IDEAS home Printed from https://ideas.repec.org/p/boe/boeewp/142.html
   My bibliography  Save this paper

Band-pass filtering, cointegration, and business cycle analysis

Author

Listed:
  • 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.

Suggested Citation

  • Luca Benati, 2001. "Band-pass filtering, cointegration, and business cycle analysis," Bank of England working papers 142, Bank of England.
  • Handle: RePEc:boe:boeewp:142
    as

    Download full text from publisher

    File URL: http://www.bankofengland.co.uk/archive/Documents/historicpubs/workingpapers/2001/wp142.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Stock, James H. & Watson, Mark W., 1999. "Business cycle fluctuations in us macroeconomic time series," Handbook of Macroeconomics,in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 1, pages 3-64 Elsevier.
    2. Campbell, John Y. & Clarida, Richard H., 1987. "The dollar and real interest rates," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 27(1), pages 103-139, January.
    3. Nelson, Charles R & Kang, Heejoon, 1984. "Pitfalls in the Use of Time as an Explanatory Variable in Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(1), pages 73-82, January.
    4. Miles S. Kimball & John G. Fernald & Susanto Basu, 2006. "Are Technology Improvements Contractionary?," American Economic Review, American Economic Association, vol. 96(5), pages 1418-1448, December.
    5. Burnside, A. Craig & Eichenbaum, Martin S. & Rebelo, Sergio T., 1996. "Sectoral Solow residuals," European Economic Review, Elsevier, vol. 40(3-5), pages 861-869, April.
    6. Casares, Miguel & McCallum, Bennett T., 2006. "An optimizing IS-LM framework with endogenous investment," Journal of Macroeconomics, Elsevier, vol. 28(4), pages 621-644, December.
    7. Susanto Basu, 1996. "Procyclical Productivity: Increasing Returns or Cyclical Utilization?," The Quarterly Journal of Economics, Oxford University Press, vol. 111(3), pages 719-751.
    8. King, Robert G & Watson, Mark W, 1996. "Money, Prices, Interest Rates and the Business Cycle," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 35-53, February.
    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. Nelson, Charles R & Kang, Heejoon, 1981. "Spurious Periodicity in Inappropriately Detrended Time Series," Econometrica, Econometric Society, vol. 49(3), pages 741-751, May.
    11. Lawrence J. Christiano & Terry J. Fitzgerald, 2003. "The Band Pass Filter," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(2), pages 435-465, May.
    12. Burnside, Craig, 1998. "Detrending and business cycle facts: A comment," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 513-532, May.
    13. Wynne, Mark A & Koo, Jahyeong, 2000. "Business Cycles under Monetary Union: A Comparison of the EU and US," Economica, London School of Economics and Political Science, vol. 67(267), pages 347-374, August.
    14. Baxter, Marianne, 1994. "Real exchange rates and real interest differentials: Have we missed the business-cycle relationship?," Journal of Monetary Economics, Elsevier, vol. 33(1), pages 5-37, February.
    15. Canova, Fabio, 1998. "Detrending and business cycle facts," Journal of Monetary Economics, Elsevier, vol. 41(3), pages 475-512, May.
    16. Hai, Weike & Mark, Nelson C & Wu, Yangru, 1997. "Understanding Spot and Forward Exchange Rate Regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(6), pages 715-734, Nov.-Dec..
    17. Christopher J. Erceg & Dale W. Henderson & Andrew T. Levin, 1998. "Tradeoffs between inflation and output-gap variances in an optimizing-agent model," International Finance Discussion Papers 627, Board of Governors of the Federal Reserve System (U.S.).
    18. Julio Rotemberg & Michael Woodford, 1997. "An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy," NBER Chapters,in: NBER Macroeconomics Annual 1997, Volume 12, pages 297-361 National Bureau of Economic Research, Inc.
    19. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 2005. "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy," Journal of Political Economy, University of Chicago Press, vol. 113(1), pages 1-45, February.
    20. Craig Burnside & Martin Eichenbaum & Sergio Rebelo, 1995. "Capital Utilization and Returns to Scale," NBER Chapters,in: NBER Macroeconomics Annual 1995, Volume 10, pages 67-124 National Bureau of Economic Research, Inc.
    21. Bennett T. McCallum & Edward Nelson, 1999. "Performance of Operational Policy Rules in an Estimated Semiclassical Structural Model," NBER Chapters,in: Monetary Policy Rules, pages 15-56 National Bureau of Economic Research, Inc.
    22. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
    23. Maravall, Agustin, 1993. "Stochastic linear trends : Models and estimators," Journal of Econometrics, Elsevier, vol. 56(1-2), pages 5-37, March.
    24. Watson, Mark W., 1986. "Univariate detrending methods with stochastic trends," Journal of Monetary Economics, Elsevier, vol. 18(1), pages 49-75, July.
    25. Peter K. Clark, 1987. "The Cyclical Component of U. S. Economic Activity," The Quarterly Journal of Economics, Oxford University Press, vol. 102(4), pages 797-814.
    26. Christiano, Lawrence J & Eichenbaum, Martin, 1992. "Current Real-Business-Cycle Theories and Aggregate Labor-Market Fluctuations," American Economic Review, American Economic Association, vol. 82(3), pages 430-450, June.
    27. Clark, Peter K., 1989. "Trend reversion in real output and unemployment," Journal of Econometrics, Elsevier, vol. 40(1), pages 15-32, January.
    28. Athanasios Orphanides, 2000. "Activist stabilization policy and inflation: the Taylor rule in the 1970s," Finance and Economics Discussion Series 2000-13, Board of Governors of the Federal Reserve System (U.S.).
    29. Pollock, D. S. G., 2000. "Trend estimation and de-trending via rational square-wave filters," Journal of Econometrics, Elsevier, vol. 99(2), pages 317-334, December.
    30. Susanto Basu & Alan M. Taylor, 1999. "Business Cycles in International Historical Perspective," Journal of Economic Perspectives, American Economic Association, vol. 13(2), pages 45-68, Spring.
    31. Agustín Maravall, 1996. "Unobserved Components in Economic Time Series," Working Papers 9609, Banco de España;Working Papers Homepage.
    32. Haldane, Andrew & Quah, Danny, 1999. "UK Phillips curves and monetary policy," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 259-278, October.
    33. Finn E. Kydland & Edward C. Prescott, 1990. "Business cycles: real facts and a monetary myth," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Spr, pages 3-18.
    34. Burnside, Craig & Eichenbaum, Martin & Rebelo, Sergio, 1993. "Labor Hoarding and the Business Cycle," Journal of Political Economy, University of Chicago Press, vol. 101(2), pages 245-273, April.
    35. Arthur F. Burns & Wesley C. Mitchell, 1946. "Measuring Business Cycles," NBER Books, National Bureau of Economic Research, Inc, number burn46-1, July.
    36. Cogley, Timothy & Nason, James M., 1995. "Effects of the Hodrick-Prescott filter on trend and difference stationary time series Implications for business cycle research," Journal of Economic Dynamics and Control, Elsevier, vol. 19(1-2), pages 253-278.
    37. Timothy Cogley, 1997. "Evaluating non-structural measures of the business cycle," Economic Review, Federal Reserve Bank of San Francisco, pages 3-21.
    38. Jeffrey C. Fuhrer & Scott Schuh, 1998. "Beyond shocks: what causes business cycles?," Conference Series ; [Proceedings], Federal Reserve Bank of Boston, vol. 42(Jun).
    39. Pedersen, Torben Mark, 2001. "The Hodrick-Prescott filter, the Slutzky effect, and the distortionary effect of filters," Journal of Economic Dynamics and Control, Elsevier, vol. 25(8), pages 1081-1101, August.
    40. King, Robert G. & Watson, Mark W., 1994. "The post-war U.S. phillips curve: a revisionist econometric history," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 41(1), pages 157-219, December.
    41. Taylor, John B., 1993. "Discretion versus policy rules in practice," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 39(1), pages 195-214, December.
    42. John H. Cochrane, 1994. "Permanent and Transitory Components of GNP and Stock Prices," The Quarterly Journal of Economics, Oxford University Press, vol. 109(1), pages 241-265.
    43. Susanto Basu, 1998. "Technology and business cycles; how well do standard models explain the facts?," Conference Series ; [Proceedings], Federal Reserve Bank of Boston, vol. 42(Jun), pages 207-269.
    44. Pollock, D. S. G., 2001. "Methodology for trend estimation," Economic Modelling, Elsevier, vol. 18(1), pages 75-96, January.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Herrerias, M.J. & Ordóñez, J., 2014. "If the United States sneezes, does the world need “pain-killers”?," International Review of Economics & Finance, Elsevier, vol. 31(C), pages 159-170.
    2. Alessandra Iacobucci, 2003. "Spectral Analysis for Economic Time Series," Documents de Travail de l'OFCE 2003-07, Observatoire Francais des Conjonctures Economiques (OFCE).
    3. Andrew C. Harvey & Thomas M. Trimbur, 2003. "General Model-Based Filters for Extracting Cycles and Trends in Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 244-255, May.
    4. Cuddington, John T. & Nülle, Grant, 2014. "Variable long-term trends in mineral prices: The ongoing tug-of-war between exploration, depletion, and technological change," Journal of International Money and Finance, Elsevier, vol. 42(C), pages 224-252.
    5. 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, vol. 38(2), pages 140-164, January.
    6. Gonzalo Llosa & Shirley Miller, 2004. "Using Additional Information in Estimating the Output Gap in Peru: a Multivariate Unobserved Component Approach," Money Affairs, Centro de Estudios Monetarios Latinoamericanos, vol. 0(1), pages 57-82, January-J.
    7. Massmann, Michael & Mitchell, James, 2003. "Reconsidering the evidence: Are Eurozone business cycles converging," ZEI Working Papers B 05-2003, University of Bonn, ZEI - Center for European Integration Studies.
    8. Alessandra Iacobucci & Alain Noullez, 2005. "A Frequency Selective Filter for Short-Length Time Series," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 75-102, February.
    9. 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.
    10. Gebhard Flaig, 2002. "Unoberserved Components Models for Quarterly German GDP," CESifo Working Paper Series 681, CESifo Group Munich.
    11. 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.
    12. Konstantakis, Konstantinos N. & Michaelides, Panayotis G., 2017. "Technology and Business Cycles: A Schumpeterian Investigation for the USA," MPRA Paper 80636, University Library of Munich, Germany.
    13. Bean, Charles & Larsen, Jens D. J. & Nikolov, Kalin, 2002. "Financial frictions and the monetary transmission mechanism: theory, evidence and policy implications," Working Paper Series 0113, European Central Bank.
    14. Joannes Mongardini & Tahsin Saadi-Sedik, 2003. "Estimating Indexes of Coincident and Leading Indicators; An Application to Jordan," IMF Working Papers 03/170, International Monetary Fund.
    15. 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.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:boe:boeewp:142. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Digital Media Team). General contact details of provider: http://edirc.repec.org/data/boegvuk.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.