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

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  • Eric Swanson
  • Gary Anderson
  • Andrew Levin

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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Bibliographic Info

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. Jeffrey Fuhrer & Brian Madigan, 1994. "Monetary policy when interest rates are bounded at zero," Working Papers 94-1, Federal Reserve Bank of Boston.
  2. Anderson, Gary & Moore, George, 1985. "A linear algebraic procedure for solving linear perfect foresight models," Economics Letters, Elsevier, vol. 17(3), pages 247-252.
  3. Jinill Kim & Sunghyun Henry Kim, 1999. "Spurious Welfare Reversals in International Business Cycle Models," Virginia Economics Online Papers 319, University of Virginia, Department of Economics.
  4. Kollmann, Robert, 2003. "Monetary Policy Rules in an Interdependent World," CEPR Discussion Papers 4012, C.E.P.R. Discussion Papers.
  5. Jess Gaspar & Kenneth L. Judd, 1997. "Solving Large Scale Rational Expectations Models," NBER Technical Working Papers 0207, National Bureau of Economic Research, Inc.
  6. 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.
  7. Kollmann, Robert, 2002. "Monetary Policy Rules in the Open Economy: Effects on Welfare and Business Cycles," CEPR Discussion Papers 3279, C.E.P.R. Discussion Papers.
  8. repec:cup:macdyn:v:1:y:1997:i:1:p:45-75 is not listed on IDEAS
  9. Aruoba, S. Boragan & Fernandez-Villaverde, Jesus & Rubio-Ramirez, Juan F., 2006. "Comparing solution methods for dynamic equilibrium economies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(12), pages 2477-2508, December.
  10. Gary S. Anderson, 2000. "A Systematic Comparison Of Alternative Linear Rational Expectation Model Solution Techniques," Computing in Economics and Finance 2000 142, Society for Computational Economics.
  11. 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.
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