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Band-pass filtering, cointegration, and business cycle analysis

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Luca Benati

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Abstract

This paper critically assesses the practice of band-pass filtering (the non-structural, frequency-domain based decomposition of economic time series into trend and cyclical components), making two main points. First, it is shown that: (a) depending on the stochastic properties of the filtered process, the band-pass filtered cyclical component is entirely authentic, partly or mostly spurious, or even entirely spurious; and (b) as a simple consequence of the Lucas critique, the degree of authenticity of band-pass filtered cyclical components crucially depends on the monetary rule followed by the policy-maker. Second, taking a number of macroeconomic models as data-generation processes it is shown that band-pass filtering: (a) may markedly distort key business cycle stylised facts, as captured by the cross-correlations and the cross-spectral statistics between the cyclical components of the variables of interest and the cyclical component of GDP; and (b) may well create entirely spurious stylised facts. For example: both productivity and the money supply may appear procyclical even when they follow random walks by construction; the real wage may appear procyclical when in fact it is countercyclical; in general, the Phillips correlation between inflation and the cyclical component of economic activity will appear weaker than it is in reality. Again, the degree of authenticity of business cycle stylised facts uncovered via band-pass filtering crucially depends on the monetary rule followed by the policy-maker.

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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Alessandra Iacobucci & Alain Noullez, 2004. "A Frequency Selective Filter for Short-Length Time Series," Documents de Travail de l'OFCE 2004-05, Observatoire Francais des Conjonctures Economiques (OFCE). [Downloadable!]
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  2. Alessandra Iacobucci, 2003. "Spectral Analysis for Economic Time Series," Documents de Travail de l'OFCE 2003-07, Observatoire Francais des Conjonctures Economiques (OFCE). [Downloadable!]
  3. Gonzalo Llosa & Shirley Miller, 2005. "Using additional information in estimating the output gap in Peru: a multivariate unobserved component approach," Working Papers 2005-004, Banco Central de Reserva del Perú. [Downloadable!]
  4. Charles Bean & Jens D.J. Larsen & Kalin Nikolov, 2002. "Financial frictions and the monetary transmission mechanism: theory; evidence and policy implications," Working Paper Series 113, European Central Bank. [Downloadable!]
  5. Martin Petri & Tahsin Saadi-Sedik, 2006. "To Smooth or Not to Smooth - The Impact of Grants and Remittances on the Equilibrium Real Exchange Rate in Jordan," IMF Working Papers 06/257, International Monetary Fund. [Downloadable!]
  6. Gebhard Flaig, 2002. "Unoberserved Components Models for Quarterly German GDP," CESifo Working Paper Series CESifo Working Paper No. , CESifo Group Munich. [Downloadable!]
  7. Gonzalo Llosa/Shirley Miller, 2004. "Using additional information in estimating output gap in Peru: a multivariate unobserved component approach," Econometric Society 2004 Latin American Meetings 243, Econometric Society. [Downloadable!]
  8. Christian Richter & Andrew Hughes Hallett, 2005. "A Time-Frequency Analysis of the Coherences of the US Business," Computing in Economics and Finance 2005 45, Society for Computational Economics. [Downloadable!]
  9. Tahsin Saadi-Sedik & Joannes Mongardini, 2003. "Estimating Indexes of Coincident and Leading Indicators: An Application to Jordan," IMF Working Papers 03/170, International Monetary Fund. [Downloadable!]
  10. Harvey, A.C. & Trimbur, T.M., 2001. "General Model-based Filters for Extracting Cycles and Trends in Economic Time Series," Cambridge Working Papers in Economics 0113, Faculty of Economics, University of Cambridge. [Downloadable!]
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  11. James Mitchell & Michael Massmann, 2004. "Reconsidering the evidence: are Eurozone business cycles converging?," Money Macro and Finance (MMF) Research Group Conference 2003 67, Money Macro and Finance Research Group. [Downloadable!]
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