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Band-pass filtering, cointegration, and business cycle analysis

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  • Luca Benati

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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Paper provided by Bank of England in its series Bank of England working papers with number 142.

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Date of creation: Sep 2001
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Handle: RePEc:boe:boeewp:142

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Cited by:
  1. Gonzalo Llosa & Shirley Miller, 2005. "Using additional information in estimating the output gap in Peru: a multivariate unobserved component approach," Working Papers, Banco Central de Reserva del Perú 2005-004, Banco Central de Reserva del Perú.
  2. 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, Faculty of Economics, University of Cambridge 0113, Faculty of Economics, University of Cambridge.
  3. Bean, Charles & Larsen, Jens D. J. & Nikolov, Kalin, 2002. "Financial frictions and the monetary transmission mechanism: theory, evidence and policy implications," Working Paper Series, European Central Bank 0113, European Central Bank.
  4. James Mitchell & Michael Massmann, 2004. "Reconsidering the evidence: are Eurozone business cycles converging?," Money Macro and Finance (MMF) Research Group Conference 2003, Money Macro and Finance Research Group 67, Money Macro and Finance Research Group.
  5. John T. Cuddington & Grant N�lle, 2013. "Variable Long-Term Trends in Mineral Prices: The Ongoing Tug-of-War between Exploration, Depletion, and Technological Change," Working Papers, Colorado School of Mines, Division of Economics and Business 2013-02, Colorado School of Mines, Division of Economics and Business.
  6. 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, Econometric Society 243, Econometric Society.
  7. Alessandra Iacobucci & Alain Noullez, 2004. "A Frequency Selective Filter for Short-Length Time Series," Documents de Travail de l'OFCE, Observatoire Francais des Conjonctures Economiques (OFCE) 2004-05, Observatoire Francais des Conjonctures Economiques (OFCE).
  8. Christian Richter & Andrew Hughes Hallett, 2005. "A Time-Frequency Analysis of the Coherences of the US Business," Computing in Economics and Finance 2005, Society for Computational Economics 45, Society for Computational Economics.
  9. Alessandra Iacobucci, 2003. "Spectral Analysis for Economic Time Series," Documents de Travail de l'OFCE, Observatoire Francais des Conjonctures Economiques (OFCE) 2003-07, Observatoire Francais des Conjonctures Economiques (OFCE).
  10. Gebhard Flaig, 2002. "Unoberserved Components Models for Quarterly German GDP," CESifo Working Paper Series 681, CESifo Group Munich.
  11. Herrerias, M.J. & Ordóñez, J., 2014. "If the United States sneezes, does the world need “pain-killers”?," International Review of Economics & Finance, Elsevier, Elsevier, vol. 31(C), pages 159-170.
  12. Theofanis Papageorgiou & Panayotis G. Michaelides & John G. Milios, 2011. "Technology and economic fluctuations in the US food sector (1958-2006): An empirical approach from a political economy perspective," International Journal of Social Economics, Emerald Group Publishing, Emerald Group Publishing, vol. 38(2), pages 140-164, January.
  13. Joannes Mongardini & Tahsin Saadi-Sedik, 2003. "Estimating Indexes of Coincident and Leading Indicators," IMF Working Papers 03/170, International Monetary Fund.
  14. Martin Petri & Tahsin Saadi-Sedik, 2006. "To Smooth or Not to Smooth," IMF Working Papers 06/257, International Monetary Fund.

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