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Estimating forward looking Euler equations with GMM estimators: an optimal instruments approach

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  • Jeffrey C. Fuhrer
  • Giovanni P. Olivei

Abstract

This paper compares different methods for estimating forward-looking output and inflation Euler equations and shows that weak identification can be an issue in conventional GMM estimation. The authors propose a GMM procedure that imposes the dynamic constraints implied by the forward-looking relation on the instruments set. This ?optimal instruments? procedure is more reliable than conventional GMM, and it provides a robust alternative to estimating dynamic macroeconomic relations. Empirical applications of this procedure suggest only a limited role for expectational terms.

Suggested Citation

  • Jeffrey C. Fuhrer & Giovanni P. Olivei, 2004. "Estimating forward looking Euler equations with GMM estimators: an optimal instruments approach," Working Papers 04-2, Federal Reserve Bank of Boston.
  • Handle: RePEc:fip:fedbwp:04-2
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    References listed on IDEAS

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    1. Fuhrer, Jeffrey C, 1997. "The (Un)Importance of Forward-Looking Behavior in Price Specifications," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(3), pages 338-350, August.
    2. Tinsley, P A, 2002. "Rational Error Correction," Computational Economics, Springer;Society for Computational Economics, vol. 19(2), pages 197-225, April.
    3. Fuhrer, Jeffrey C. & Rudebusch, Glenn D., 2004. "Estimating the Euler equation for output," Journal of Monetary Economics, Elsevier, vol. 51(6), pages 1133-1153, September.
    4. 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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    6. Anderson, Gary & Moore, George, 1985. "A linear algebraic procedure for solving linear perfect foresight models," Economics Letters, Elsevier, vol. 17(3), pages 247-252.
    7. Arturo Estrella & Jeffrey C. Fuhrer, 2002. "Dynamic Inconsistencies: Counterfactual Implications of a Class of Rational-Expectations Models," American Economic Review, American Economic Association, vol. 92(4), pages 1013-1028, September.
    8. Gali, Jordi & Gertler, Mark, 1999. "Inflation dynamics: A structural econometric analysis," Journal of Monetary Economics, Elsevier, vol. 44(2), pages 195-222, October.
    9. Buiter, Willem H & Jewitt, Ian, 1981. "Staggered Wage Setting with Real Wage Relativities: Variations on a Theme of Taylor," The Manchester School of Economic & Social Studies, University of Manchester, vol. 49(3), pages 211-228, September.
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    11. repec:cup:etheor:v:9:y:1993:i:2:p:222-40 is not listed on IDEAS
    12. John Shea, 1997. "Instrument Relevance in Multivariate Linear Models: A Simple Measure," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 348-352, May.
    13. Jeffrey C. Fuhrer, 2000. "Habit Formation in Consumption and Its Implications for Monetary-Policy Models," American Economic Review, American Economic Association, vol. 90(3), pages 367-390, June.
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    Cited by:

    1. Mazumder, Sandeep, 2010. "The new Keynesian Phillips curve and the cyclicality of marginal cost," Journal of Macroeconomics, Elsevier, vol. 32(3), pages 747-765, September.
    2. Ramos-Francia, Manuel & Torres, Alberto, 2008. "Inflation dynamics in Mexico: A characterization using the New Phillips curve," The North American Journal of Economics and Finance, Elsevier, vol. 19(3), pages 274-289, December.
    3. Dufour, Jean-Marie & Khalaf, Lynda & Kichian, Maral, 2006. "Inflation dynamics and the New Keynesian Phillips Curve: An identification robust econometric analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 30(9-10), pages 1707-1727.
    4. Dibartolomeo, Giovanni & Rossi, Lorenza & Tancioni, Massimiliano, 2004. "Monetary Policy under Rule-of-Thumb Consumers and External Habits: An International Empirical Comparison," MPRA Paper 1094, University Library of Munich, Germany, revised Jun 2006.
    5. Bilbiie, Florin O. & Straub, Roland, 2012. "Changes in the output Euler equation and asset markets participation," Journal of Economic Dynamics and Control, Elsevier, vol. 36(11), pages 1659-1672.
    6. Oscar Jorda & Sharon Kozicki, 2006. "Projection Minimum Distance: An Estimator for Dynamic Macroeconomic Models," Working Papers 623, University of California, Davis, Department of Economics.
    7. Gourieroux, C. & Jasiak, J. & Monfort, A., 2020. "Stationary bubble equilibria in rational expectation models," Journal of Econometrics, Elsevier, vol. 218(2), pages 714-735.
    8. Scheufele, Rolf, 2010. "Evaluating the German (New Keynesian) Phillips curve," The North American Journal of Economics and Finance, Elsevier, vol. 21(2), pages 145-164, August.
    9. Oscar Jorda & Sharon Kozicki, 2007. "Estimation and Inference by the Method of Projection Minimum Distance," Working Papers 148, University of California, Davis, Department of Economics.
    10. Michelle L. Barnes & Fabia Gumbau-Brisa & Denny Lie & Giovanni P. Olivei, 2011. "Estimation of forward-looking relationships in closed form: an application to the New Keynesian Phillips curve," Working Papers 11-3, Federal Reserve Bank of Boston.
    11. Morrisy, Stephen D., 2017. "Efficient estimation of macroeconomic equations with unobservable states," Economic Modelling, Elsevier, vol. 60(C), pages 408-423.
    12. Òscar Jordà & Sharon Kozicki, 2007. "Estimation and Inference by the Method of Projection Minimum Distance," Staff Working Papers 07-56, Bank of Canada.
    13. Pym Manopimoke, 2016. "The Output Euler Equation and Real Interest Rate Regimes," PIER Discussion Papers 33, Puey Ungphakorn Institute for Economic Research.
    14. Sophocles Mavroeidis, 2006. "Testing the New Keynesian Phillips Curve Without Assuming Identification," Working Papers 2006-13, Brown University, Department of Economics.
    15. Mazumder, Sandeep, 2011. "The empirical validity of the New Keynesian Phillips curve using survey forecasts of inflation," Economic Modelling, Elsevier, vol. 28(6), pages 2439-2450.
    16. Mazumder, Sandeep, 2011. "Cost-based Phillips Curve forecasts of inflation," Journal of Macroeconomics, Elsevier, vol. 33(4), pages 553-567.
    17. Ben Ali, Samir, 2010. "A New Keynesian Phillips curve for Tunisia : Estimation and analysis of sensitivity," MPRA Paper 29624, University Library of Munich, Germany.
    18. Anna Florio, 2013. "The Implied Consumer Euler Rate: What Role for Financial Frictions?," CESifo Economic Studies, CESifo, vol. 59(4), pages 650-675, December.

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