IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Log in (now much improved!) to save this paper

The Band Pass Filter

Author Info

Listed author(s):
  • Lawrence J. Christiano
  • Terry J. Fitzgerald

Abstract

The `ideal' band pass filter can be used to isolate the component of a time series that lies within a particular band of frequencies. However, applying this filter requires a dataset of infinite length. In practice, some sort of approximation is needed. Using projections, we derive approximations that are optimal when the time series representations underlying the raw data have a unit root, or are stationary about a trend. We identify one approximation which, though it is only optimal for one particular time series representation, nevertheless works well for standard macroeconomic time series. To illustrate the use of this approximation, we use it to characterize the change in the nature of the Phillips curve and the money-inflation relation before and after the 1960s. We find that there is surprisingly little change in the Phillips curve and substantial change in money growth-inflation relation.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.nber.org/papers/w7257.pdf
Download Restriction: no

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 7257.

as
in new window

Length:
Date of creation: Jul 1999
Publication status: published as Christiano, Lawrence J. and Terry J. Fitzgerald. "The Band Pass Filter," International Economic Review, 2003, v44(2,May), 435-465.
Handle: RePEc:nbr:nberwo:7257
Note: EFG
Contact details of provider: Postal:
National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.

Phone: 617-868-3900
Web page: http://www.nber.org
Email:


More information through EDIRC

Keywords:

Other versions of this item:

  • 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, 05.
Find related papers by JEL classification:
  • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
  • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

This paper has been announced in the following NEP Reports:

References listed on IDEAS
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.:

as
in new window


  1. Prescott, Edward C., 1986. "Theory ahead of business-cycle measurement," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 25(1), pages 11-44, January.
  2. Lawrence J. Christiano & Terry J. Fitzgerald, 1998. "The business cycle: it's still a puzzle," Economic Perspectives, Federal Reserve Bank of Chicago, issue Q IV, pages 56-83.
  3. 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.
  4. William Poole, 1999. "Monetary policy rules?," Review, Federal Reserve Bank of St. Louis, issue Mar, pages 3-12.
  5. Chistiano, Lawrence J & den Haan, Wouter J, 1996. "Small-Sample Properties of GMM for Business-Cycle Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 309-327, July.
  6. 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.
  7. Barro, Robert J & Gordon, David B, 1983. "A Positive Theory of Monetary Policy in a Natural Rate Model," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 589-610, August.
  8. Athanasios Orphanides & Simon van Norden, 2002. "The Unreliability of Output-Gap Estimates in Real Time," The Review of Economics and Statistics, MIT Press, vol. 84(4), pages 569-583, November.
  9. Christiano, Lawrence J. & Eichenbaum, Martin, 1990. "Unit roots in real GNP: Do we know, and do we care?," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 32(1), pages 7-61, January.
  10. Cooley, Thomas F. & Ohanian, Lee E., 1991. "The cyclical behavior of prices," Journal of Monetary Economics, Elsevier, vol. 28(1), pages 25-60, August.
  11. Chari, V. V. & Christiano, Lawrence J. & Eichenbaum, Martin, 1998. "Expectation Traps and Discretion," Journal of Economic Theory, Elsevier, vol. 81(2), pages 462-492, August.
  12. Orphanides, Athanasios, 2003. "The quest for prosperity without inflation," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 633-663, April.
  13. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May.
  14. 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.
  15. King, Robert G. & Rebelo, Sergio T., 1993. "Low frequency filtering and real business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 17(1-2), pages 207-231.
  16. John B. Taylor, 1999. "Monetary Policy Rules," NBER Books, National Bureau of Economic Research, Inc, number tayl99-1, June.
  17. Lucas, Robert E, Jr, 1980. "Two Illustrations of the Quantity Theory of Money," American Economic Review, American Economic Association, vol. 70(5), pages 1005-1014, December.
  18. St-Amant, P. & van Norden, S., 1997. "Measurement of the Output Gap: A Discussion of Recent Research at the Bank of Canada," Technical Reports 79, Bank of Canada.
  19. Ball, Laurence & Mankiw, N. Gregory, 1994. "A sticky-price manifesto," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 41(1), pages 127-151, December.
  20. Singleton, Kenneth J., 1988. "Econometric issues in the analysis of equilibrium business cycle models," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 361-386.
  21. Edmund S. Phelps, 1968. "Money-Wage Dynamics and Labor-Market Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 76, pages 678-678.
  22. Andreas Hornstein, 1998. "Inventory investment and the business cycle," Economic Quarterly, Federal Reserve Bank of Richmond, issue Spr, pages 49-71.
  23. Engle, Robert F, 1974. "Band Spectrum Regression," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 1-11, February.
  24. Ireland, Peter N., 1999. "Does the time-consistency problem explain the behavior of inflation in the United States?," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 279-291, October.
  25. Ireland, Peter N., 1997. "Sustainable monetary policies," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 87-108, November.
  26. Whiteman, Charles H, 1984. "Lucas on the Quantity Theory: Hypothesis Testing without Theory," American Economic Review, American Economic Association, vol. 74(4), pages 742-749, September.
  27. 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.
  28. Kydland, Finn E & Prescott, Edward C, 1977. "Rules Rather Than Discretion: The Inconsistency of Optimal Plans," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 473-491, June.
Full references (including those not matched with items on IDEAS)

Blog mentions

As found by EconAcademics.org, the blog aggregator for Economics research:
  1. Potential supply, the output gap and inflation
    by bankunderground in Bank Underground on 2016-01-25 07:30:48
  2. The long and short of the AIG bailout
    by Scott Condie in econosseur on 2009-01-08 23:19:13
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as
in new window


Cited by:
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page.

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Access and download statistics

When requesting a correction, please mention this item's handle: RePEc:nbr:nberwo:7257. 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: ()

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.