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Estimating Deterministic Trends In The Presence Of Serially Correlated Errors

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Author Info
Eugene Canjels
Mark W. Watson
Abstract

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. © 2000 by the President and Fellows of Harvard College and the Massachusetts Institute of Technolog

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Article provided by MIT Press in its journal The Review of Economics and Statistics.

Volume (Year): 79 (1997)
Issue (Month): 2 (May)
Pages: 184-200
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Handle: RePEc:tpr:restat:v:79:y:1997:i:2:p:184-200

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  1. Bunzel, Helle, 2003. "Fixed-b Asymptotics in Single Equation Cointegration Models with Endogenous Regressors," Staff General Research Papers 10685, Iowa State University, Department of Economics.
  2. Hyungsik R. Moon & Peter C.B. Phillips, 1999. "Estimation of Autoregressive Roots Near Unity Using Panel Data," Cowles Foundation Discussion Papers 1224, Cowles Foundation, Yale University. [Downloadable!]
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  3. Valentina Meliciani & Franco Peracchi, 2004. "Convergence in Per-capita GDP Across European Regions: A Reappraisal," CEIS Research Paper 58, Tor Vergata University, CEIS. [Downloadable!]
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  4. Hyungsik Roger Moon & Peter C.B. Phillips, 2003. "GMM Estimation of Autoregressive Roots Near Unity with Panel Data," Cowles Foundation Discussion Papers 1390, Cowles Foundation, Yale University. [Downloadable!]
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  5. Serena Ng & Timothy Vogelsang, 1999. "Forecasting Dynamic Time Series in the Presence of Deterministic Components," Boston College Working Papers in Economics 445, Boston College Department of Economics. [Downloadable!]
  6. Zhijie Xiao & Peter C.B. Phillips, 1997. "An ADF Coefficient Test for a Unit Root in ARMA Models of Unknown Order with Empirical Applications to the U.S. Economy," Cowles Foundation Discussion Papers 1161, Cowles Foundation, Yale University. [Downloadable!]
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  7. Peter C.B. Phillips & Hyungsik R. Moon, 1999. "Nonstationary Panel Data Analysis: An Overview of Some Recent Developments," Cowles Foundation Discussion Papers 1221, Cowles Foundation, Yale University. [Downloadable!]
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  8. Galip Altinay, 2003. "Estimating growth rate in the presence of serially correlated errors," Applied Economics Letters, Taylor and Francis Journals, vol. 10(15), pages 967-970, December. [Downloadable!] (restricted)
  9. Pierre Perron & Tomoyoshi Yabu, . "Estimating Deterministic Trends with an Integrated or Stationary Noise Component," Boston University - Department of Economics - Working Papers Series WP2006-012, Boston University - Department of Economics, revised Feb 2006. [Downloadable!]
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  10. James H. Stock & Mark W. Watson, 1998. "Business Cycle Fluctuations in U.S. Macroeconomic Time Series," NBER Working Papers 6528, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  11. H.P. Boswijk & P.H. Franses, 2001. "Robust inference on average economic growth," Econometric Institute Report 252, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
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  12. Fabio Busetti & Andrew Harvey, 2007. "Testing for trend," Temi di discussione (Economic working papers) 614, Bank of Italy, Economic Research Department. [Downloadable!]
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  13. Jamie Emerson & Chihwa Kao, 2006. "Testing for structural change in panel data: GDP growth, consumption growth, and productivity growth," Economics Bulletin, Economics Bulletin, vol. 3(14), pages 1-12. [Downloadable!]
  14. Francis X. Diebold & Lutz Kilian, 1999. "Unit Root Tests Are Useful for Selecting Forecasting Models," NBER Working Papers 6928, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  15. Helle Bunzel, 2004. "Fixed Bandwidth Asymptotics in Single Equation Models of Cointegration with an Application to Money Demand," Econometric Society 2004 North American Summer Meetings 219, Econometric Society. [Downloadable!]
  16. Peter C.B. Phillips & Zhijie Xiao, 1998. "A Primer on Unit Root Testing," Cowles Foundation Discussion Papers 1189, Cowles Foundation, Yale University. [Downloadable!]
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  17. Mynbaev, Kairat, 2001. "The strengths and weaknesses of L2 approximable regressors," MPRA Paper 9056, University Library of Munich, Germany. [Downloadable!]
  18. H. Peter Boswijk & Philip Hans Franses, 2002. "How Large is Average Economic Growth? Evidence from a Robust Method," Tinbergen Institute Discussion Papers 02-002/4, Tinbergen Institute. [Downloadable!]
  19. T.J. Vogelsang & P.H. Franses, 2001. "Testing for common deterministic trend slopes," Econometric Institute Report 224, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
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