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Higher-order perturbation solutions to dynamic, discrete-time rational expectations models

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Author Info
Eric Swanson
Gary Anderson
Andrew Levin

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Abstract

We present an algorithm and software routines for computing nth order Taylor series approximate solutions to dynamic, discrete-time rational expectations models around a nonstochastic steady state. The primary advantage of higher-order (as opposed to first- or second-order) approximations is that they are valid not just locally, but often globally (i.e., over nonlocal, possibly very large compact sets) in a rigorous sense that we specify. We apply our routines to compute first- through seventh-order approximate solutions to two standard macroeconomic models, a stochastic growth model and a life-cycle consumption model, and discuss the quality and global properties of these solutions.

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Paper provided by Federal Reserve Bank of San Francisco in its series Working Paper Series with number 2006-01.

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Date of creation: 2006
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Handle: RePEc:fip:fedfwp:2006-01

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Keywords: Macroeconomics - Econometric models ; Business cycles ; Monetary policy;

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  1. Kollmann, Robert, 2002. "Monetary policy rules in the open economy: effects on welfare and business cycles," Journal of Monetary Economics, Elsevier, vol. 49(5), pages 989-1015, July. [Downloadable!] (restricted)
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  2. S. B. Aruoba & Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez, 2005. "Comparing Solution Methods for Dynamic Equilibrium Economies," Levine's Bibliography 122247000000000855, UCLA Department of Economics. [Downloadable!]
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  3. Kim, Jinill & Kim, Sunghyun Henry, 2003. "Spurious welfare reversals in international business cycle models," Journal of International Economics, Elsevier, vol. 60(2), pages 471-500, August. [Downloadable!] (restricted)
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  4. repec:cup:macdyn:v:1:y:1997:i:1:p:45-75 is not listed on IDEAS
  5. Kollmann, Robert, 2003. "Monetary Policy Rules in an Interdependent World," CEPR Discussion Papers 4012, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  6. Gaspar, Jess & L. Judd, Kenneth, 1997. "Solving Large-Scale Rational-Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 1(01), pages 45-75, January. [Downloadable!]
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  7. Jeffrey C. Fuhrer & Brian F. Madigan, 1997. "Monetary Policy When Interest Rates Are Bounded At Zero," The Review of Economics and Statistics, MIT Press, vol. 79(4), pages 573-585, November. [Downloadable!] (restricted)
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  8. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July. [Downloadable!] (restricted)
  9. Stephanie Schmitt-Grohe & Martin Uribe, 2001. "Solving Dynamic General Equilibrium Models Using a Second-Order Approximation to the Policy Function," Departmental Working Papers 200106, Rutgers University, Department of Economics. [Downloadable!]
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  10. Anderson, Gary & Moore, George, 1985. "A linear algebraic procedure for solving linear perfect foresight models," Economics Letters, Elsevier, vol. 17(3), pages 247-252. [Downloadable!] (restricted)
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  1. Glenn Rudebusch & Eric Swanson, 2008. "The bond premium in a DSGE model with long-run real and nominal risks," Working Paper Series 2008-31, Federal Reserve Bank of San Francisco. [Downloadable!]
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  2. Marzo, Massimiliano & Strid, Ingvar & Zagaglia, Paolo, 2006. "Optimal Opportunistic Monetary Policy in a New-Keynesian Model," Research Papers in Economics 2006:8, Stockholm University, Department of Economics. [Downloadable!]
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  3. Paolo Zagaglia, 2007. "Operational Fiscal and Monetary Policy with Staggered Wage and Price Dynamics," Finnish Economic Papers, Finnish Economic Association, vol. 20(2), pages 121-138, Autumn. [Downloadable!]
  4. Yi Wen & Huabin Wu, 2008. "Dynamics of externalities: a second-order perspective," Working Papers 2008-044, Federal Reserve Bank of St. Louis. [Downloadable!]
  5. Glenn D. Rudebusch & Brian P. Sack & Eric T. Swanson, 2007. "Macroeconomic implications of changes in the term premium," Review, Federal Reserve Bank of St. Louis, issue Jul, pages 241-270. [Downloadable!]
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  6. Zagaglia, Paolo, 2007. "Distortionary Tax Instruments and Implementable Monetary Policy," Research Papers in Economics 2007:5, Stockholm University, Department of Economics. [Downloadable!]
  7. An, Sungbae & Schorfheide, Frank, 2005. "Bayesian Analysis of DSGE Models," CEPR Discussion Papers 5207, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  8. Glenn D. Rudebusch & Eric T. Swanson, 2007. "Examining the bond premium puzzle with a DSGE model," Working Paper Series 2007-25, Federal Reserve Bank of San Francisco. [Downloadable!]
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