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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. 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.
  2. 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.
  3. 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.
  4. Jordi Gali & Mark Gertler, 2000. "Inflation Dynamics: A Structural Econometric Analysis," NBER Working Papers 7551, National Bureau of Economic Research, Inc.
  5. James M. Nason & Gregor W. Smith, 2005. "Identifying the New Keynesian Phillips Curve," Working Papers 1026, Queen's University, Department of Economics.
  6. Jeffrey C. Fuhrer & Glenn D. Rudebusch, 2002. "Estimating the Euler equation for output," Working Papers 02-3, Federal Reserve Bank of Boston.
  7. Jeff Fuhrer & George Moore, 1993. "Inflation persistence," Proceedings, Federal Reserve Bank of San Francisco, issue Mar.
  8. 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.
  9. 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.
  10. Eric Jondeau & Hervé Le Bihan, 2001. "Testing for a Forward-Looking Phillips Curve. Additional Evidence from European and US data," Macroeconomics 0111005, EconWPA.
  11. Sbordone, Argia M., 2005. "Do expected future marginal costs drive inflation dynamics?," Journal of Monetary Economics, Elsevier, vol. 52(6), pages 1183-1197, September.
  12. 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.).
  13. 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.
  14. Ireland, Peter N., 2001. "Sticky-price models of the business cycle: Specification and stability," Journal of Monetary Economics, Elsevier, vol. 47(1), pages 3-18, February.
  15. 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.
  16. Roberts, John M., 1997. "Is inflation sticky?," Journal of Monetary Economics, Elsevier, vol. 39(2), pages 173-196, July.
  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. Alexander L. Wolman, 2000. "The frequency and costs of individual price adjustments," Economic Quarterly, Federal Reserve Bank of Richmond, issue Fall, pages 1-22.
  19. Martin Eichenbaum & Jonas D.M. Fisher, 2004. "Evaluating the Calvo Model of Sticky Prices," NBER Working Papers 10617, National Bureau of Economic Research, Inc.
  20. Bils, Mark, 1987. "The Cyclical Behavior of Marginal Cost and Price," American Economic Review, American Economic Association, vol. 77(5), pages 838-55, December.
  21. 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.).
  22. 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.
  23. Richard Clarida & Jordi Gali & Mark Gertler, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," NBER Working Papers 7147, National Bureau of Economic Research, Inc.
  24. 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.
  25. 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.
  26. Calvo, Guillermo A., 1983. "Staggered prices in a utility-maximizing framework," Journal of Monetary Economics, Elsevier, vol. 12(3), pages 383-398, September.
  27. 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.
  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. 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.
  30. Ma, Adrian, 2002. "GMM estimation of the new Phillips curve," Economics Letters, Elsevier, vol. 76(3), pages 411-417, August.
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Citations

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Cited by:
  1. Bakhshi, Hasan & Khan, Hashmat & Rudolf, Barbara, 2007. "The Phillips curve under state-dependent pricing," Journal of Monetary Economics, Elsevier, vol. 54(8), pages 2321-2345, November.
  2. Fanelli, Luca, 2008. "Evaluating the New Keynesian Phillips Curve under VAR-Based Learning," Economics Discussion Papers 2008-15, Kiel Institute for the World Economy.
  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. 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.
  5. 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.
  6. Rudolf, B. & Bakhshi, H., 2005. "The Phillips Curve Under State-Dependent Pricing," Computing in Economics and Finance 2005 68, Society for Computational Economics.
  7. André Kurmann, 2003. "Quantifying the Uncertainty about the Fit of a New Keynesian Pricing Model: Extended Version," Cahiers de recherche 0344, CIRPEE.
  8. Kevin D. Sheedy, 2007. "Intrinsic inflation persistence," LSE Research Online Documents on Economics 3739, London School of Economics and Political Science, LSE Library.
  9. Lindé, Jesper, 2001. "Estimating New-Keynesian Phillips Curves: A Full Information Maximum Likelihood Approach," Working Paper Series 129, Sveriges Riksbank (Central Bank of Sweden), revised 30 Apr 2001.
  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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