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Trend-cycle decomposition: implications from an exact structural identification

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Listed:
  • Mardi Dungey
  • Jan P. A. M. Jacobs
  • Jing Tian
  • 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 cyclic shocks enter the trend and that identification restrictions are necessary to make this structural distinction. A reduced-form unrestricted version such as that of 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.

Suggested Citation

  • Mardi Dungey & Jan P. A. M. Jacobs & Jing Tian & Simon van Norden, 2013. "Trend-cycle decomposition: implications from an exact structural identification," Working Papers 13-22, Federal Reserve Bank of Philadelphia.
  • Handle: RePEc:fip:fedpwp:13-22
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    References listed on IDEAS

    as
    1. Perron, Pierre & Wada, Tatsuma, 2009. "Let's take a break: Trends and cycles in US real GDP," Journal of Monetary Economics, Elsevier, vol. 56(6), pages 749-765, September.
    2. 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.
    3. Tommaso Proietti, 2006. "Trend-Cycle Decompositions with Correlated Components," Econometric Reviews, Taylor & Francis Journals, vol. 25(1), pages 61-84.
    4. 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, March.
    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. 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.
    7. Morley, James C., 2002. "A state-space approach to calculating the Beveridge-Nelson decomposition," Economics Letters, Elsevier, vol. 75(1), pages 123-127, March.
    8. Morley, James C., 2011. "The Two Interpretations Of The Beveridge–Nelson Decomposition," Macroeconomic Dynamics, Cambridge University Press, vol. 15(03), pages 419-439, June.
    9. 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.
    10. 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.
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    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C82 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Macroeconomic Data; Data Access

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