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The Unique Minimum State Variable RE Soluiton is E-Stable in All Well Formulated Linear Models

  • Bennett T. McCallum

This paper explores the relationship between the closely linked concepts of E-stability and least-squares learnability, featured in important recent work by Evans and Honkapohja (1999, 2001), and the minimum-state-variable (MSV) solution concept introduced by McCallum (1983) and used by many researchers for rational expectations (RE) analysis. It is shown that the MSV solution, which is unique by construction, is E-stable—and therefore LS learnable if nonexplosive—in all linear RE models that satisfy conditions for being “well formulated.” The latter property, introduced in the paper, consists of two requirements. The first is that a model’s structural parameters are restricted so as to avoid any infinite discontinuity, of the steady state values of endogenous variables, in response to small changes in these parameters. (It can be expressed cleanly in terms of the eigenvalues of a matrix that is the sum of those attached to the one period ahead and one period lagged values of the endogenous variables in a first-order vector formulation of the model.) The second, which is needed infrequently, is that the parameters are restricted to prevent any infinite discontinuities in the MSV solution response coefficients.

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Paper provided by Carnegie Mellon University, Tepper School of Business in its series GSIA Working Papers with number 2003-25.

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Date of creation: Nov 2002
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Handle: RePEc:cmu:gsiawp:906654633
Contact details of provider: Postal: Tepper School of Business, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213-3890
Web page: http://www.tepper.cmu.edu/

Order Information: Web: http://student-3k.tepper.cmu.edu/gsiadoc/GSIA_WP.asp

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  1. Robert A. Driskill, 2002. "A Proposal for a Selection Criterion in a Class of Dynamic Rational Expectations Models with Multiple Equilibria," Vanderbilt University Department of Economics Working Papers 0210, Vanderbilt University Department of Economics.
  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. Benhabib, Jess & Schmitt-Grohé, Stephanie & Uribe, Martín, 1999. "The Perils of Taylor Rules," CEPR Discussion Papers 2314, C.E.P.R. Discussion Papers.
  4. King, Robert G & Watson, Mark W, 1998. "The Solution of Singular Linear Difference Systems under Rational Expectations," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1015-26, November.
  5. G. Desgranges & Stéphane Gauthier, 2003. "Uniqueness of bubble-free solution in linear rational expectations models," Post-Print halshs-00069498, HAL.
  6. repec:cup:macdyn:v:7:y:2003:i:1:p:63-88 is not listed on IDEAS
  7. McCallum, Bennett T., 1983. "On non-uniqueness in rational expectations models : An attempt at perspective," Journal of Monetary Economics, Elsevier, vol. 11(2), pages 139-168.
  8. Ben S. Bernanke & Michael Woodford, 1997. "Inflation Forecasts and Monetary Policy," NBER Working Papers 6157, National Bureau of Economic Research, Inc.
  9. Gauthier, St phane, 2003. "Dynamic Equivalence Principle In Linear Rational Expectations Models," Macroeconomic Dynamics, Cambridge University Press, vol. 7(01), pages 63-88, February.
  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. Binder,M. & Pesaran,H.M., 1995. "Multivariate Rational Expectations Models and Macroeconomic Modelling: A Review and Some New Results," Cambridge Working Papers in Economics 9415, Faculty of Economics, University of Cambridge.
  12. James Bullard & Kaushik Mitra, 2002. "Learning about monetary policy rules," Working Papers 2000-001, Federal Reserve Bank of St. Louis.
  13. 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.
  14. Bennett T. McCallum, 2002. "Consistent Expectations, Rational Expectations, Multiple-Solution Indeterminacies, and Least-Squares Learnability," NBER Working Papers 9218, National Bureau of Economic Research, Inc.
  15. repec:cup:macdyn:v:7:y:2003:i:2:p:171-91 is not listed on IDEAS
  16. John H. Cochrane, 1998. "A Frictionless View of U.S. Inflation," NBER Working Papers 6646, National Bureau of Economic Research, Inc.
  17. DeCanio, Stephen J, 1979. "Rational Expectations and Learning from Experience," The Quarterly Journal of Economics, MIT Press, vol. 93(1), pages 47-57, February.
  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. 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.
  20. Wenzelburger, Jan, 2006. "Learning in linear models with expectational leads," Journal of Mathematical Economics, Elsevier, vol. 42(7-8), pages 854-884, November.
  21. 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.
  22. Desgranges, G. & Gauthier, S., 1999. "On the Uniqueness of the Bubble-Free Solution in Linear Rational Expectations Models," G.R.E.Q.A.M. 99a45, Universite Aix-Marseille III.
  23. Anderson, Gary & Moore, George, 1985. "A linear algebraic procedure for solving linear perfect foresight models," Economics Letters, Elsevier, vol. 17(3), pages 247-252.
  24. 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.
  25. Bray, Margaret, 1982. "Learning, estimation, and the stability of rational expectations," Journal of Economic Theory, Elsevier, vol. 26(2), pages 318-339, April.
  26. 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.
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