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

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  • Bennett T. McCallum

Abstract

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
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Publication status: published as Minford, Patrick (ed.) Money Matters: Essays in Honour of Alan Walters. Edward Elgar Publishing, 2004.
Handle: RePEc:nbr:nberwo:9218

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  1. 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, vol. 4(3), pages 381-99.
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Cited by:
  1. Eran Guse, 2004. "Learning with Heterogeneous Expectations in an Evolutionary World," Computing in Economics and Finance 2004 99, Society for Computational Economics.
  2. Bennett T. Mccallum, 2003. "Is The Fiscal Theory of the Price Level Learnable?," Scottish Journal of Political Economy, Scottish Economic Society, vol. 50(5), pages 634-649, November.
  3. Martin ZUMPE (GREThA UMR CNRS 5113), 2010. "Monetary Policy Rules, Learning and Stability: a Survey of the Recent Literature (In French)," Cahiers du GREThA 2010-01, Groupe de Recherche en Economie Théorique et Appliquée.
  4. Bennett T. McCallum, 2002. "The Unique Minimum State Variable RE Soluiton is E-Stable in All Well Formulated Linear Models," GSIA Working Papers 2003-25, Carnegie Mellon University, Tepper School of Business.

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