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The Hodrick-Prescott Filter, the Slutzky Effect, and the Distortionary Effect of Filters

Author

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  • Torben Mark Pedersen

    (University of Copenhagen Institute of Economics)

Abstract

The main contribution of this paper is the construction of a metric based on optimal filtering for measuring the distortionary effect of filters. The Hodrick-Prescott filter (HP-filter) has been critizised for inducing spurious cycles when filtering macroeconomic time series with the "typical spectral shape", the so-called Slutzky-effect. It is shown that the HP-filter is not subject to that critique and that the Slutzky-effect is a special case of a more general pattern of distortions of filters. Based on the theory of optimal filtering, we derive a frequency domain measure of the size of distortions when defining business cycles as cycles with a period less than a prespecified number of years. The metric is used for two purposes. First, to determine the optimal value of the smoothing parameter in the HP-filter. Secondly, to measure the size of distortions of ten filters including a new Hodrick-Prescott based band pass filter. The main conclusions are that the standard value of the smoothing parameter of the HP-filter, = 1600, is close to being the optimal value when filtering near-integrated time series and that the HP-filter is less distorting than any of the other filters studied.

Suggested Citation

  • Torben Mark Pedersen, 1998. "The Hodrick-Prescott Filter, the Slutzky Effect, and the Distortionary Effect of Filters," Discussion Papers 98-09, University of Copenhagen. Department of Economics.
    • Handle: RePEc:kud:kuiedp:9809
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    Citations

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    Cited by:

    1. Simon van Norden, 2002. "Filtering for Current Analysis," Staff Working Papers 02-28, Bank of Canada.
    2. João Valle e Azevedo, 2002. "Business Cycles: Cyclical Comovement Within the European Union in the Period 1960-1999. A Frequency Domain Approach," Working Papers w200205, Banco de Portugal, Economics and Research Department.
    3. Van Norden, Simon, 2004. "Filtres pour l’analyse courante," L'Actualité Economique, Société Canadienne de Science Economique, vol. 80(2), pages 523-546, Juin-Sept.
    4. Arby, Muhammad Farooq, 2001. "Long-run trend, Business Cycle & Short-run shocks in real GDP," MPRA Paper 4929, University Library of Munich, Germany.
    5. Bouthevillain, Carine & Cour-Thimann, Philippine & van de Dool, Gerrit & Hernández de Cos, Pablo & Langenus, Geert & Mohr, Matthias & Momigliano, Sandro & Tujula, Mika, 2001. "Cyclically adjusted budget balances: an alternative approach," Working Paper Series 77, European Central Bank.
    6. Bouoiyour, Jamal & Ibourk, Aomar, 2005. "Le Cycle des affaires dans les pays MENA Une Application du Filtre Hodrick-Prescott [The Business Cycle in MENA Application of a Hodrick-Prescott Filter]," MPRA Paper 46115, University Library of Munich, Germany.

    More about this item

    Keywords

    detrending; Hodrick-Prescott filter; Slutzky effect; optimal filtering; spectral analysis; business cycles;
    All these keywords.

    JEL classification:

    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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