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Determinacy, Learnability, And Plausibility In Monetary Policy Analysis: Additional Results

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  • Bennett T. McCallum

Abstract

In contrast with recent research in monetary policy analysis which has featured a great deal of work concerning conditions for determinacy, I have argued in recent publications that least-squares (LS) learnability is a compelling necessary condition for a rational expectations (RE) equilibrium to be considered plausible. As I have demonstrated in a previous paper, in a very wide class of linear RE models, determinacy implies LS learnability (but not the converse) when individuals have knowledge of current conditions available for use in the learning process. This strong result does not pertain, however, if individuals have available, in the learning process, only information regarding previous values of endogenous variables. One task of the present paper, accordingly, is to investigate the situation that is obtained when only lagged information is available. In particular, it is shown that models that are well formulated, often (but not invariably) possess the property of E-stability and hence LS learnability if current-period information is available in the learning process, even if determinacy does not prevail. Thus plausibility of a RE solution requires both that it be learnable and that the model at hand be well formulated. A sufficient condition for both of these to hold, requiring that certain matrices have positive dominant diagonals, is introduced and considered. Unfortunately, the situation in the case of lagged information is less favorable—that is, learnability can be assured only in special cases, for which no general characterization has been found.

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Bibliographic Info

Paper provided by Central Bank of Chile in its series Working Papers Central Bank of Chile with number 502.

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Date of creation: Oct 2008
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Handle: RePEc:chb:bcchwp:502

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  1. Robert E. Lucas, Jr., 1980. "Rules, Discretion, and the Role of the Economic Advisor," NBER Chapters, in: Rational Expectations and Economic Policy, pages 199-210 National Bureau of Economic Research, Inc.
  2. Benhabib, Jess & Schmitt-Grohe, Stephanie & Uribe, Martin, 2001. "The Perils of Taylor Rules," Journal of Economic Theory, Elsevier, vol. 96(1-2), pages 40-69, January.
  3. Ben S. Bernanke & Michael Woodford, 1997. "Inflation forecasts and monetary policy," Proceedings, Federal Reserve Bank of Cleveland, pages 653-686.
  4. Clarida, Richard & Galí, Jordi & Gertler, Mark, 1999. "The Science of Monetary Policy: A New Keynesian Perspective," CEPR Discussion Papers 2139, C.E.P.R. Discussion Papers.
  5. Kaushik Mitra & James Bullard, . "Learning About Monetary Policy Rules," Discussion Papers 00/41, Department of Economics, University of York.
  6. George W. Evans & Seppo Honkapohja, 2003. "Expectations and the Stability Problem for Optimal Monetary Policies," Review of Economic Studies, Oxford University Press, vol. 70(4), pages 807-824.
  7. Uhlig, H., 1995. "A toolkit for analyzing nonlinear dynamic stochastic models easily," Discussion Paper 1995-97, Tilburg University, Center for Economic Research.
  8. 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.
  9. Athanasios Orphanides & John C. Williams, 2002. "Imperfect knowledge, inflation expectations, and monetary policy," Working Paper Series 2002-04, Federal Reserve Bank of San Francisco.
  10. 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.
  11. 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.
  12. Bennett McCallum, . "On the Relationship Between Determinate and MSV Solutions in Linear RE Models," GSIA Working Papers 2003-E78, Carnegie Mellon University, Tepper School of Business.
  13. McCallum, Bennett T., 1998. "Solutions to linear rational expectations models: a compact exposition," Economics Letters, Elsevier, vol. 61(2), pages 143-147, November.
  14. Evans, George W., 1986. "Selection criteria for models with non-uniqueness," Journal of Monetary Economics, Elsevier, vol. 18(2), pages 147-157, September.
  15. Klein, Paul, 2000. "Using the generalized Schur form to solve a multivariate linear rational expectations model," Journal of Economic Dynamics and Control, Elsevier, vol. 24(10), pages 1405-1423, September.
  16. 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.
  17. Bennett T. McCallum, 2006. "E-Stability vis-a-vis Determinacy Results for a Broad Class of Linear Rational Expectations Models," NBER Working Papers 12441, National Bureau of Economic Research, Inc.
  18. Evans, George W. & Honkapohja, Seppo, 1999. "Learning dynamics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 7, pages 449-542 Elsevier.
  19. James B. Bullard, 2006. "The learnability criterion and monetary policy," Review, Federal Reserve Bank of St. Louis, issue May, pages 203-217.
  20. Blanchard, Olivier Jean & Kahn, Charles M, 1980. "The Solution of Linear Difference Models under Rational Expectations," Econometrica, Econometric Society, vol. 48(5), pages 1305-11, July.
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Cited by:
  1. Vicente da Gama Machado, 2012. "Monetary Policy, Asset Prices and Adaptive Learning," Working Papers Series 274, Central Bank of Brazil, Research Department.

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