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

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  • Lawrence J. Christiano
  • Robert J. Vigfusson

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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References

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  1. 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.
  2. Mark W. Watson, 1991. "Measures of Fit for Calibrated Models," NBER Technical Working Papers 0102, National Bureau of Economic Research, Inc.
  3. Christiano, Lawrence J. & Eichenbaum, Martin, 1987. "Temporal aggregation and structural inference in macroeconomics," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 26(1), pages 63-130, January.
  4. Harvey,Andrew C., 1990. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521321969, October.
  5. Lawrence J. Christiano & Martin Eichenbaum, 1990. "Current real business cycle theories and aggregate labor market fluctuations," Discussion Paper / Institute for Empirical Macroeconomics 24, Federal Reserve Bank of Minneapolis.
  6. 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.
  7. Christiano, Lawrence J., 1985. "A method for estimating the timing interval in a linear econometric model, with an application to Taylor's model of staggered contracts," Journal of Economic Dynamics and Control, Elsevier, vol. 9(4), pages 363-404, December.
  8. 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.
  9. 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.
  10. McGrattan, Ellen R., 1994. "The macroeconomic effects of distortionary taxation," Journal of Monetary Economics, Elsevier, vol. 33(3), pages 573-601, June.
  11. 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.
  12. George J. Hall, 1994. "Overtime, effort and the propagation of business cycle shocks," Working Paper Series, Macroeconomic Issues 94-25, Federal Reserve Bank of Chicago.
  13. Sumru Altug, 1986. "Time to build and aggregate fluctuations: some new evidence," Working Papers 277, Federal Reserve Bank of Minneapolis.
  14. 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.
  15. Christiano, Lawrence J & Eichenbaum, Martin & Marshall, David, 1991. "The Permanent Income Hypothesis Revisited," Econometrica, Econometric Society, vol. 59(2), pages 397-423, March.
  16. Christiano, Lawrence J., 1988. "Why does inventory investment fluctuate so much?," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 247-280.
  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. 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.
  19. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November.
  20. Timothy Cogley & James M. Nason, 1993. "Output dynamics in real business cycle models," Working Papers in Applied Economic Theory 93-10, Federal Reserve Bank of San Francisco.
  21. Rouwenhorst, K. Geert, 1991. "Time to build and aggregate fluctuations : A reconsideration," Journal of Monetary Economics, Elsevier, vol. 27(2), pages 241-254, April.
  22. Robert G. King, 1995. "Quantitative theory and econometrics," Economic Quarterly, Federal Reserve Bank of Richmond, issue Sum, pages 53-105.
  23. Jeffrey Fuhrer & George Moore & Scott Schuh, 1993. "Estimating the linear-quadratic inventory model: maximum likelihood versus generalized method of moments," Finance and Economics Discussion Series 93-11, Board of Governors of the Federal Reserve System (U.S.).
  24. 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.
  25. 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.
  26. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-52, July.
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Cited by:
  1. 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.
  2. Svensson, Lars E O & Woodford, Michael, 2004. "Implementing Optimal Policy Through Inflation-Forecast Targeting," CEPR Discussion Papers 4229, C.E.P.R. Discussion Papers.
  3. Patrick Francois & Huw Lloyd-Ellis, 2004. "Investment Cycles," Macroeconomics 0405005, EconWPA, revised 05 May 2004.
  4. 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.
  5. Michael Reiter & Ulrich Woitek, 1999. "Are There Classical Business Cycles?," Working Papers 1999_05, Business School - Economics, University of Glasgow.

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