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Tracking Growth and the Business Cycle: a Stochastic Common Cycle Model for the Euro Area

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  • João Valle e Azevedo
  • Siem Jan Koopman
  • António Rua

Abstract

This paper proposes a new model-based method to obtain a coincident indicator for the business cycle. A dynamic factor model with trend components and a common cycle component is considered which can be estimated using standard maximum likelihood methods. The multivariate unobserved components model includes a stationary higher order cycle. Also higher order trends can be part of the analysis. These generalisations lead to a business cycle that is similar to a band-pass one. Furthermore, cycle shifts for individual time series are incorporated within the model and estimated simultaneously with the remaining parameters. This feature permits the use of leading, coincident and lagging variables to obtain the business cycle coincident indicator without prior analysis of their lead-lag relationship. Besides the business cycle indicator, the model-based approach also allows to get a growth rate indicator. In the empirical analysis for the Euro area, both indicators are obtained based on nine key economic time series including gross domestic product, industrial production, unemployment, confidence indicators and interest rate spread. This analysis contrasts sharply with earlier multivariate approaches. In particular, our more parsimonious approach leads to a growth rate indicator for the Euro area that is similar to the one of EuroCOIN. The latter is based on a more involved approach by any standard and uses hundreds of time series from individual countries belonging to the Euro area.

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Bibliographic Info

Paper provided by Banco de Portugal, Economics and Research Department in its series Working Papers with number w200316.

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Date of creation: 2003
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Handle: RePEc:ptu:wpaper:w200316

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  1. Fagan, Gabriel & Henry, Jérôme & Mestre, Ricardo, 2001. "An area-wide model (AWM) for the euro area," Working Paper Series 0042, European Central Bank.
  2. Harvey, A C, 1985. "Trends and Cycles in Macroeconomic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(3), pages 216-27, June.
  3. Stock, James H. & Watson, Mark W., 1999. "Business cycle fluctuations in us macroeconomic time series," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 1, pages 3-64 Elsevier.
  4. Lawrence J. Christiano & Terry J. Fitzgerald, 2003. "The Band Pass Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(2), pages 435-465, 05.
  5. 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.
  6. Mario Forni & Marc Hallin & Marco Lippi & Lucrezia Reichlin, 2000. "The Generalized Dynamic-Factor Model: Identification And Estimation," The Review of Economics and Statistics, MIT Press, vol. 82(4), pages 540-554, November.
  7. Koopman, S.J.M. & Shephard, N. & Doornik, J.A., 1998. "Statistical Algorithms for Models in State Space Using SsfPack 2.2," Discussion Paper 1998-141, Tilburg University, Center for Economic Research.
  8. Mario Forno & Marco Lippi & Lucrezia Reichlin & Filippo Altissimo & Antonio Bassanetti, 2003. "Eurocoin: A Real Time Coincident Indicator Of The Euro Area Business Cycle," Computing in Economics and Finance 2003 242, Society for Computational Economics.
  9. 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.
  10. Roberto S. Mariano & Yasutomo Murasawa, 2003. "A new coincident index of business cycles based on monthly and quarterly series," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(4), pages 427-443.
  11. Fagan, Gabriel & Henry, Jerome & Mestre, Ricardo, 2005. "An area-wide model for the euro area," Economic Modelling, Elsevier, vol. 22(1), pages 39-59, January.
  12. Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 575-593, November.
  13. James H. Stock & Mark W. Watson, 1989. "New Indexes of Coincident and Leading Economic Indicators," NBER Chapters, in: NBER Macroeconomics Annual 1989, Volume 4, pages 351-409 National Bureau of Economic Research, Inc.
  14. Koopman, S.J.M. & Durbin, J., 1998. "Fast Filtering and Smoothing for Multivariate State Space Models," Discussion Paper 1998-18, Tilburg University, Center for Economic Research.
  15. Gerhard Runstler, 2004. "Modelling phase shifts among stochastic cycles," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 232-248, 06.
  16. Athanasios Orphanides & Simon van Norden, 1999. "The Reliability of Output Gap Estimates in Real Time," Macroeconomics 9907006, EconWPA.
  17. Durbin, James & Koopman, Siem Jan, 2001. "Time Series Analysis by State Space Methods," OUP Catalogue, Oxford University Press, number 9780198523543.
  18. Robert J. Hodrick & Edward Prescott, 1981. "Post-War U.S. Business Cycles: An Empirical Investigation," Discussion Papers 451, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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Cited by:
  1. Edoardo Otranto, 2005. "Extraction of Common Signal from Series with Different Frequency," Econometrics 0502011, EconWPA.
  2. Cayen, Jean-Philippe & van Norden, Simon, 2005. "The reliability of Canadian output-gap estimates," The North American Journal of Economics and Finance, Elsevier, vol. 16(3), pages 373-393, December.

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