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Logical Pitfalls of Assuming Bounded Solutions to Expectational Difference Equations

Listed author(s):
  • David Eagle

    (Eastern Washington University)

  • Elizabeth Murff

    (Eastern Washington University)

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.

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Paper provided by EconWPA in its series GE, Growth, Math methods with number 0501002.

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Date of creation: 20 Jan 2005
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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  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.
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