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

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  • André Kurmann

    (Université du Québec à Montréal, CIRPÉE)

Abstract

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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Bibliographic Info

Paper provided by EconWPA in its series Macroeconomics with number 0409028.

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Length: 37 pages
Date of creation: 29 Sep 2004
Date of revision:
Handle: RePEc:wpa:wuwpma:0409028

Note: Type of Document - pdf; pages: 37
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Web page: http://128.118.178.162

Related research

Keywords: Maximum Likelihood; Rational Expectations; New Keynesian Phillips Curve; Inflation; Real marginal cost.;

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References

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  1. 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.
  2. 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.
  3. Martin Eichenbaum & Jonas D.M. Fisher, 2003. "Evaluating the Calvo model of sticky prices," Working Paper Series WP-03-23, Federal Reserve Bank of Chicago.
  4. 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.
  5. Jordi Gali & Mark Gertler, 2000. "Inflation Dynamics: A Structural Econometric Analysis," NBER Working Papers 7551, National Bureau of Economic Research, Inc.
  6. 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.
  7. 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.
  8. Argia M. Sbordone, 2005. "Do expected future marginal costs drive inflation dynamics?," Staff Reports 204, Federal Reserve Bank of New York.
  9. Roberts, John M., 1997. "Is inflation sticky?," Journal of Monetary Economics, Elsevier, vol. 39(2), pages 173-196, July.
  10. Ma, Adrian, 2002. "GMM estimation of the new Phillips curve," Economics Letters, Elsevier, vol. 76(3), pages 411-417, August.
  11. Sharon Kozicki & P.A. Tinsley, 2002. "Alternative sources of the lag dynamics of inflation," Research Working Paper RWP 02-12, Federal Reserve Bank of Kansas City.
  12. Jeff Fuhrer & George Moore, 1993. "Inflation persistence," Proceedings, Board of Governors of the Federal Reserve System (U.S.).
  13. 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.
  14. 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.
  15. Eric JONDEAU & Hervé LE BIHAN, 2003. "ML vs GMM Estimates of Hybrid Macroeconomic Models (With an Application to the "New Phillips Curve")," Econometrics 0303004, EconWPA.
  16. Eric Jondeau & Hervé Le Bihan, 2001. "Testing for a Forward-Looking Phillips Curve. Additional Evidence from European and US data," Macroeconomics 0111005, EconWPA.
  17. Alexander L. Wolman, 2000. "The frequency and costs of individual price adjustments," Economic Quarterly, Federal Reserve Bank of Richmond, issue Fall, pages 1-22.
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  19. 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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  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. Jeffrey C. Fuhrer & Glenn D. Rudebusch, 2002. "Estimating the Euler equation for output," Working Papers 02-3, Federal Reserve Bank of Boston.
  24. 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.
  25. 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.
  26. 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.
  27. 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.
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  29. 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.
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Citations

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Cited by:
  1. Jordi Galí & Mark Gertler & David López-Salido, 2005. "Robustness of the Estimates of the Hybrid New Keynesian Phillips Curve," Banco de Espa�a Working Papers 0520, Banco de Espa�a.
  2. Luca Fanelli, 2008. "Testing the New Keynesian Phillips Curve Through Vector Autoregressive Models: Results from the Euro Area," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(1), pages 53-66, 02.
  3. Linde, Jesper, 2005. "Estimating New-Keynesian Phillips curves: A full information maximum likelihood approach," Journal of Monetary Economics, Elsevier, vol. 52(6), pages 1135-1149, September.
  4. Kevin D. Sheedy, 2007. "Intrinsic Inflation Persistence," CEP Discussion Papers dp0837, Centre for Economic Performance, LSE.
  5. Eric JONDEAU & Herve LE BIHAN, 2003. "ML vs GMM Estimates of Hybrid Macroeconomic Models (With an Application to the "New Phillips Curve")," Econometrics 0303006, EconWPA.
  6. Bakhshi Hasan & Hashmat Khan & Barbara Rudolf, 2005. "The Phillips curve under state-dependent pricing," Working Papers 2005-01, Swiss National Bank.
  7. Fanelli, Luca, 2007. "Evaluating the New Keynesian Phillips Curve under VAR-based learning," MPRA Paper 1616, University Library of Munich, Germany.
  8. André Kurmann, 2003. "Quantifying the Uncertainty about the Fit of a New Keynesian Pricing Model: Extended Version," Cahiers de recherche 0344, CIRPEE.
  9. Rudolf, B. & Bakhshi, H., 2005. "The Phillips Curve Under State-Dependent Pricing," Computing in Economics and Finance 2005 68, Society for Computational Economics.
  10. Fanelli, Luca, 2008. "Evaluating New Keynesian Phillips Curve under VAR-Based Learning," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 2(33), pages 1-24.

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