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The Relationship between the Beveridge-Nelson Decomposition andUnobserved Component Models with Correlated Shocks

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Author Info

  • Kum Hwa Oh

    (Bank of Korea)

  • Eric Zivot

    (University of Washington)

  • Drew Creal

    (Free University Amsterdam)

Abstract

Many researchers believe that the Beveridge-Nelson decomposition leads to permanent and transitory components whose shocks are perfectly negatively correlated. Indeed, some even consider it to be a property of the decomposition. We demonstrate that the Beveridge-Nelson decomposition does not provide definitive information about the correlation between permanent and transitory shocks in an unobserved components model. Given an ARIMA model describing the evolution of U.S. real GDP, we show that there are many state space representations that generate the Beveridge-Nelson decomposition. These include unobserved components models with perfectly correlated shocks and partially correlated shocks. In our applications, the only knowledge we have about the correlation is that it lies in a restricted interval that does not include zero. Although the filtered estimates of the trend and cycle are identical for models with different correlations, the observationally equivalent unobserved components models produce different smoothed estimates.

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Bibliographic Info

Paper provided by University of Washington, Department of Economics in its series Working Papers with number UWEC-2006-16-FC.

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Date of creation: Jul 2006
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Publication status: Forthcoming in JOURNAL OF ECONOMETRICS
Handle: RePEc:udb:wpaper:uwec-2006-16-fc

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References

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  1. Kum Hwa Oh & Eric Zivot, 2006. "The Clark Model with Correlated Components," Working Papers UWEC-2006-06, University of Washington, Department of Economics.
  2. Harvey, A C & Jaeger, A, 1993. "Detrending, Stylized Facts and the Business Cycle," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(3), pages 231-47, July-Sept.
  3. James C. Morley & Charles Nelson & Eric Zivot, 2000. "Why Are Beveridge-Nelson and Unobserved-Component Decompositions of GDP So Different?," Working Papers 0013, University of Washington, Department of Economics.
  4. Tommaso Proietti, 2006. "Trend-Cycle Decompositions with Correlated Components," Econometric Reviews, Taylor & Francis Journals, vol. 25(1), pages 61-84.
  5. Marco Lippi & Lucrezia Reichlin, 1992. "On persistence of shocks to economic variables: a common misconception," ULB Institutional Repository 2013/10161, ULB -- Universite Libre de Bruxelles.
  6. Harvey, A.C. & Trimbur, T.M., 2001. "General Model-based Filters for Extracting Cycles and Trends in Economic Time Series," Cambridge Working Papers in Economics 0113, Faculty of Economics, University of Cambridge.
  7. Campbell, John Y & Mankiw, N Gregory, 1987. "Are Output Fluctuations Transitory?," The Quarterly Journal of Economics, MIT Press, vol. 102(4), pages 857-80, November.
  8. Matthew D. Shapiro & Mark W. Watson, 1988. "Sources of Business Cycle Fluctuations," Cowles Foundation Discussion Papers 870, Cowles Foundation for Research in Economics, Yale University.
  9. Cuddington, John T. & Winters, L. Alan, 1987. "The Beveridge-Nelson decomposition of economic time series : A quick computational method," Journal of Monetary Economics, Elsevier, vol. 19(1), pages 125-127, January.
  10. Gomez, Victor, 2001. "The Use of Butterworth Filters for Trend and Cycle Estimation in Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(3), pages 365-73, July.
  11. Neil Shephard & Jurgen Doornik & Siem Jan Koopman, 1998. "Statistical algorithms for models in state space using SsfPack 2.2," Economics Series Working Papers 1998-W06, University of Oxford, Department of Economics.
  12. Arino, Miguel A. & Newbold, Paul, 1998. "Computation of the Beveridge-Nelson decomposition for multivariate economic time series," Economics Letters, Elsevier, vol. 61(1), pages 37-42, October.
  13. Danny Quah, 1991. "The Relative Importance of Permanent and Transitory Components: Identi- fication and Some Theoretical Bounds," NBER Technical Working Papers 0106, National Bureau of Economic Research, Inc.
  14. Ord, J.K. & Koehler, A. & Snyder, R.D., 1995. "Estimation and Prediction for a Class of Dynamic Nonlinear Statistical Models," Monash Econometrics and Business Statistics Working Papers 4/95, Monash University, Department of Econometrics and Business Statistics.
  15. 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.
  16. Harvey,Andrew & Koopman,Siem Jan & Shephard,Neil (ed.), 2004. "State Space and Unobserved Component Models," Cambridge Books, Cambridge University Press, number 9780521835954, December.
  17. Harvey, A.C. & Koopman, S.J.M., 1999. "Signal Extraction and the Formulation of Unobserved Components Models," Discussion Paper 1999-44, Tilburg University, Center for Economic Research.
  18. Morley, James C., 2002. "A state-space approach to calculating the Beveridge-Nelson decomposition," Economics Letters, Elsevier, vol. 75(1), pages 123-127, March.
  19. James C. Morley & Charles R. Nelson & Eric Zivot, 2003. "Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different?," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 235-243, May.
  20. Daisuke Nagakura & Eric Zivot, 2007. "Implications of Two Measures of Persistence for Correlation Between Permanent and Transitory Shocks in U.S. Real GDP," Working Papers UWEC-2007-07, University of Washington, Department of Economics.
  21. 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.
  22. Proietti, Tommaso & Harvey, Andrew, 2000. "A Beveridge-Nelson smoother," Economics Letters, Elsevier, vol. 67(2), pages 139-146, May.
  23. Evans, George W & Reichlin, Lucrezia, 1993. "Information, Forecasts and Measurement of the Business Cycle," CEPR Discussion Papers 756, C.E.P.R. Discussion Papers.
  24. Clark, Peter K, 1987. "The Cyclical Component of U.S. Economic Activity," The Quarterly Journal of Economics, MIT Press, vol. 102(4), pages 797-814, November.
  25. Gomez, Victor, 1999. "Three Equivalent Methods for Filtering Finite Nonstationary Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 109-16, January.
  26. Newbold, Paul, 1990. "Precise and efficient computation of the Beveridge-Nelson decomposition of economic time series," Journal of Monetary Economics, Elsevier, vol. 26(3), pages 453-457, December.
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Cited by:
  1. Tommaso Proietti, 2009. "The Multistep Beveridge-Nelson Decomposition," EERI Research Paper Series EERI_RP_2009_24, Economics and Econometrics Research Institute (EERI), Brussels.

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