Empirical Economics

, Volume 51, Issue 4, pp 1415–1441 | Cite as

The Beveridge–Nelson decomposition of mixed-frequency series

An application to simultaneous measurement of classical and deviation cycles
Article
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Abstract

Gibbs sampling for Bayesian VAR with mixed-frequency series draws latent high-frequency series and model parameters sequentially. Applying the multivariate Beveridge–Nelson (B–N) decomposition in each Gibbs step, one can simulate the joint posterior distribution of the B–N permanent and transitory components in latent and observable high-frequency series. This paper applies the method to mixed-frequency series of macroeconomic variables including quarterly real GDP to estimate the monthly natural rates and gaps of output, inflation, interest, and unemployment jointly. The resulting monthly real GDP and GDP gap are complementary coincident indices, measuring classical and deviation cycles, respectively.

Keywords

Bayesian Gap Growth cycle Monthly GDP Natural rate Trend–cycle decomposition 

JEL classification

C11 C32 C43 C82 E32 

Notes

Acknowledgments

I thank two referees, Manabu Asai, David Garcia-Leon, and Yohei Yamamoto for useful comments. This work was supported by JSPS KAKENHI Grant Number 23530255.

References

  1. Artis M, Marcellino M, Proietti T (2004) Dating business cycles: a methodological contribution with an application to the euro area. Oxf Bull Econ Stat 66:537–565CrossRefGoogle Scholar
  2. Bańbura M, Giannone D, Reichlin L (2010) Large Bayesian vector auto regressions. J Appl Econ 25:71–92CrossRefGoogle Scholar
  3. Beveridge S, Nelson CR (1981) A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the ‘business cycle’. J Monet Econ 7:151–174CrossRefGoogle Scholar
  4. Bos CS (2011) A Bayesian analysis of unobserved component models using Ox. J Stat Softw 41(13):1–24CrossRefGoogle Scholar
  5. Bry G, Boschan C (1971) Cyclical analysis of time series: selected procedures and computer programs. Technical Paper 20, National Bureau of Economic ResearchGoogle Scholar
  6. Burns AF, Mitchell WC (1946) Measuring business cycles. National Bureau of Economic ResearchGoogle Scholar
  7. Chib S, Greenberg E (1994) Bayes inference in regression models with ARAM\((p, q)\) errors. J Econ 64:183–206CrossRefGoogle Scholar
  8. Chib S, Greenberg E (1995) Hierarchical analysis of SUR models with extensions to correlated serial errors and time-varying parameter models. J Econ 68:339–360CrossRefGoogle Scholar
  9. Cogley T, Sargent TJ (2001) Evolving post-World War II U.S. inflation dynamics. NBER Macroecon Ann 16:331–373Google Scholar
  10. Cogley T, Sargent TJ (2005) Drifts and volatilities: monetary policies and outcomes in the post WWII US. Rev Econ Dyn 8:262–302CrossRefGoogle Scholar
  11. Doornik JA (2007) Object-oriented matrix programming using Ox, 3rd edn. Timberlake ConsultantsGoogle Scholar
  12. Durbin J, Koopman SJ (2002) A simple and efficient simulation smoother for state space time series analysis. Biometrika 89:603–615CrossRefGoogle Scholar
  13. Eraker B, Chiu CWJ, Foerster AT, Kim TB, Seoane HD (2015) Bayesian mixed frequency VARs. J Financ Econ 13:698–721Google Scholar
  14. Friedman M (1968) The role of monetary policy. Am Econ Rev 58:1–21Google Scholar
  15. Garratt A, Robertson D, Wright S (2006) Permanent vs transitory components and economic fundamentals. J Appl Econ 21:521–542CrossRefGoogle Scholar
  16. Hamilton JD, Owyang MT (2012) The propagation of regional recessions. Rev Econ Stat 94:935–947CrossRefGoogle Scholar
  17. Harding D, Pagan A (2002) Dissecting the cycle: a methodological investigation. J Monet Econ 49:365–381CrossRefGoogle Scholar
  18. Harding D, Pagan A (2005) A suggested framework for classifying the mode of cycle research. J Appl Econ 20:151–159CrossRefGoogle Scholar
  19. Harvey AC, Proietti T (eds) (2005) Readings in unobserved components models. Oxford University Press, OxfordGoogle Scholar
  20. Kadiyala KR, Karlsson S (1997) Numerical methods for estimation and inference in Bayesian VAR-models. J Appl Econ 12:99–132CrossRefGoogle Scholar
  21. King TB, Morley J (2007) In search of the natural rate of unemployment. J Monet Econ 54:550–564CrossRefGoogle Scholar
  22. Koopman SJ, Shephard N, Doornik JA (1999) Statistical algorithms for models in state space using SsfPack 2.2. Econ J 2:107–160Google Scholar
  23. Litterman RB (1986) Forecasting with Bayesian vector autoregressions–five years of experience. J Bus Econ Stat 4:25–38Google Scholar
  24. Mariano RS, Murasawa Y (2003) A new coincident index of business cycles based on monthly and quarterly series. J Appl Econ 18:427–443CrossRefGoogle Scholar
  25. Mariano RS, Murasawa Y (2010) A coincident index, common factors, and monthly real GDP. Oxf Bull Econ Stat 72:27–46CrossRefGoogle Scholar
  26. Mintz I (1969) Dating postwar business cycles: Methods and their application to Western Germany, 1950–1967. Occasional Paper 107, National Bureau of Economic ResearchGoogle Scholar
  27. Mintz I (1972) Dating American growth cycles. In: Zarnowitz V (ed) The business cycle today, economic research: retrospect and prospect, vol 1, National Bureau of Economic Research, pp 39–88Google Scholar
  28. Mitchell J, Smith RJ, Weale MR, Wright S, Salazar EL (2005) An indicator of monthly GDP and an early estimate of quarterly GDP growth. Econ J 115:F108–F129CrossRefGoogle Scholar
  29. Morley JC (2002) A state-space approach to calculating the Beveridge–Nelson decomposition. Econ Lett 75:123–127CrossRefGoogle Scholar
  30. Morley JC, Piger J (2008) Trend/cycle decomposition of regime-switching processes. J Econ 146:220–226CrossRefGoogle Scholar
  31. Morley JC, Piger J (2012) The asymmetric business cycle. Rev Econ Stat 94:208–221CrossRefGoogle Scholar
  32. Murasawa Y (2014) Measuring the natural rates, gaps, and deviation cycles. Empir Econ 47:495–522CrossRefGoogle Scholar
  33. Orphanides A, van Norden S (2002) The unreliability of output-gap estimates in real time. Rev Econ Stat 84:569–583CrossRefGoogle Scholar
  34. Perron P, Wada T (2009) Let’s take a break: trends and cycles in US real GDP. J Monet Econ 56:749–765CrossRefGoogle Scholar
  35. Phelps ES (1995) The origins and further development of the natural rate of unemployment. In: Cross R (ed) The natural rate of unemployment: reflections on 25 years of the hypothesis, Cambridge University Press, chap 2, pp 15–31Google Scholar
  36. Qian H (2013) Vector autoregression with mixed-frequency data. MRPA Paper 47856Google Scholar
  37. Qian H (2014) A flexible state space model and its applications. J Time Ser Anal 35:79–88CrossRefGoogle Scholar
  38. Schorfheide F, Song D (2015) Real-time forecasting with a mixed-frequency VAR. J Bus Econ Stat 33:366–380CrossRefGoogle Scholar
  39. Stock JH, Watson MW (2010) Indicators for dating business cycles: cross-history selection and comparisons. Am Econ Rev 100:16–19CrossRefGoogle Scholar
  40. Stock JH, Watson MW (2014) Estimating turning points using large data sets. J Econ 178:368–381CrossRefGoogle Scholar
  41. Viefers P (2011) Bayesian inference for the mixed-frequency VAR model. Discussion Paper 1172, Deutsches Institut für WirtschaftsforschungGoogle Scholar
  42. Zarnowitz V, Ozyildirim A (2006) Time series decomposition and measurement of business cycles, trends, and growth cycles. J Monet Econ 53:1717–1739CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Faculty of EconomicsKonan UniversityKobeJapan

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