Estimating deterministic trends in the presence of serially correlated errors
AbstractThis paper studies the problems of estimation and inference in the linear trend model y t = Î± + Î²t + u t, where u t follows an autoregressive process with largest root Ï and Î² is the parameter of interest. We contrast asymptotic results for the cases |Ï| < 1 and Ï = 1 and argue that the most useful asymptotic approximations obtain from modeling Ï 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 Îº. 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 Ï and Îº. The paper develops methods for constructing confidence intervals for Î² that account for uncertainty in Ï and Îº. We use these results to estimate growth rates for real per-capita GDP in 128 countries. ÃÂ© 1997 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology
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Bibliographic InfoPaper provided by Federal Reserve Bank of Chicago in its series Working Paper Series, Macroeconomic Issues with number 94-19.
Date of creation: 1994
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Other versions of this item:
- Eugene Canjels & Mark W. Watson, 1997. "Estimating Deterministic Trends In The Presence Of Serially Correlated Errors," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 184-200, May.
- Eugene Canjels & Mark W. Watson, 1994. "Estimating Deterministic Trends in the Presence of Serially Correlated Errors," NBER Technical Working Papers 0165, National Bureau of Economic Research, Inc.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
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- Beach, Charles M & MacKinnon, James G, 1978. "A Maximum Likelihood Procedure for Regression with Autocorrelated Errors," Econometrica, Econometric Society, vol. 46(1), pages 51-58, January.
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