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Do the Hodrick-Prescott and Baxter-King Filters Provide a Good Approximation of Business Cycles?

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Abstract

In this paper, the authors examine how well the Hodrick-Prescott (HP) and the band-pass filter recently proposed by Baxter and King (BK) extract the business-cycle component of macroeconomic time series. The authors assess these filters using two different definitions of the business-cycle component. First, they define that component to be fluctuations lasting no fewer than six and no more than thirty-two quarters; this is the definition of business-cycle frequencies used by Baxter and King. Second, they define the business-cycle component on the basis of a decomposition of the series into permanent and transitory components. In both cases the conclusions are the same. The filters perform adequately when the spectrum of the original series has a peak at business-cycle frequencies. When the spectrum is dominated by low frequencies, the filters provide a distorted business cycle. Since most macroeconomic series have the typical Granger shape, the HP and BK filters perform poorly in terms of identifying the business cycles of these series. Dans la présente étude, les auteurs cherchent à évaluer l'efficacité avec laquelle le filtre de Hodrick-Prescott (HP) et le filtre passe-bande récemment proposé par Baxter et King (BK) permettent d'isoler la composante cyclique des séries macroéconomiques. Ils utilisent deux définitions du cycle économique pour comparer la performance de ces filtres. Selon la première définition (celle que retiennent Baxter et King), la composante cyclique correspond à des fluctuations d'une durée minimale de six trimestres et maximale de trente-deux trimestres. L'autre définition du cycle consiste dans la décomposition de la série en deux composantes, l'une permanente et l'autre transitoire. Les auteurs parviennent aux mêmes conclusions peu importe la définition utilisée. Les filtres donnent des résultats satisfaisants lorsque le spectre de la série initiale atteint un sommet au voisinage des fréquences comprises entre six et trente-deux trimestres. Lorsque le spectre est dominé par les basses fréquences, le cycle économique obtenu donne une image faussée de la réalité. Comme la forme spectrale de la plupart des séries macroéconomiques ressemble à celle que Granger a mise en lumière, les filtres HP et BK réussissent mal à isoler la composante cyclique de ces séries.

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  • Alain Guay & Pierre St-Amant, 1997. "Do the Hodrick-Prescott and Baxter-King Filters Provide a Good Approximation of Business Cycles?," Cahiers de recherche CREFE / CREFE Working Papers 53, CREFE, Université du Québec à Montréal.
  • Handle: RePEc:cre:crefwp:53
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    More about this item

    Keywords

    Mechanical filters; business cycles; spectrum;
    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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