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

  • Eric T. Swanson
  • Gary S. Anderson
  • Andrew T. Levin

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
Date of revision:
Handle: RePEc:fip:fedfwp:2006-01
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  1. 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.
  2. S. Boragan Aruoba & Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2003. "Comparing solution methods for dynamic equilibrium economies," FRB Atlanta Working Paper 2003-27, Federal Reserve Bank of Atlanta.
  3. Jeff Fuhrer & Brian Madigan, 1994. "Monetary policy when interest rates are bounded at zero," Working Papers in Applied Economic Theory 94-06, Federal Reserve Bank of San Francisco.
  4. Gaspar, Jess & L. Judd, Kenneth, 1997. "Solving Large-Scale Rational-Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 1(01), pages 45-75, January.
  5. 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.
  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. repec:cup:macdyn:v:1:y:1997:i:1:p:45-75 is not listed on IDEAS
  8. Jinill Kim and Sunghyun Henry Kim, 2001. "Spurious Welfare Reversals in International Business Cycle Models," Computing in Economics and Finance 2001 3, Society for Computational Economics.
  9. 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.
  10. Kollmann, Robert, 2003. "Monetary Policy Rules in an Interdependent World," CEPR Discussion Papers 4012, C.E.P.R. Discussion Papers.
  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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