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Potential Product, Output Gap and Uncertainty Rate Associated with Their Determination while Using the Hodrick-Prescott Filter

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  • Miroslav Plašil

Abstract

In various fields of macroeconomic modelling, researchers often face the problem of decomposing time series into trend component and cycle fluctuations. While there are several potentially useful methods to perform the task in question, Hodrick-Prescott (HP) fi lter seems to have remained (despite some serious criticism) the most popular approach over the past decade. In this article I propose a straightforward and easy-to-implement bootstrap procedure for building pointwise and simultaneous confidence intervals around "point estimates" produced by HP filter. The principle of proposed method can be described as follows: first, we use maximum entropy bootstrap (Vinod, 2004, 2006) to approximate ensemble from which original time series is drawn and then apply the HP filter directly to each bootstrap replication. If necessary, the proposed method can be adapted to allow for uncertainty in the smoothing parameter. Practical usefulness of our approach is demonstrated with an application to the GDP data. Results are encouraging - obtained confi dence intervals for the trend and cyclical component are overall plausible thus supplying a researcher with some measure of uncertainty related to HP filtering. Finally, we demonstrate that a former approach to build confidence intervals for HP filter (Gallego and Johnson, 2005) leads to erratic inference for cycle due to the shape-destroying block bootstrap sampling.

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Bibliographic Info

Article provided by University of Economics, Prague in its journal Politická ekonomie.

Volume (Year): 2011 (2011)
Issue (Month): 4 ()
Pages: 490-507

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Handle: RePEc:prg:jnlpol:v:2011:y:2011:i:4:id:801:p:490-507

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Related research

Keywords: r; potential product; output gap; Hodrick-Prescott filter; confidence intervals; bootstrap;

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References

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  1. Schlicht, Ekkehart, 2004. "Estimating the Smoothing Parameter in the So-Called Hodrick-Prescott Filter," Discussion Papers in Economics 304, University of Munich, Department of Economics.
  2. Vinod, H. D., 2004. "Ranking mutual funds using unconventional utility theory and stochastic dominance," Journal of Empirical Finance, Elsevier, vol. 11(3), pages 353-377, June.
  3. Vinod, Hrishikesh D., 2006. "Maximum entropy ensembles for time series inference in economics," Journal of Asian Economics, Elsevier, vol. 17(6), pages 955-978, December.
  4. Marcet, Albert & Ravn, Morten O., 2004. "The HP-Filter in Cross-Country Comparisons," CEPR Discussion Papers 4244, C.E.P.R. Discussion Papers.
  5. Regina Kaiser & Agustín Maravall, 1999. "Estimation of the Business Cycle: a Modified Hodrick-Prescott Filter," Banco de Espa�a Working Papers 9912, Banco de Espa�a.
  6. Timothy Cogley & James M. Nason, 1993. "Effects of the Hodrick-Prescott filter on trend and difference stationary time series: implications for business cycle research," Working Papers in Applied Economic Theory 93-01, Federal Reserve Bank of San Francisco.
  7. King, Robert G. & Rebelo, Sergio T., 1993. "Low frequency filtering and real business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 17(1-2), pages 207-231.
  8. Hrishikesh D. Vinod & Javier Lopez-de-Lacalle, . "Maximum Entropy Bootstrap for Time Series: The meboot R Package," Journal of Statistical Software, American Statistical Association, vol. 29(i05).
  9. 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.
  10. Andreas Billmeier, 2004. "Ghostbusting," IMF Working Papers 04/146, International Monetary Fund.
  11. Thomas M. Trimbur, 2006. "Detrending economic time series: a Bayesian generalization of the Hodrick-Prescott filter," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(4), pages 247-273.
  12. Canova, Fabio, 1998. "Detrending and business cycle facts: A user's guide," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 533-540, May.
  13. International Monetary Fund, 2010. "Estimating Potential Output with a Multivariate Filter," IMF Working Papers 10/285, International Monetary Fund.
  14. 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.
  15. Regina Kaiser & Agustín Maravall, 1999. "Estimation of the Business Cycle: a Modified Hodrick-Prescott Filter," Banco de Espa�a Working Papers 9912, Banco de Espa�a.
  16. Morten O. Ravn & Harald Uhlig, 2002. "On adjusting the Hodrick-Prescott filter for the frequency of observations," The Review of Economics and Statistics, MIT Press, vol. 84(2), pages 371-375.
  17. Danthine, Jean-Pierre & Girardin, Michel, 1989. "Business cycles in Switzerland : A comparative study," European Economic Review, Elsevier, vol. 33(1), pages 31-50, January.
  18. Alasdair Scott, 2000. "Stylised facts from output gap measures," Reserve Bank of New Zealand Discussion Paper Series DP2000/07, Reserve Bank of New Zealand.
  19. Francisco Gallego & Christian Johnson, 2005. "Building confidence intervals for band-pass and Hodrick-Prescott filters: an application using bootstrapping," Applied Economics, Taylor & Francis Journals, vol. 37(7), pages 741-749.
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