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Testing for a Deterministic Trend when there is Evidence of Unit-Root

  • Manuel Gomez

    ()

    (Department of Economics and Finance, Universidad de Guanajuato)

  • Daniel Ventosa-Santaularia

    ()

    (Department of Economics and Finance, Universidad de Guanajuato)

Whilst the existence of a unit root implies that current shocks have permanent effects, in the long run, the simultaneous presence of a deterministic trend obliterates that consequence. As such, the long-run level of macroeconomic series depends upon the existence of a deterministic trend. This paper proposes a formal statistical procedure to distinguish between the null hypothesis of unit root and that of unit root with drift. Our procedure is asymptotically robust with regard to autocorrelation and takes into account a potential single structural break. Empirical results show that most of the macroeconomic time series originally analyzed by Nelson and Plosser (1982) are characterized by their containing both a deterministic and a stochastic trend.

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File URL: http://economia.ugto.org/WorkingPapers/EM200801.pdf
File Function: Revised version, 2010
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Paper provided by Universidad de Guanajuato, Department of Economics and Finance in its series Department of Economics and Finance Working Papers with number EM200801.

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Length: 19 pages
Date of creation: Feb 2008
Date of revision: Jun 2010
Handle: RePEc:gua:wpaper:em200801
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  1. Peter C.B. Phillips & Steven N. Durlauf, 1985. "Multiple Time Series Regression with Integrated Processes," Cowles Foundation Discussion Papers 768, Cowles Foundation for Research in Economics, Yale University.
  2. Mohitosh Kejriwal & Pierre Perron, 2006. "Unit Root Tests Allowing for a Break in the Trend Function at an Unknown Time Under Both the Null and Alternative Hypotheses," Boston University - Department of Economics - Working Papers Series WP2006-052, Boston University - Department of Economics.
  3. Zivot, Eric & Andrews, Donald W K, 2002. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 25-44, January.
  4. Manuel Gomez & Daniel Ventosa-Santaularia, 2007. "Income Convergence: The Dickey-Fuller Test under the Simultaneous Presence of Stochastic and Deterministic Trends," Department of Economics and Finance Working Papers EM200703, Universidad de Guanajuato, Department of Economics and Finance.
  5. Josep Lluís Carrion-i-Silvestre & Andreu Sansó, 2006. "Joint hypothesis specification for unit root tests with a structural break *," Econometrics Journal, Royal Economic Society, vol. 9(2), pages 196-224, 07.
  6. Nelson, Charles R. & Plosser, Charles I., 1982. "Trends and random walks in macroeconmic time series : Some evidence and implications," Journal of Monetary Economics, Elsevier, vol. 10(2), pages 139-162.
  7. Peter C.B. Phillips, 1985. "Understanding Spurious Regressions in Econometrics," Cowles Foundation Discussion Papers 757, Cowles Foundation for Research in Economics, Yale University.
  8. Carrion-i-Silvestre, Josep Lluís & Kim, Dukpa & Perron, Pierre, 2009. "Gls-Based Unit Root Tests With Multiple Structural Breaks Under Both The Null And The Alternative Hypotheses," Econometric Theory, Cambridge University Press, vol. 25(06), pages 1754-1792, December.
  9. Perron, P, 1988. "The Great Crash, The Oil Price Shock And The Unit Root Hypothesis," Papers 338, Princeton, Department of Economics - Econometric Research Program.
  10. Christiano, Lawrence J, 1992. "Searching for a Break in GNP," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 237-50, July.
  11. Vogelsang, T.J. & Perron, P., 1994. "Additional Tests for a Unit Root Allowing for a Break in the Trend Function at an Unknown Time," Cahiers de recherche 9422, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  12. Perron, Pierre & Zhu, Xiaokang, 2005. "Structural breaks with deterministic and stochastic trends," Journal of Econometrics, Elsevier, vol. 129(1-2), pages 65-119.
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