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Why are Beveridge-Nelson and Unobserved-component decompositions of GDP so Different?

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  • James Morley
  • Charles Nelson
  • Eric Zivot

Abstract

This paper reconciles two widely-used decompositions of GDP into trend and cycle that yield starkly different results. Beveridge-Nelson (BN) implies that a stochastic trend accounts for most of the variation in output, while Unobserved-Components (UC) implies cyclical variation is dominant. Which is correct has broad implications for the relative importance of real versus nominal shocks. We show the difference arises from the restriction imposed in UC that trend and cycle innovations are uncorrelated. When this restriction is relaxed, the UC decomposition is identical to the BN decompositions. Furthermore, the zero correlation restriction can be rejected for U.S. quarterly GDP, with the estimated correlation being -0.9.

Suggested Citation

  • James Morley & Charles Nelson & Eric Zivot, 2003. "Why are Beveridge-Nelson and Unobserved-component decompositions of GDP so Different?," Working Papers UWEC-2002-18-P, University of Washington, Department of Economics.
  • Handle: RePEc:udb:wpaper:uwec-2002-18-p
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    1. Blanchard, Olivier Jean & Quah, Danny, 1989. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, American Economic Association, vol. 79(4), pages 655-673, September.
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    5. 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.
    6. Sichel, Daniel E, 1994. "Inventories and the Three Phases of the Business Cycle," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 269-277, July.
    7. Peter K. Clark, 1987. "The Cyclical Component of U. S. Economic Activity," The Quarterly Journal of Economics, Oxford University Press, vol. 102(4), pages 797-814.
    8. Cochrane, John H, 1988. "How Big Is the Random Walk in GNP?," Journal of Political Economy, University of Chicago Press, vol. 96(5), pages 893-920, October.
    9. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-227, June.
    10. Neftci, Salih N, 1984. "Are Economic Time Series Asymmetric over the Business Cycle?," Journal of Political Economy, University of Chicago Press, vol. 92(2), pages 307-328, April.
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