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Logical Pitfalls of Assuming Bounded Solutions to Expectational Difference Equations

Author

Listed:
  • David Eagle

    (Eastern Washington University)

  • Elizabeth Murff

    (Eastern Washington University)

Abstract

The precedent for solving expectational difference equations has been to solve converging equations backwards and diverging equations forward by assuming the solution is bounded. This precedent often leads to incorrect solutions and has less than rigorous foundations. More rigorous procedures would be to determine the terminal condition in a finite model and take the limit of that terminal condition as the horizon goes to infinity. Also, whether one solves forward or backwards depends on the context of the difference equation, not on convergence or divergence. These new procedures reveal Woodford’s (2003) model of a cashless economy to be incomplete.

Suggested Citation

  • David Eagle & Elizabeth Murff, 2005. "Logical Pitfalls of Assuming Bounded Solutions to Expectational Difference Equations," GE, Growth, Math methods 0501002, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpge:0501002
    Note: Type of Document - pdf. Shows limitations of Sargent's precedent for solving expectational difference equations. It also shows Woodford's use of Sargent's precedent to be inappropriate.
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/ge/papers/0501/0501002.pdf
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    References listed on IDEAS

    as
    1. Sargent, Thomas J & Wallace, Neil, 1975. ""Rational" Expectations, the Optimal Monetary Instrument, and the Optimal Money Supply Rule," Journal of Political Economy, University of Chicago Press, vol. 83(2), pages 241-254, April.
    2. Aoki, Kosuke, 2001. "Optimal monetary policy responses to relative-price changes," Journal of Monetary Economics, Elsevier, vol. 48(1), pages 55-80, August.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. David Eagle, 2005. "The Inflation Dynamics of Pegging Interest Rates," Macroeconomics 0502029, University Library of Munich, Germany.
    2. David Eagle, 2005. "Multiple Critiques of Woodford’s Model of a Cashless Economy," Macroeconomics 0504028, University Library of Munich, Germany.

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    More about this item

    Keywords

    expectational difference equations; infinite horizons; Woodford's cashless economy; price indeterminacy; pegging interest rates;
    All these keywords.

    JEL classification:

    • E10 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - General

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