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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

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. Exploiting these observations, the authors devise diagnostic methods that are useful for interpreting maximum-likelihood parameter estimates and likelihood ratio tests. They apply the methods to estimating and testing two real business-cycle models and reject the standard model in favor of an alternative in which capital investment requires a planning period.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Cleveland in its series Working Paper with number 9901.

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Date of creation: 1999
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Handle: RePEc:fip:fedcwp:9901

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Keywords: Business cycles ; Econometric models;

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  1. 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.
  2. Lawrence J. Christiano & Martin Eichenbaum, 1987. "Temporal aggregation and structural inference in macroeconomics," Working Papers 306, Federal Reserve Bank of Minneapolis.
  3. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November.
  4. Lars Peter Hansen & Thomas J. Sargent, 1979. "Formulating and estimating dynamic linear rational expectations models," Working Papers 127, Federal Reserve Bank of Minneapolis.
  5. 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.
  6. Robert G. King, 1995. "Quantitative theory and econometrics," Economic Quarterly, Federal Reserve Bank of Richmond, issue Sum, pages 53-105.
  7. 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.
  8. 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.
  9. Diebold, Francis X & Ohanian, Lee E & Berkowitz, Jeremy, 1998. "Dynamic Equilibrium Economies: A Framework for Comparing Models and Data," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 433-51, July.
  10. 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.
  11. McGrattan, Ellen R., 1994. "The macroeconomic effects of distortionary taxation," Journal of Monetary Economics, Elsevier, vol. 33(3), pages 573-601, June.
  12. Lawrence J. Christiano & Martin Eichenbaum & David Marshall, 1990. "The permanent income hypothesis revisited," Staff Report 129, Federal Reserve Bank of Minneapolis.
  13. 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.
  14. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737, April.
  15. Christiano, Lawrence J., 1988. "Why does inventory investment fluctuate so much?," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 247-280.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. 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.
  21. 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.
  22. 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.
  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.
  24. Rouwenhorst, K. Geert, 1991. "Time to build and aggregate fluctuations : A reconsideration," Journal of Monetary Economics, Elsevier, vol. 27(2), pages 241-254, April.
  25. Sumru Altug, 1986. "Time to build and aggregate fluctuations: some new evidence," Working Papers 277, Federal Reserve Bank of Minneapolis.
  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 E. O. Svensson & Michael Woodford, 2003. "Implementing Optimal Policy through Inflation-Forecast Targeting," NBER Working Papers 9747, National Bureau of Economic Research, Inc.
  2. 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.
  3. Michael Reiter & Ulrich Woitek, 1999. "Are these classical business cycles?," Economics Working Papers 398, Department of Economics and Business, Universitat Pompeu Fabra.
  4. 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.
  5. Patrick Francois & Huw Lloyd-Ellis, 2004. "Investment Cycles," Macroeconomics 0405005, EconWPA, revised 05 May 2004.

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