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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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Bibliographic Info

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. Bullard, James & Mitra, Kaushik, 2002. "Learning about monetary policy rules," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1105-1129, September.
  2. 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.
  3. Mark Gertler & Jordi Gali & Richard Clarida, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," Journal of Economic Literature, American Economic Association, vol. 37(4), pages 1661-1707, December.
  4. Gauthier, St phane, 2003. "Dynamic Equivalence Principle In Linear Rational Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 7(01), pages 63-88, February.
  5. Ragna Alstadheim & Dale W. Henderson, 2004. "Price-level determinacy, lower bounds on the nominal interest rate, and liquidity traps," International Finance Discussion Papers 795, Board of Governors of the Federal Reserve System (U.S.).
  6. 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.
  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. Walters, A A, 1971. "Consistent Expectations, Distributed Lags and the Quantity Theory," Economic Journal, Royal Economic Society, vol. 81(322), pages 273-81, June.
  9. 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.
  10. 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.
  11. Jess Benhabib & Stephanie Schmitt-Grohe & Martin Uribe, 1998. "The perils of Taylor Rules," Departmental Working Papers 199831, Rutgers University, Department of Economics.
  12. 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.
  13. 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.
  14. Bennett T. McCallum, 1982. "Price Level Determinacy with an Interest Rate Policy Rule and Rational Expectations," NBER Working Papers 0559, National Bureau of Economic Research, Inc.
  15. Lucas, Robert Jr., 1972. "Expectations and the neutrality of money," Journal of Economic Theory, Elsevier, vol. 4(2), pages 103-124, April.
  16. Ann-Charlotte Eliasson & Peter Isard & Douglas Laxton, 1999. "Simple Monetary Policy Rules Under Model Uncertainty," IMF Working Papers 99/75, International Monetary Fund.
  17. Ben S. Bernanke & Michael Woodford, 1997. "Inflation forecasts and monetary policy," Proceedings, Federal Reserve Bank of Cleveland, pages 653-686.
  18. Stephanie Schmitt-Grohé & Martín Uribe, 2009. "Liquidity traps with global Taylor Rules," International Journal of Economic Theory, The International Society for Economic Theory, vol. 5(1), pages 85-106.
  19. Wenzelburger, Jan, 2006. "Learning in linear models with expectational leads," Journal of Mathematical Economics, Elsevier, vol. 42(7-8), pages 854-884, November.
  20. repec:cup:macdyn:v:7:y:2003:i:1:p:63-88 is not listed on IDEAS
  21. 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.
  22. 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.
  23. 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.
  24. 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.
  25. 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.
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Cited by:
  1. 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.
  2. Bennett T. McCallum, . "Is The Fiscal Theory of the Price Level Learnable?," GSIA Working Papers 2003-24, Carnegie Mellon University, Tepper School of Business.
  3. Eran Guse, 2004. "Learning with Heterogeneous Expectations in an Evolutionary World," Computing in Economics and Finance 2004 99, Society for Computational Economics.
  4. Bennett T. McCallum, 2003. "The Unique Minimum State Variable RE Solution is E-Stable in All Well Formulated Linear Models," NBER Working Papers 9960, National Bureau of Economic Research, Inc.

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