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Consistent Expectations, Rational Expectations, Multiple-Solution Indeterminacies, and Least-Squares Learnability

  • Bennett T. McCallum

After some historical discussion of the rational expectations (RE) solution procedures of John Muth, Alan Walters, and Robert Lucas, this paper considers the relevance for actual economies of issues stemming from the existence of multiple RE equilibria. In all linear models, the minimum state variable (MSV) solution as defined by the author (JME, 1983) is unique by construction. While it might be argued that the MSV solution warrants special status as the bubble-free solution, the focus in this paper is on its adaptive, least-squares learnability by individual agents, as discussed extensively in important recent publications by George Evans and Seppo Honkapohja. Although the MSV solution is learnable and the main alternatives are not, in most standard models, Evans and Honkapohja have stressed an example in which the opposite is true. The present paper shows, however, that parameter values yielding that result are such that the model is not well formulated, in a specified sense (one that avoids implausible discontinuities). More generally, analysis of a pair of prominent univariate specifications, featured by Evans and Honkapohja, shows that the MSV solution is invariably learnable in these structures, if they are well formulated.

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Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 9218.

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Date of creation: Sep 2002
Date of revision:
Publication status: published as Minford, Patrick (ed.) Money Matters: Essays in Honour of Alan Walters. Edward Elgar Publishing, 2004.
Handle: RePEc:nbr:nberwo:9218
Note: EFG ME
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  1. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August.
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  7. Michael Woodford, 1994. "Nonstandard Indicators for Monetary Policy: Can Their Usefulness Be Judged from Forecasting Regressions?," NBER Chapters, in: Monetary Policy, pages 95-115 National Bureau of Economic Research, Inc.
  8. Sims, Christopher A, 1994. "A Simple Model for Study of the Determination of the Price Level and the Interaction of Monetary and Fiscal Policy," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 381-99.
  9. McCallum, Bennett T., 1981. "Price level determinacy with an interest rate policy rule and rational expectations," Journal of Monetary Economics, Elsevier, vol. 8(3), pages 319-329.
  10. Ragna Alstadheim & Dale Henderson, 2006. "Price-level determinacy, lower bounds on the nominal interest rate, and liquidity traps," Working Paper 2006/03, Norges Bank.
  11. Benhabib, Jess & Schmitt-Grohe, Stephanie & Uribe, Martin, 1998. "The Perils of Taylor Rules," Working Papers 98-37, C.V. Starr Center for Applied Economics, New York University.
  12. Narayana R. Kocherlakota & Christopher Phelan, 1999. "Explaining the fiscal theory of the price level," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 14-23.
  13. Clarida, Richard & Galí, Jordi & Gertler, Mark, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," CEPR Discussion Papers 2139, C.E.P.R. Discussion Papers.
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  17. Peter Isard & Douglas Laxton & Ann-Charlotte Eliasson, 1999. "Simple Monetary Policy Rules Under Model Uncertainty," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 6(4), pages 537-577, November.
  18. Evans, George W & Honkapohja, Seppo, 1992. "On the Robustness of Bubbles in Linear RE Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 1-14, February.
  19. Gauthier, St phane, 2003. "Dynamic Equivalence Principle In Linear Rational Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 7(01), pages 63-88, February.
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