Logical Pitfalls of Assuming Bounded Solutions to Expectational Difference Equations
AbstractThe 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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Bibliographic InfoPaper provided by EconWPA in its series GE, Growth, Math methods with number 0501002.
Date of creation: 20 Jan 2005
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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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expectational difference equations; infinite horizons; Woodford's cashless economy; price indeterminacy; pegging interest rates;
Find related papers by JEL classification:
- E10 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - General
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- Aoki, Kosuke, 2001. "Optimal monetary policy responses to relative-price changes," Journal of Monetary Economics, Elsevier, vol. 48(1), pages 55-80, August.
- 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 241-54, April.
- David Eagle, 2005. "Multiple Critiques of Woodford’s Model of a Cashless Economy," Macroeconomics 0504028, EconWPA.
- David Eagle, 2005. "The Inflation Dynamics of Pegging Interest Rates," Macroeconomics 0502029, EconWPA.
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