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

  • Lawrence J. Christiano
  • Robert J. Vigfusson

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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  1. 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.
  2. Robert G. King, 1995. "Quantitative theory and econometrics," Economic Quarterly, Federal Reserve Bank of Richmond, issue Sum, pages 53-105.
  3. 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.
  4. Altug, Sumru, 1989. "Time-to-Build and Aggregate Fluctuations: Some New Evidence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 30(4), pages 889-920, November.
  5. Christiano, Lawrence J, 2002. "Solving Dynamic Equilibrium Models by a Method of Undetermined Coefficients," Computational Economics, Springer;Society for Computational Economics, vol. 20(1-2), pages 21-55, October.
  6. 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.
  7. Rouwenhorst, K. Geert, 1991. "Time to build and aggregate fluctuations : A reconsideration," Journal of Monetary Economics, Elsevier, vol. 27(2), pages 241-254, April.
  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. 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. Christiano, Lawrence J., 1988. "Why does inventory investment fluctuate so much?," Journal of Monetary Economics, Elsevier, vol. 21(2-3), pages 247-280.
  11. Lawrence J. Christiano & Martin Eichenbaum, 1987. "Temporal aggregation and structural inference in macroeconomics," Working Papers 306, Federal Reserve Bank of Minneapolis.
  12. 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.
  13. Darrell Duffie & Kenneth J. Singleton, 1990. "Simulated Moments Estimation of Markov Models of Asset Prices," NBER Technical Working Papers 0087, National Bureau of Economic Research, Inc.
  14. Francis X. Diebold & Lee E. Ohanian & Jeremy Berkowitz, 1997. "Dynamic equilibrium economies: a framework for comparing models and data," Working Papers 97-7, Federal Reserve Bank of Philadelphia.
  15. 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.
  16. Ellen R. McGrattan, 1991. "The macroeconomic effects of distortionary taxation," Discussion Paper / Institute for Empirical Macroeconomics 37, Federal Reserve Bank of Minneapolis.
  17. 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.
  18. 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.
  19. Jeffrey C. Fuhrer & George R. 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.).
  20. Lawrence J. Christiano & Martin Eichenbaum & David A. Marshall, 1990. "The permanent income hypothesis revisited," Staff Report 129, Federal Reserve Bank of Minneapolis.
  21. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-70, November.
  22. 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.
  23. Ellen R. 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.
  24. 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.
  25. 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.
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