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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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  14. 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.
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  18. 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.
  19. Robert G. King, 2000. "The new IS-LM model : language, logic, and limits," Economic Quarterly, Federal Reserve Bank of Richmond, issue Sum, pages 45-103.
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