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Higher-Order Perturbation Solutions to Dynamic, Discrete-Time Rational Expectations Models

Author

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

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.

Suggested Citation

  • Gary S. Anderson & Andrew T. Levin & Eric T. Swanson, 2006. "Higher-Order Perturbation Solutions to Dynamic, Discrete-Time Rational Expectations Models," Working Paper Series 2006-01, Federal Reserve Bank of San Francisco.
    • Handle: RePEc:fip:fedfwp:2006-01
    DOI: 10.24148/wp2006-01
    Note: PDF date: This version: January 12, 2006. First Version: December 2002.
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    References listed on IDEAS

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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