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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
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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
Note: EFG ME
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  1. 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.
  2. Narayana Kocherlakota & Christopher Phelan, 1999. "Explaining the fiscal theory of the price level," Quarterly Review, Federal Reserve Bank of Minneapolis, issue Fall, pages 14-23.
  3. Ann-Charlotte Eliasson & Peter Isard & Douglas Laxton, 1999. "Simple Monetary Policy Rules Under Model Uncertainty," IMF Working Papers 99/75, International Monetary Fund.
  4. John H. Cochrane, 1998. "A Frictionless View of U.S. Inflation," CRSP working papers 479, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
  5. James Bullard & Kaushik Mitra, 2002. "Learning about monetary policy rules," Working Papers 2000-001, Federal Reserve Bank of St. Louis.
  6. 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.
  7. Ragna Alstadheim & Dale Henderson, 2006. "Price-level determinacy, lower bounds on the nominal interest rate, and liquidity traps," Working Paper 2006/03, Norges Bank.
  8. Sargent, Thomas J, 1971. "A Note on the 'Accelerationist' Controversy," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 3(3), pages 721-25, August.
  9. Ben S. Bernanke & Michael Woodford, 1997. "Inflation forecasts and monetary policy," Proceedings, Federal Reserve Bank of Cleveland, pages 653-686.
  10. Flood, Robert P & Garber, Peter M, 1980. "An Economic Theory of Monetary Reform," Journal of Political Economy, University of Chicago Press, vol. 88(1), pages 24-58, February.
  11. Richard Clarida & Jordi Galí & Mark Gertler, 1997. "The science of monetary policy: A new Keynesian perspective," Economics Working Papers 356, Department of Economics and Business, Universitat Pompeu Fabra, revised Apr 1999.
  12. Walters, A A, 1971. "Consistent Expectations, Distributed Lags and the Quantity Theory," Economic Journal, Royal Economic Society, vol. 81(322), pages 273-81, June.
  13. 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.
  14. Wenzelburger, Jan, 2006. "Learning in linear models with expectational leads," Journal of Mathematical Economics, Elsevier, vol. 42(7-8), pages 854-884, November.
  15. 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.
  16. 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.
  17. Schmitt-Grohé, Stephanie & Uribe, Martín, 2001. "Liquidity Traps with Global Taylor Rules," CEPR Discussion Papers 2969, C.E.P.R. Discussion Papers.
  18. Stéphane Gauthier, 2003. "Dynamic equivalence principle in linear rational expectations models," Post-Print halshs-00069499, HAL.
  19. Taylor, John B., 1993. "Discretion versus policy rules in practice," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 39(1), pages 195-214, December.
  20. repec:cup:macdyn:v:7:y:2003:i:1:p:63-88 is not listed on IDEAS
  21. Lucas, Robert Jr., 1972. "Expectations and the neutrality of money," Journal of Economic Theory, Elsevier, vol. 4(2), pages 103-124, April.
  22. 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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  24. Brayton, Flint & Levin, Andrew & Lyon, Ralph & Williams, John C., 1997. "The evolution of macro models at the Federal Reserve Board," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 47(1), pages 43-81, December.
  25. Evans, George, 1985. "Expectational Stability and the Multiple Equilibria Problem in Linear Rational Expectations Models," The Quarterly Journal of Economics, MIT Press, vol. 100(4), pages 1217-33, November.
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