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Maximum Likelihood Estimation of Dynamic Stochastic Theories with an Application to New Keynesian Pricing

  • André Kurmann

This paper proposes a novel Maximum Likelihood (ML) strategy to estimate Euler equations implied by dynamic stochastic theories. The strategy exploits rational expectations cross-equation restrictions, but circumvents the problem of multiple solutions that arises in Sargent's (1979) original work by imposing the restrictions on the forcing variable rather than the endogenous variable of the Euler equation. The paper then contrasts the proposed strategy to an alternative, widely employed method that avoids the multiplicity problem by constraining the ML estimates to yield a unique stable solution. I argue that imposing such a uniqueness condition makes little economic sense and can lead to severe misspecification. To illustrate this point, I estimate Gali and Gertler's (1999) hybrid New Keynesian Phillips Curve using labor income share as the measure of real marginal cost. My ML estimates indicate that forward-looking behavior is predominant and that the model provides a good approximation of U.S. inflation dynamics. By contrast, if the same estimates are constrained to yield a unique stable solution, forward-looking behavior becomes much less important and the model as a whole is rejected.

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Paper provided by CIRPEE in its series Cahiers de recherche with number 0421.

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Date of creation: 2004
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Handle: RePEc:lvl:lacicr:0421
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  1. Mark Bils & Peter J. Klenow, 2004. "Some Evidence on the Importance of Sticky Prices," Journal of Political Economy, University of Chicago Press, vol. 112(5), pages 947-985, October.
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  3. King, Robert G & Watson, Mark W, 1998. "The Solution of Singular Linear Difference Systems under Rational Expectations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1015-26, November.
  4. Bils, Mark, 1987. "The Cyclical Behavior of Marginal Cost and Price," American Economic Review, American Economic Association, vol. 77(5), pages 838-55, December.
  5. Mark Gertler & Jordi Gali & Richard Clarida, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.
  6. Sargent, Thomas J., 1979. "A note on maximum likelihood estimation of the rational expectations model of the term structure," Journal of Monetary Economics, Elsevier, vol. 5(1), pages 133-143, January.
  7. Frank Smets & Raf Wouters, 2003. "An Estimated Dynamic Stochastic General Equilibrium Model of the Euro Area," Journal of the European Economic Association, MIT Press, vol. 1(5), pages 1123-1175, 09.
  8. Jondeau, E. & Le Bihan, H., 2003. "ML vs GMM Estimates of Hybrid Macroeconomic Models (With an Application to the New Phillips Curve)," Working papers 103, Banque de France.
  9. Sbordone, Argia M., 2005. "Do expected future marginal costs drive inflation dynamics?," Journal of Monetary Economics, Elsevier, vol. 52(6), pages 1183-1197, September.
  10. Jeffrey C. Fuhrer & Glenn D. Rudebusch, 2002. "Estimating the Euler equation for output," Working Papers 02-3, Federal Reserve Bank of Boston.
  11. John M. Roberts, 1994. "Is inflation sticky?," Working Paper Series / Economic Activity Section 152, Board of Governors of the Federal Reserve System (U.S.).
  12. Jordi Galí & Mark Gertler, 1998. "Inflation dynamics: A structural econometric analysis," Economics Working Papers 341, Department of Economics and Business, Universitat Pompeu Fabra.
  13. James M. Nason & Gregor W. Smith, 2008. "Identifying the new Keynesian Phillips curve," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(5), pages 525-551.
  14. Alexander L. Wolman, 2000. "The frequency and costs of individual price adjustments," Economic Quarterly, Federal Reserve Bank of Richmond, issue Fall, pages 1-22.
  15. Eric Jondeau & Hervé Le Bihan, 2001. "Testing for a Forward-Looking Phillips Curve. Additional Evidence from European and US data," Macroeconomics 0111005, EconWPA.
  16. Robrt G. King & André Kurmann, 2002. "Expectations and the term structure of interest rates : evidence and implications," Economic Quarterly, Federal Reserve Bank of Richmond, issue Fall, pages 49-95.
  17. Lubik, Thomas A. & Schorfheide, Frank, 2003. "Computing sunspot equilibria in linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, vol. 28(2), pages 273-285, November.
  18. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448 Elsevier.
  19. Ma, Adrian, 2002. "GMM estimation of the new Phillips curve," Economics Letters, Elsevier, vol. 76(3), pages 411-417, August.
  20. John M. Roberts, 2001. "How well does the New Keynesian sticky-price model fit the data?," Finance and Economics Discussion Series 2001-13, Board of Governors of the Federal Reserve System (U.S.).
  21. Peter N. Ireland, 1999. "Sticky-Price Models of the Business Cycle: Specification and Stability," Boston College Working Papers in Economics 426, Boston College Department of Economics.
  22. Julio Rotemberg & Michael Woodford, 1997. "An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy," NBER Chapters, in: NBER Macroeconomics Annual 1997, Volume 12, pages 297-361 National Bureau of Economic Research, Inc.
  23. James H. Stock & Motohiro Yogo, 2002. "Testing for Weak Instruments in Linear IV Regression," NBER Technical Working Papers 0284, National Bureau of Economic Research, Inc.
  24. Peter Tinsley & Sharon Kozicki, 2003. "Alternative Sources of the Lag Dynamics of Inflation," Computing in Economics and Finance 2003 92, Society for Computational Economics.
  25. Lars Peter Hansen & Thomas J. Sargent, 1979. "Formulating and estimating dynamic linear rational expectations models," Working Papers 127, Federal Reserve Bank of Minneapolis.
  26. 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.
  27. Martin Eichenbaum & Jonas D.M. Fisher, 2004. "Evaluating the Calvo Model of Sticky Prices," NBER Working Papers 10617, National Bureau of Economic Research, Inc.
  28. Goffe William L., 1996. "SIMANN: A Global Optimization Algorithm using Simulated Annealing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 1(3), pages 1-9, October.
  29. Stock, James H & Wright, Jonathan H & Yogo, Motohiro, 2002. "A Survey of Weak Instruments and Weak Identification in Generalized Method of Moments," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(4), pages 518-29, October.
  30. Calvo, Guillermo A., 1983. "Staggered prices in a utility-maximizing framework," Journal of Monetary Economics, Elsevier, vol. 12(3), pages 383-398, September.
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