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Maximum Likelihood in the Frequency Domain: a Time to Build Example

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Author Info

  • Christiano, L.J.
  • Vigfusson, R.J.

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 parameter estimates and 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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Bibliographic Info

Paper provided by London School of Economics - Centre for Labour Economics in its series Papers with number 9901.

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Length: 15 pages
Date of creation: 1999
Date of revision:
Handle: RePEc:fth:lseple:9901

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Postal: LONDON SCHOOL OF ECONOMICS AND POLITICAL SCIENCE, CENTER FOR LABOUR ECONOMICS, HOUGHTON STREET LONDON WC2A 2AE ENGLAND.
Phone: +44 (020) 7405 7686
Web page: http://www.lse.ac.uk/
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Keywords: ECONOMIC MODELS ; TESTS;

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References

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  1. Francis X. Diebold & Lee E. Ohanian & Jeremy Berkowitz, 1997. "Dynamic equilibrium economies: a framework for comparing models and data," Finance and Economics Discussion Series 1997-23, Board of Governors of the Federal Reserve System (U.S.).
  2. 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.
  3. 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.
  4. 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.
  5. Mark W. Watson, 1991. "Measures of fit for calibrated models," Working Paper Series, Macroeconomic Issues 91-9, Federal Reserve Bank of Chicago.
  6. Christiano, Lawrence J, 2002. "Solving Dynamic Equilibrium Models by a Method of Undetermined Coefficients," Computational Economics, Society for Computational Economics, vol. 20(1-2), pages 21-55, October.
  7. 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.
  8. Ellen McGrattan & Richard Rogerson & Randall Wright, 1995. "An equilibrium model of the business cycle with household production and fiscal policy," Staff Report 191, Federal Reserve Bank of Minneapolis.
  9. Robert G. King, 1995. "Quantitative theory and econometrics," Economic Quarterly, Federal Reserve Bank of Richmond, issue Sum, pages 53-105.
  10. Lawrence J. Christiano & Martin Eichenbaum & David Marshall, 1987. "The Permanent Income Hypothesis Revisited," NBER Working Papers 2209, National Bureau of Economic Research, Inc.
  11. 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.
  12. 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.
  13. 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.
  14. Harvey,Andrew C., 1990. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521321969.
  15. Sumru Altug, 1986. "Time to build and aggregate fluctuations: some new evidence," Working Papers 277, Federal Reserve Bank of Minneapolis.
  16. 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.
  17. 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.
  18. Rouwenhorst, K. Geert, 1991. "Time to build and aggregate fluctuations : A reconsideration," Journal of Monetary Economics, Elsevier, vol. 27(2), pages 241-254, April.
  19. Fuhrer, Jeffrey C. & Moore, George R. & Schuh, Scott D., 1995. "Estimating the linear-quadratic inventory model Maximum likelihood versus generalized method of moments," Journal of Monetary Economics, Elsevier, vol. 35(1), pages 115-157, February.
  20. McGrattan, Ellen R., 1994. "The macroeconomic effects of distortionary taxation," Journal of Monetary Economics, Elsevier, vol. 33(3), pages 573-601, June.
  21. 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.
  22. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November.
  23. Christiano, Lawrence J., 1988. "Why does inventory investment fluctuate so much?," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 247-280.
  24. 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.
  25. 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.
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Citations

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Cited by:
  1. Lars E.O. Svensson & Michael Woodford, 2004. "Implementing Optimal Policy through Inflation-Forecast Targeting," NBER Chapters, in: The Inflation-Targeting Debate, pages 19-92 National Bureau of Economic Research, Inc.
  2. Michael Reiter & Ulrich Woitek, 1999. "Are these classical business cycles?," Economics Working Papers 398, Department of Economics and Business, Universitat Pompeu Fabra.
  3. Lars Jonung, 2005. "Proceedings of the 2004 first annual DG ECFIN research conference on “Business Cycles and Growth in Europeâ€," European Economy - Economic Papers 227, Directorate General Economic and Monetary Affairs (DG ECFIN), European Commission.
  4. Patrick Francois & Huw Lloyd-Ellis, 2004. "Investment Cycles," Macroeconomics 0405005, EconWPA, revised 05 May 2004.
  5. Lawrence J. Christiano & Michele Boldrin & Jonas D. M. Fisher, 2001. "Habit Persistence, Asset Returns, and the Business Cycle," American Economic Review, American Economic Association, vol. 91(1), pages 149-166, March.

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