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Maximum likelihood in the frequency domain: a time to build example

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Author Info
Lawrence J. Christiano
Robert J. Vigfusson

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Abstract

A well known result is that the Gaussian log-likelihood can be expressed as the sum over different frequency components. This implies that the likelihood ratio statistic has a similar linear decomposition. We exploit these observations to devise diagnostic methods that are useful for interpreting maximum likelihood ratio tests. We apply the methods to the estimation and testing of two real business cycle models. The standard real business cycle model is rejected in favor of an alternative in which capital investment requires a planning period.

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Paper provided by Federal Reserve Bank of Chicago in its series Working Paper Series with number WP-99-4.

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Date of creation: 1999
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Handle: RePEc:fip:fedhwp:wp-99-4

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Keywords: Business cycles ; Investments;

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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.:
  1. Lawrence J. Christiano & Martin S. Eichenbaum, 1986. "Temporal Aggregation and Structural Inference in Macroeconomics," NBER Technical Working Papers 0060, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  2. Lawrence J. Christiano & Richard M. Todd, 1996. "Time to plan and aggregate fluctuations," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Win, pages 14-27. [Downloadable!]
  3. Lars Peter Hansen & Thomas J. Sargent, 1980. "Methods for estimating continuous time Rational Expectations models from discrete time data," Staff Report 59, Federal Reserve Bank of Minneapolis. [Downloadable!]
  4. Watson, Mark W, 1993. "Measures of Fit for Calibrated Models," Journal of Political Economy, University of Chicago Press, vol. 101(6), pages 1011-41, December. [Downloadable!] (restricted)
  5. 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 430-50, June. [Downloadable!] (restricted)
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  6. Robert G. King, 1995. "Quantitative theory and econometrics," Economic Quarterly, Federal Reserve Bank of Richmond, issue Sum, pages 53-105. [Downloadable!]
  7. Ireland, Peter N., 1997. "A small, structural, quarterly model for monetary policy evaluation," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 47(1), pages 83-108, December. [Downloadable!] (restricted)
  8. Lawrence J. Christiano., 1985. "A method for estimating the timing interval in a linear econometric model, with an application to Taylor's model of staggered contracts," Staff Report 101, Federal Reserve Bank of Minneapolis. [Downloadable!]
  9. Cogley, Timothy & Nason, James M, 1995. "Output Dynamics in Real-Business-Cycle Models," American Economic Review, American Economic Association, vol. 85(3), pages 492-511, June. [Downloadable!] (restricted)
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  10. Sumru Altug, 1986. "Time to build and aggregate fluctuations: some new evidence," Working Papers 277, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  11. Hall, George J., 1996. "Overtime, effort, and the propagation of business cycle shocks," Journal of Monetary Economics, Elsevier, vol. 38(1), pages 139-160, August. [Downloadable!] (restricted)
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  12. McGrattan, Ellen R & Rogerson, Richard & Wright, Randall, 1997. "An Equilibrium Model of the Business Cycle with Household Production and Fiscal Policy," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 38(2), pages 267-90, May.
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  13. Francis X. Diebold & Lee E. Ohanian & Jeremy Berkowitz, 1998. "Dynamic equilibrium economies: a framework for comparing models and data," Staff Report 243, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  14. Christiano, Lawrence J & Eichenbaum, Martin & Marshall, David, 1991. "The Permanent Income Hypothesis Revisited," Econometrica, Econometric Society, vol. 59(2), pages 397-423, March. [Downloadable!] (restricted)
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  15. Long, John B, Jr & Plosser, Charles I, 1983. "Real Business Cycles," Journal of Political Economy, University of Chicago Press, vol. 91(1), pages 39-69, February. [Downloadable!] (restricted)
  16. Lawrence J. Christiano, 1998. "Solving Dynamic Equilibrium Models by a Method of Undetermined Coefficients," NBER Technical Working Papers 0225, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  17. Rouwenhorst, K. Geert, 1991. "Time to build and aggregate fluctuations : A reconsideration," Journal of Monetary Economics, Elsevier, vol. 27(2), pages 241-254, April. [Downloadable!] (restricted)
  18. McGrattan, Ellen R., 1994. "The macroeconomic effects of distortionary taxation," Journal of Monetary Economics, Elsevier, vol. 33(3), pages 573-601, June. [Downloadable!] (restricted)
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  19. Hansen, Lars Peter & Sargent, Thomas J., 1980. "Formulating and estimating dynamic linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 7-46, May. [Downloadable!] (restricted)
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  20. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November. [Downloadable!] (restricted)
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  21. Christiano, Lawrence J., 1988. "Why does inventory investment fluctuate so much?," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 247-280. [Downloadable!] (restricted)
  22. Hansen, Lars Peter & Singleton, Kenneth J, 1982. "Generalized Instrumental Variables Estimation of Nonlinear Rational Expectations Models," Econometrica, Econometric Society, vol. 50(5), pages 1269-86, September. [Downloadable!] (restricted)
  23. Hansen, Lars Peter & Sargent, Thomas J., 1993. "Seasonality and approximation errors in rational expectations models," Journal of Econometrics, Elsevier, vol. 55(1-2), pages 21-55. [Downloadable!] (restricted)
Full references

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. Patrick Francois & Huw Lloyd-Ellis, 2004. "Investment Cycles," Macroeconomics 0405005, EconWPA, revised 05 May 2004. [Downloadable!]
  2. Lars E. O. Svensson & Michael Woodford, 2003. "Implementing Optimal Policy through Inflation-Forecast Targeting," NBER Working Papers 9747, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
    Other versions:
  3. Michele Boldrin & Lawrence J. Christiano & Jonas D. M. Fisher, 2000. "Habit persistence, asset returns and the business cycle," Staff Report 280, Federal Reserve Bank of Minneapolis. [Downloadable!]
    Other versions:
  4. Michael Reiter & Ulrich Woitek, 1999. "Are These Classical Business Cycles?," Economics Working Papers 398, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
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