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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. Ma, Adrian, 2002. "GMM estimation of the new Phillips curve," Economics Letters, Elsevier, vol. 76(3), pages 411-417, August.
  2. 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.
  3. Roberts, John M., 1997. "Is inflation sticky?," Journal of Monetary Economics, Elsevier, vol. 39(2), pages 173-196, July.
  4. Clarida, R. & Gali, J. & Gertler, M., 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Working Papers 99-13, C.V. Starr Center for Applied Economics, New York University.
  5. Jeff Fuhrer & George Moore, 1993. "Inflation persistence," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
  6. 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.
  7. Jondeau, E. & Le Bihan, H., 2001. "Testing for a Forward-Looking Phillips Curve. Additional Evidence from European and US Data," Working papers 86, Banque de France.
  8. Bils, Mark, 1987. "The Cyclical Behavior of Marginal Cost and Price," American Economic Review, American Economic Association, vol. 77(5), pages 838-55, December.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. Gali, Jordi & Gertler, Mark, 1999. "Inflation dynamics: A structural econometric analysis," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 195-222, October.
  14. James M. Nason & Gregor W. Smith, 2005. "Identifying the New Keynesian Phillips curve," Working Paper 2005-01, Federal Reserve Bank of Atlanta.
  15. Eric JONDEAU & Herve LE BIHAN, 2004. "ML vs GMM Estimates of Hybrid Macroeconomic Models (With an Application to the "New Phillips Curve")," Econometric Society 2004 North American Summer Meetings 270, Econometric Society.
  16. 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.
  17. Jeffrey C. Fuhrer & Glenn D. Rudebusch, 2002. "Estimating the Euler equation for output," Working Papers 02-3, Federal Reserve Bank of Boston.
  18. Alexander L. Wolman, 2007. "The frequency and costs of individual price adjustment," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 28(6), pages 531-552.
  19. 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.
  20. 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 93-11, Board of Governors of the Federal Reserve System (U.S.).
  21. Roberts John M., 2005. "How Well Does the New Keynesian Sticky-Price Model Fit the Data?," The B.E. Journal of Macroeconomics, De Gruyter, vol. 5(1), pages 1-39, September.
  22. 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.
  23. 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.
  24. Argia M. Sbordone, 2005. "Do expected future marginal costs drive inflation dynamics?," Staff Reports 204, Federal Reserve Bank of New York.
  25. 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.
  26. Martin Eichenbaum & Jonas D.M. Fisher, 2004. "Evaluating the Calvo Model of Sticky Prices," NBER Working Papers 10617, National Bureau of Economic Research, Inc.
  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.
  28. 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.
  29. 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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Citations

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Cited by:
  1. Hasan Bakhshi & Hashmat Khan & Barbara Rudolf, 2004. "The Phillips curve under state-dependent pricing," Bank of England working papers 227, Bank of England.
  2. Jordi Galí & Mark Gertler & J. David López-Salido, 2001. "Robustness of the Estimates of the Hybrid New Keynesian Phillips Curve," Working Papers 44, Barcelona Graduate School of Economics.
  3. Luca Fanelli, 2006. "Testing the New Keynesian Phillips Curve through Vector Autoregressive models : Results from the Euro area," Quaderni di Dipartimento 0, Department of Statistics, University of Bologna.
  4. Sheedy, Kevin D., 2010. "Intrinsic inflation persistence," Journal of Monetary Economics, Elsevier, vol. 57(8), pages 1049-1061, November.
  5. 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.
  6. Eric JONDEAU & Herve LE BIHAN, 2004. "ML vs GMM Estimates of Hybrid Macroeconomic Models (With an Application to the "New Phillips Curve")," Econometric Society 2004 North American Summer Meetings 270, Econometric Society.
  7. André Kurmann, 2003. "Quantifying the Uncertainty about the Fit of a New Keynesian Pricing Model: Extended Version," Cahiers de recherche 0344, CIRPEE.
  8. Fanelli, Luca, 2007. "Evaluating the New Keynesian Phillips Curve under VAR-based learning," MPRA Paper 1616, University Library of Munich, Germany.
  9. 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.
  10. Rudolf, B. & Bakhshi, H., 2005. "The Phillips Curve Under State-Dependent Pricing," Computing in Economics and Finance 2005 68, Society for Computational Economics.

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