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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)

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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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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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  1. 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. [Downloadable!] (restricted)
  2. Lippi, Marco & Reichlin, Lucrezia, 1992. "On persistence of shocks to economic variables : A common misconception," Journal of Monetary Economics, Elsevier, vol. 29(1), pages 87-93, February. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. Morley, James C., 2002. "A state-space approach to calculating the Beveridge-Nelson decomposition," Economics Letters, Elsevier, vol. 75(1), pages 123-127, March. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  6. Andrew C. Harvey & Thomas M. Trimbur, 2003. "General Model-Based Filters for Extracting Cycles and Trends in Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 244-255, 03. [Downloadable!] (restricted)
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  7. 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.
  8. Evans, George & Reichlin, Lucrezia, 1994. "Information, forecasts, and measurement of the business cycle," Journal of Monetary Economics, Elsevier, vol. 33(2), pages 233-254, April. [Downloadable!] (restricted)
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  9. 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. [Downloadable!] (restricted)
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  10. 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. [Downloadable!] (restricted)
  11. 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. [Downloadable!] (restricted)
  12. 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. [Downloadable!] (restricted)
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  13. 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. [Downloadable!]
  14. Siem Jan Koopman & Neil Shephard & Jurgen A. Doornik, 1999. "Statistical algorithms for models in state space using SsfPack 2.2," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 107-160.
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  15. 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. [Downloadable!] (restricted)
  16. 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.
  17. Charles Nelson & Eric Zivot, 2000. "Why are Beveridge-Nelson and Unobserved-Component Decompositions of GDP so Different?," Econometric Society World Congress 2000 Contributed Papers 0692, Econometric Society. [Downloadable!]
  18. 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.
  19. Quah, Danny, 1992. "The Relative Importance of Permanent and Transitory Components: Identification and Some Theoretical Bounds," Econometrica, Econometric Society, vol. 60(1), pages 107-18, January. [Downloadable!] (restricted)
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  20. Andrew Harvey & Siem Jan Koopman, 2000. "Signal extraction and the formulation of unobserved components models," Econometrics Journal, Royal Economic Society, vol. 3(1), pages 84-107.
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  21. Kum Hwa Oh & Eric Zivot, 2006. "The Clark Model with Correlated Components," Working Papers UWEC-2006-06, University of Washington, Department of Economics. [Downloadable!]
  22. Matthew D. Shapiro & Mark W. Watson, 1989. "Sources of Business Cycle Fluctuations," NBER Working Papers 2589, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  23. Proietti, Tommaso & Harvey, Andrew, 2000. "A Beveridge-Nelson smoother," Economics Letters, Elsevier, vol. 67(2), pages 139-146, May. [Downloadable!] (restricted)
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