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Trend-Cycle Decomposition: Implications from an Exact Structural Identification

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  • Mardi Dungey
  • Jan P. A. M. Jacobs

    ()

  • Jing Jian
  • Simon van Norden

    ()

Abstract

A well-documented property of the Beveridge-Nelson trend-cycle decomposition is the perfect negative correlation between trend and cycle innovations. We show how this may be consistent with a structural model where trend shocks enter the cycle, or cycle shocks enter the trend and that identification restrictions are necessary to make this structural distinction. A reduced form unrestricted version such as Morley, Nelson and Zivot (2003) is compatible with either option, but cannot distinguish which is relevant. We discuss economic interpretations and implications using US real GDP data. Une caractéristique bien connue de la décomposition Beveridge-Nelson est la corrélation négative parfaite entre les innovations aux cycles et aux tendances. Nous montrons comment cette corrélation est compatible avec des modèles structurels où les chocs aux tendances entrent par les cycles, ou les chocs aux cycles entrent par les tendances et que des restrictions d’identification sont nécessaires pour faire cette distinction structurelle. Une forme réduite sans restriction comme celle de Morley, Nelson et Zivot (2003) est compatible avec les deux options, mais ne peut pas les distinguer. Nous discutons des interprétations économiques et les implications en utilisant des données réelles du PIB américain.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2013s-23.

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Date of creation: 01 Jul 2013
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Handle: RePEc:cir:cirwor:2013s-23

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Keywords: trend-cycle decomposition; data revision; state-space form;

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  1. Anderson, Heather M. & Low, Chin Nam & Snyder, Ralph, 2006. "Single source of error state space approach to the Beveridge Nelson decomposition," Economics Letters, Elsevier, vol. 91(1), pages 104-109, April.
  2. Morley, James C., 2002. "A state-space approach to calculating the Beveridge-Nelson decomposition," Economics Letters, Elsevier, vol. 75(1), pages 123-127, March.
  3. Tara M. Sinclair, 2009. "The Relationships between Permanent and Transitory Movements in U.S. Output and the Unemployment Rate," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(2-3), pages 529-542, 03.
  4. Pierre Perron & Tatsuma Wada, 2005. "Let’s Take a Break: Trends and Cycles in US Real GDP," Boston University - Department of Economics - Working Papers Series wp2009-006, Boston University - Department of Economics, revised Feb 2009.
  5. Enzo Weber, 2011. "Analyzing U.S. Output and the Great Moderation by Simultaneous Unobserved Components," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 43(8), pages 1579-1597, December.
  6. Jacobs, Jan P.A.M. & van Norden, Simon, 2011. "Modeling data revisions: Measurement error and dynamics of "true" values," Journal of Econometrics, Elsevier, vol. 161(2), pages 101-109, April.
  7. Beveridge, Stephen & Nelson, Charles R., 1981. "A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the `business cycle'," Journal of Monetary Economics, Elsevier, vol. 7(2), pages 151-174.
  8. Oh, Kum Hwa & Zivot, Eric & Creal, Drew, 2008. "The relationship between the Beveridge-Nelson decomposition and other permanent-transitory decompositions that are popular in economics," Journal of Econometrics, Elsevier, vol. 146(2), pages 207-219, October.
  9. Tommaso Proietti, 2006. "Trend-Cycle Decompositions with Correlated Components," Econometric Reviews, Taylor & Francis Journals, vol. 25(1), pages 61-84.
  10. Morley, James C., 2011. "The Two Interpretations Of The Beveridge–Nelson Decomposition," Macroeconomic Dynamics, Cambridge University Press, vol. 15(03), pages 419-439, June.
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