Estimating Deterministic Trends in the Presence of Serially Correlated Errors

This paper studies the problems of estimation and inference in the linear trend model: yt=à+þt+ut, where ut follows an autoregressive process with largest root þ, and þ is the parameter of interest. We contrast asymptotic results for the cases þþþ < 1 and þ=1, and argue that the most useful asymptotic approximations obtain from modeling þ 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, þ. 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 þ and þ. The paper develops methods for constructing confidence intervals for þ that account for uncertainty in þ and þ. We use these results to estimate growth rates for real per capita GDP in 128 countries.