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

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  • André Kurmann

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 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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Keywords: Maximum Likelihood; Rational Expectations; New Keynesian Phillips Curve; Inflation; Real Marginal Cost;

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References

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  1. Richard Clarida & Jordi Galí & Mark Gertler, 1997. "The science of monetary policy: A new Keynesian perspective," Economics Working Papers 356, Department of Economics and Business, Universitat Pompeu Fabra, revised Apr 1999.
  2. Argia M. Sbordone, 2005. "Do expected future marginal costs drive inflation dynamics?," Staff Reports 204, Federal Reserve Bank of New York.
  3. Peter Tinsley & Sharon Kozicki, 2003. "Alternative Sources of the Lag Dynamics of Inflation," Computing in Economics and Finance 2003 92, Society for Computational Economics.
  4. Mark Bils & Peter J. Klenow, 2002. "Some Evidence on the Importance of Sticky Prices," NBER Working Papers 9069, National Bureau of Economic Research, Inc.
  5. Jeff Fuhrer & George Moore, 1993. "Inflation persistence," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 93-17, Board of Governors of the Federal Reserve System (U.S.).
  6. John M. Roberts, 2001. "How well does the New Keynesian sticky-price model fit the data?," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 2001-13, Board of Governors of the Federal Reserve System (U.S.).
  7. Lars Peter Hansen & Thomas J. Sargent, 1979. "Formulating and estimating dynamic linear rational expectations models," Working Papers 127, Federal Reserve Bank of Minneapolis.
  8. Eric JONDEAU & Herve LE BIHAN, 2003. "ML vs GMM Estimates of Hybrid Macroeconomic Models (With an Application to the "New Phillips Curve")," Econometrics, EconWPA 0303006, EconWPA.
  9. Frank Smets & Raf Wouters, 2002. "An estimated dynamic stochastic general equilibrium model of the euro area," Working Paper Research, National Bank of Belgium 35, National Bank of Belgium.
  10. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, Elsevier, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448 Elsevier.
  11. 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.
  12. 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.
  13. James M. Nason & Gregor W. Smith, 2005. "Identifying the New Keynesian Phillips curve," Working Paper, Federal Reserve Bank of Atlanta 2005-01, Federal Reserve Bank of Atlanta.
  14. 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.
  15. Calvo, Guillermo A., 1983. "Staggered prices in a utility-maximizing framework," Journal of Monetary Economics, Elsevier, Elsevier, vol. 12(3), pages 383-398, September.
  16. Jeffrey C. Fuhrer & Glenn D. Rudebusch, 2002. "Estimating the Euler equation for output," Working Papers, Federal Reserve Bank of Boston 02-3, Federal Reserve Bank of Boston.
  17. Ma, Adrian, 2002. "GMM estimation of the new Phillips curve," Economics Letters, Elsevier, vol. 76(3), pages 411-417, August.
  18. 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.
  19. John M. Roberts, 1994. "Is inflation sticky?," Working Paper Series / Economic Activity Section 152, Board of Governors of the Federal Reserve System (U.S.).
  20. Martin Eichenbaum & Jonas D.M. Fisher, 2003. "Evaluating the Calvo model of sticky prices," Working Paper Series, Federal Reserve Bank of Chicago WP-03-23, Federal Reserve Bank of Chicago.
  21. Alexander L. Wolman, 2000. "The frequency and costs of individual price adjustments," Economic Quarterly, Federal Reserve Bank of Richmond, Federal Reserve Bank of Richmond, issue Fall, pages 1-22.
  22. Eric Jondeau & Hervé Le Bihan, 2001. "Testing for a Forward-Looking Phillips Curve. Additional Evidence from European and US data," Macroeconomics, EconWPA 0111005, EconWPA.
  23. Thomas J. Sargent, 1978. "A note on maximum likelihood estimation of the rational expectations model of the term structure," Staff Report, Federal Reserve Bank of Minneapolis 26, Federal Reserve Bank of Minneapolis.
  24. Jordi Galí & Mark Gertler, 1998. "Inflation dynamics: A structural econometric analysis," Economics Working Papers 341, Department of Economics and Business, Universitat Pompeu Fabra.
  25. Lubik, Thomas A. & Schorfheide, Frank, 2003. "Computing sunspot equilibria in linear rational expectations models," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 28(2), pages 273-285, November.
  26. 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, American Statistical Association, vol. 20(4), pages 518-29, October.
  27. Bils, Mark, 1987. "The Cyclical Behavior of Marginal Cost and Price," American Economic Review, American Economic Association, vol. 77(5), pages 838-55, December.
  28. 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, Board of Governors of the Federal Reserve System (U.S.) 93-11, Board of Governors of the Federal Reserve System (U.S.).
  29. Robrt G. King & André Kurmann, 2002. "Expectations and the term structure of interest rates : evidence and implications," Economic Quarterly, Federal Reserve Bank of Richmond, Federal Reserve Bank of Richmond, issue Fall, pages 49-95.
  30. 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.
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Citations

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Cited by:
  1. Eric JONDEAU & Hervé LE BIHAN, 2003. "ML vs GMM Estimates of Hybrid Macroeconomic Models (With an Application to the "New Phillips Curve")," Econometrics, EconWPA 0303004, EconWPA.
  2. 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.
  3. 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.
  4. Linde, Jesper, 2005. "Estimating New-Keynesian Phillips curves: A full information maximum likelihood approach," Journal of Monetary Economics, Elsevier, Elsevier, vol. 52(6), pages 1135-1149, September.
  5. Bakhshi, Hasan & Khan, Hashmat & Rudolf, Barbara, 2007. "The Phillips curve under state-dependent pricing," Journal of Monetary Economics, Elsevier, Elsevier, vol. 54(8), pages 2321-2345, November.
  6. André Kurmann, 2003. "Quantifying the Uncertainty about the Fit of a New Keynesian Pricing Model: Extended Version," Cahiers de recherche, CIRPEE 0344, CIRPEE.
  7. Kevin D. Sheedy, 2007. "Intrinsic Inflation Persistence," CEP Discussion Papers dp0837, Centre for Economic Performance, LSE.
  8. Fanelli, Luca, 2007. "Evaluating the New Keynesian Phillips Curve under VAR-based learning," MPRA Paper 1616, University Library of Munich, Germany.
  9. Rudolf, B. & Bakhshi, H., 2005. "The Phillips Curve Under State-Dependent Pricing," Computing in Economics and Finance 2005, Society for Computational Economics 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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