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A Higher-Order Taylor Expansion Approach to Simulation of Stochastic Forward-Looking Models with an Application to a Nonlinear Phillips Curve Model

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  • Collard, Fabrice
  • Juillard, Michel

Abstract

We propose to apply to the simulation of general nonlinear rational-expectation models a method where the expectation functions are approximated through a higher-order Taylor expansion. This method has been advocated by Judd (1998) and others for the simulation of stochastic optimal-control problems and we extend its application to more general cases. The coefficients for the first-order approximation of the expectation function are obtained using a generalized eigen value decomposition as it is usual for the simulation of linear rational-expectation models. Coefficients for higher-order terms in the Taylor expansion are then obtained by solving a succession of linear systems. In addition, we provide a method to reduce a bias in the computation of the stochastic equilibrium of such models. These procedures are made available in DYNARE, a MATLAB and GAUSS based simulation program. This method is then applied to the simulation of a macroeconomic model embodying a nonlinear Phillips curve. We show that in this case a quadratic approximation is sufficient, but different in important ways from the simulation of a linearized version of the model. Copyright 2001 by Kluwer Academic Publishers

Suggested Citation

  • Collard, Fabrice & Juillard, Michel, 2001. "A Higher-Order Taylor Expansion Approach to Simulation of Stochastic Forward-Looking Models with an Application to a Nonlinear Phillips Curve Model," Computational Economics, Springer;Society for Computational Economics, vol. 17(2-3), pages 125-139, June.
  • Handle: RePEc:kap:compec:v:17:y:2001:i:2-3:p:125-39
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    Cited by:

    1. Victor Dorofeenko & Gabriel S. Lee & Kevin D. Salyer, 2008. "Time-Varying Uncertainty And The Credit Channel," Bulletin of Economic Research, Wiley Blackwell, vol. 60(4), pages 375-403, October.
    2. Faia, Ester & Iliopulos, Eleni, 2011. "Financial openness, financial frictions and optimal monetary policy," Journal of Economic Dynamics and Control, Elsevier, vol. 35(11), pages 1976-1996.
    3. Collard, Fabrice & Juillard, Michel, 2001. "Accuracy of stochastic perturbation methods: The case of asset pricing models," Journal of Economic Dynamics and Control, Elsevier, vol. 25(6-7), pages 979-999, June.
    4. Laxton, Douglas & Pesenti, Paolo & Juillard, Michel & Karam, Philippe, 2006. "Welfare-based monetary policy rules in an estimated DSGE model of the US economy," Working Paper Series 613, European Central Bank.
    5. Ahmad, Yamin & Lo, Ming Chien & Mykhaylova, Olena, 2013. "Volatility and persistence of simulated DSGE real exchange rates," Economics Letters, Elsevier, vol. 119(1), pages 38-41.
    6. Ahmad, Yamin & Lo, Ming Chien & Mykhaylova, Olena, 2013. "Causes of nonlinearities in low-order models of the real exchange rate," Journal of International Economics, Elsevier, vol. 91(1), pages 128-141.
    7. Valdivia, Daney, 2015. "Handbook on DSGE models: some useful tips in modeling a DSGE models," MPRA Paper 61347, University Library of Munich, Germany.
    8. Davide Debortoli & Junior Maih & Ricardo Nunes, 2010. "Loose commitment in medium-scale macroeconomic models: Theory and an application," Working Paper 2010/25, Norges Bank.
    9. Beetsma, Roel & Ribeiro, Marcos Poplawski & Schabert, Andreas, 2008. "A Comparison of Debt and Primary-deficit Constraints," CEPR Discussion Papers 6897, C.E.P.R. Discussion Papers.
    10. Ester Faia & Eleni Iliopulos, 2010. "Financial Globalization, Financial Frictions and Optimal Monetary Policy," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00497486, HAL.
    11. Kline, Patrick, 2008. "Understanding Sectoral Labor Market Dynamics: An Equilibrium Analysis of the Oil and Gas Field Services Industry," Working Papers 43, Yale University, Department of Economics.
    12. Oscar Jorda, 2003. "Model-Free Impulse Responses," Working Papers 38, University of California, Davis, Department of Economics.
    13. Julio J. Rotemberg, 2008. "Cyclical Wages in a Search-and-Bargaining Model with Large Firms," NBER Chapters,in: NBER International Seminar on Macroeconomics 2006, pages 65-114 National Bureau of Economic Research, Inc.
    14. repec:bla:reviec:v:25:y:2017:i:5:p:1046-1077 is not listed on IDEAS
    15. Ahmad, Yamin S. & Staveley-O’Carroll, Olena M., 2017. "Exploring international differences in inflation dynamics," Journal of International Money and Finance, Elsevier, vol. 79(C), pages 115-135.
    16. Charles Olivier Mao Takongmo, 2017. "Government-spending multipliers and the zero lower bound in an open economy," Review of International Economics, Wiley Blackwell, vol. 25(5), pages 1046-1077, November.
    17. Alain Gabler, 2007. "Sector-specific Markup Fluctuations and the Business Cycle," Economics Working Papers ECO2007/25, European University Institute.
    18. Debortoli, Davide & Maih, Junior & Nunes, Ricardo, 2014. "Loose Commitment In Medium-Scale Macroeconomic Models: Theory And Applications," Macroeconomic Dynamics, Cambridge University Press, vol. 18(01), pages 175-198, January.
    19. Lilia Maliar & Serguei Maliar & Sébastien Villemot, 2013. "Taking Perturbation to the Accuracy Frontier: A Hybrid of Local and Global Solutions," Computational Economics, Springer;Society for Computational Economics, vol. 42(3), pages 307-325, October.
    20. repec:lus:reveco:v:68:y:2017:i:2:p:117-151:n:3 is not listed on IDEAS
    21. Lan, Hong & Meyer-Gohde, Alexander, 2013. "Solving DSGE models with a nonlinear moving average," Journal of Economic Dynamics and Control, Elsevier, vol. 37(12), pages 2643-2667.
    22. Valdivia, Daney & Pérez, Danyira, 2013. "Dinámica económica y coordinación de políticas fiscal – monetaria en América Latina: Evaluación a través de una DSGE
      [Dynamic economic and coordination on fiscal – monetary policies in Latin Améric
      ," MPRA Paper 51562, University Library of Munich, Germany.
    23. Phillips, Kerk L., 2017. "Solving and simulating unbalanced growth models using linearization about the current state," Economics Letters, Elsevier, vol. 151(C), pages 35-38.
    24. Mykhaylova, Olena, 2010. "Optimal Monetary Policy with Non-Zero Net Foreign Wealth," MPRA Paper 23598, University Library of Munich, Germany.

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