Mark W. Watson

Research output: Contribution to journalArticlepeer-review

95 Scopus citations


This paper studies the problems of estimation and inference in the linear trend model yt = α + βt + ut, where ut 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.

Original languageEnglish (US)
Pages (from-to)184-197
Number of pages14
JournalReview of Economics and Statistics
Issue number2
StatePublished - May 1997

All Science Journal Classification (ASJC) codes

  • Social Sciences (miscellaneous)
  • Economics and Econometrics


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