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The Band Pass Filter

  • Lawrence J. Christiano
  • Terry J. Fitzgerald

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.

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File URL: http://www.nber.org/papers/w7257.pdf
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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 7257.

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Date of creation: Jul 1999
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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
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  1. 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.
  2. V.V. Chari & Lawrence J. Christiano & Martin Eichenbaum, 1996. "Expectation traps and discretion," Working Paper Series, Macroeconomic Issues WP-96-5, Federal Reserve Bank of Chicago.
  3. Athanasios Orphanides & Simon van Norden, 1999. "The Reliability of Output Gap Estimates in Real Time," Macroeconomics 9907006, EconWPA.
  4. 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.
  5. Lawrence J. Christiano & Wouter den Haan, 1995. "Small sample properties of GMM for business cycle analysis," Working Paper Series, Macroeconomic Issues 95-3, Federal Reserve Bank of Chicago.
  6. 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.
  7. Robert G. King & Mark W. Watson, 1994. "The post-war U.S. Phillips curve: a revisionist econometric history," Working Paper Series, Macroeconomic Issues 94-14, Federal Reserve Bank of Chicago.
  8. Lawrence J. Christiano & Martin Eichenbaum, 1990. "Unit roots in real GNP: do we know, and do we care?," Working Paper Series, Macroeconomic Issues 90-2, Federal Reserve Bank of Chicago.
  9. 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.
  10. 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.
  11. Orphanides, Athanasios, 2003. "The quest for prosperity without inflation," Journal of Monetary Economics, Elsevier, vol. 50(3), pages 633-663, April.
  12. Edmund S. Phelps, 1968. "Money-Wage Dynamics and Labor-Market Equilibrium," Journal of Political Economy, University of Chicago Press, vol. 76, pages 678.
  13. Ireland, Peter N., 1997. "Sustainable monetary policies," Journal of Economic Dynamics and Control, Elsevier, vol. 22(1), pages 87-108, November.
  14. Laurence Ball & N. Gregory Mankiw, 1994. "A sticky-price manifesto," Proceedings, Federal Reserve Bank of Dallas, issue Apr.
  15. Marianne Baxter & Robert G. King, 1995. "Measuring Business Cycles Approximate Band-Pass Filters for Economic Time Series," NBER Working Papers 5022, National Bureau of Economic Research, Inc.
  16. Cooley, Thomas F. & Ohanian, Lee E., 1991. "The cyclical behavior of prices," Journal of Monetary Economics, Elsevier, vol. 28(1), pages 25-60, August.
  17. James H. Stock & Mark W. Watson, 1998. "Business Cycle Fluctuations in U.S. Macroeconomic Time Series," NBER Working Papers 6528, National Bureau of Economic Research, Inc.
  18. 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.
  19. Lawrence J. Cristiano & 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.
  20. 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.
  21. Lucas, Robert E, Jr, 1980. "Two Illustrations of the Quantity Theory of Money," American Economic Review, American Economic Association, vol. 70(5), pages 1005-14, December.
  22. 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 473-91, June.
  23. 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.
  24. 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.
  25. William Poole, 1999. "Monetary policy rules?," Speech 81, Federal Reserve Bank of St. Louis.
  26. Andreas Hornstein, 1998. "Inventory investment and the business cycle," Economic Quarterly, Federal Reserve Bank of Richmond, issue Spr, pages 49-71.
  27. Whiteman, Charles H, 1984. "Lucas on the Quantity Theory: Hypothesis Testing without Theory," American Economic Review, American Economic Association, vol. 74(4), pages 742-49, September.
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