Determinacy and Stability under Learning of Rational Expectations Equilibria
AbstractThis paper studies relationships between the local determinacy of a stationary equilibrium in the perfect foresight dynamics, and its local stability in dynamics arising from econometric learning procedures. Attention is focused on linear scalar economies where agents forecast only one period ahead, and with an arbitrary, but fixed, number of predetermined variables. In such a framework, it is well known that there are no clear links between the determinacy of the stationary state in the perfect foresight dynamics on the levels of the state variable, and its stability under learning. The paper emphasizes, however, that this is not the right perfect foresight dynamics to look at whenever agents try to learn the coefficients of the perfect foresight dynamics restricted to an eigenspace of lower dimension. Indeed the paper introduces a growth rate perfect foresight dynamics on these coefficients and proves equivalence between determinacy in that dynamics and stability under learning provided that a simple sign condition is satisfied.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by HAL in its series Post-Print with number hal-00731065.
Date of creation: Feb 2002
Date of revision:
Publication status: Published, Journal of Economic Theory, 2002, 102, 2, 354-374
Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00731065
Contact details of provider:
Web page: http://hal.archives-ouvertes.fr/
rational expectations; determinacy; learning; expectational stability;
Other versions of this item:
- Gauthier, Stephane, 2002. "Determinacy and Stability under Learning of Rational Expectations Equilibria," Journal of Economic Theory, Elsevier, Elsevier, vol. 102(2), pages 354-374, February.
- Gauthier, S., 1999. "Determinacy and Stability under Learning of Rational Expectations Equilibria," DELTA Working Papers, DELTA (Ecole normale supÃ©rieure) 1999-22, DELTA (Ecole normale supérieure).
- Gauthier, S., 1999. "Determinacy and Stability Under Learning of Rational Expectations Equilibria," G.R.E.Q.A.M., Universite Aix-Marseille III 99a46, Universite Aix-Marseille III.
- E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Evans, George W. & Honkapohja, S., 1998.
"Stochastic gradient learning in the cobweb model,"
Economics Letters, Elsevier,
Elsevier, vol. 61(3), pages 333-337, December.
- Evans, G.W. & Honkapohja, S., 1998. "Stochastic Gradient Learning in the Cobweb Model," University of Helsinki, Department of Economics, Department of Economics 438, Department of Economics.
- Grandmont, Jean-Michel & Laroque, Guy, 1986.
"Stability of cycles and expectations,"
Journal of Economic Theory, Elsevier,
Elsevier, vol. 40(1), pages 138-151, October.
- Woodford, Michael, 1990.
"Learning to Believe in Sunspots,"
Econometrica, Econometric Society,
Econometric Society, vol. 58(2), pages 277-307, March.
- Woodford, Michael, 1986. "Learning to Believe in Sunspots," Working Papers, C.V. Starr Center for Applied Economics, New York University 86-16, C.V. Starr Center for Applied Economics, New York University.
- GRANDMONT, Jean-Michel, 1997.
"Expectations formation and stability of large socioeconomic systems,"
CORE Discussion Papers, UniversitÃ© catholique de Louvain, Center for Operations Research and Econometrics (CORE)
1997088, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Jean-Michel Grandmont, 1998. "Expectations Formation and Stability of Large Socioeconomic Systems," Econometrica, Econometric Society, Econometric Society, vol. 66(4), pages 741-782, July.
- Jean-Michel Grandmont, 1997. "Expectations Formation and Stability of Large Socioeconomic Systems," Working Papers, Centre de Recherche en Economie et Statistique 97-27, Centre de Recherche en Economie et Statistique.
- Grandmont, Jean-Michel, 1994. "Expectations formation and stability of large socioeconomic systems," CEPREMAP Working Papers (Couverture Orange) 9424, CEPREMAP.
- Duffy John, 1994. "On Learning and the Nonuniqueness of Equilibrium in an Overlapping Generations Model with Fiat Money," Journal of Economic Theory, Elsevier, Elsevier, vol. 64(2), pages 541-553, December.
- Reichlin, Pietro, 1986. "Equilibrium cycles in an overlapping generations economy with production," Journal of Economic Theory, Elsevier, Elsevier, vol. 40(1), pages 89-102, October.
- Lucas, Robert E, Jr, 1986. "Adaptive Behavior and Economic Theory," The Journal of Business, University of Chicago Press, University of Chicago Press, vol. 59(4), pages S401-26, October.
- Evans, George W., 1989. "The fragility of sunspots and bubbles," Journal of Monetary Economics, Elsevier, Elsevier, vol. 23(2), pages 297-317, March.
- Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, Elsevier, vol. 48(2), pages 337-368, August.
- Roger Guesnerie, 2008.
"Macroeconomic And Monetary Policies From The Eductive Viewpoint,"
Working Papers Central Bank of Chile, Central Bank of Chile
498, Central Bank of Chile.
- Roger Guesnerie, 2009. "Macroeconomic and Monetary Policies from the Eductive Viewpoint," Central Banking, Analysis, and Economic Policies Book Series, Central Bank of Chile, in: Klaus Schmidt-Hebbel & Carl E. Walsh & Norman Loayza (Series Editor) & Klaus Schmidt-Hebbel (Series (ed.), Monetary Policy under Uncertainty and Learning, edition 1, volume 13, chapter 6, pages 171-202 Central Bank of Chile.
- Roger Guesnerie, 2008. "Macroeconomic and monetary policies from the "eductive" viewpoint," PSE Working Papers halshs-00586749, HAL.
- repec:hal:wpaper:halshs-00586749 is not listed on IDEAS
- Bennett McCallum, 2004.
"On the Relationship Between Determinate and MSV Solutions in Linear RE Models,"
NBER Technical Working Papers
0297, National Bureau of Economic Research, Inc.
- McCallum, Bennett T., 2004. "On the relationship between determinate and MSV solutions in linear RE models," Economics Letters, Elsevier, Elsevier, vol. 84(1), pages 55-60, July.
- Bennett McCallum, . "On the Relationship Between Determinate and MSV Solutions in Linear RE Models," GSIA Working Papers, Carnegie Mellon University, Tepper School of Business 2003-E78, Carnegie Mellon University, Tepper School of Business.
- Desgranges, Gabriel & Negroni, Giorgio, 2003.
"Expectations Coordination On A Sunspot Equilibrium: An Eductive Approach,"
Macroeconomic Dynamics, Cambridge University Press,
Cambridge University Press, vol. 7(01), pages 7-41, February.
- G. Desgranges & G. Negroni, 2001. "Expectations Coordination on a Sunspot Equilibrium: an Eductive Approach," THEMA Working Papers 2001-13, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
- Roger Guesnerie & Pedro Jara-Moroni, 2011. "Expectational coordination in simple economic contexts," Economic Theory, Springer, Springer, vol. 47(2), pages 205-246, June.
- repec:hal:wpaper:halshs-00574957 is not listed on IDEAS
- Jara-Moroni, Pedro, 2012. "Rationalizability in games with a continuum of players," Games and Economic Behavior, Elsevier, Elsevier, vol. 75(2), pages 668-684.
- Seonghoon Cho & Antonio Moreno, 2006. "Expectational Stability in Multivariate Models," Faculty Working Papers, School of Economics and Business Administration, University of Navarra 06/08, School of Economics and Business Administration, University of Navarra.
- Gauthier, Stephane, 2004.
"Determinacy in linear rational expectations models,"
Journal of Mathematical Economics,
Elsevier, vol. 40(7), pages 815-830, November.
- Stéphane Gauthier, 2004. "Determinacy in Linear Rational Expectations Models," Post-Print, HAL hal-00731138, HAL.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.