This paper employs the Hopf bifurcation theorem to prove the existence of complicated equilibrium trajectories under least squares learning in a standard version of the overlapping generations model. The periodic and quasiperiodic learning equilibria exist when the locally unique perfect foresight equilibrium is the monetary steady state, and thus are induced by the introduction of learning alone. Learning equilibria can be stable or unstable depending on higher order derivatives of the underlying utility function not specified by economic theory; examples of both attracting and repelling invariant dosed curves are provided. This research confirms the intuition of some previous authors, who have suggested that stationary equilibrium trajectories under learning may differ from those under rational expectations. I would like to thank Robert Becker and members of my dissertation committee for helpful comments on this and related work. Suggestions made by Michael Woodford materially improved this paper. I also thank Albert Marcet, Mark Salmon, George Evans, Seppo Honkapohja, and participants at the June 1991 Meetings of the Society for Economic Dynamics and Control in Capri, Italy, and the May 1991 Midwest Mathematical Economics meeting at Northwestern University, for helpful discussions. All errors are the author's responsibility.
(This abstract was borrowed from another version of this item.)
References listed on IDEAS
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.:
- Marcet, Albert & Sargent, Thomas J, 1988. "The Fate of Systems with "Adaptive" Expectations," American Economic Review, American Economic Association, vol. 78(2), pages 168-172, May.
- Marcet, Albert & Sargent, Thomas J, 1989. "Convergence of Least-Squares Learning in Environments with Hidden State Variables and Private Information," Journal of Political Economy, University of Chicago Press, vol. 97(6), pages 1306-1322, December.
- Sargent, Thomas J., 1991. "Equilibrium with signal extraction from endogenous variables," Journal of Economic Dynamics and Control, Elsevier, vol. 15(2), pages 245-273, April.
- 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.
- Grandmont, Jean-Michel, 1985.
"On Endogenous Competitive Business Cycles,"
Econometric Society, vol. 53(5), pages 995-1045, September.
- Grandmont Jean-michel, 1983. "On endogenous competitive business cycles," CEPREMAP Working Papers (Couverture Orange) 8316, CEPREMAP.
- George Evans, 1985. "Expectational Stability and the Multiple Equilibria Problem in Linear Rational Expectations Models," The Quarterly Journal of Economics, Oxford University Press, vol. 100(4), pages 1217-1233.
- Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December. Full references (including those not matched with items on IDEAS)
When requesting a correction, please mention this item's handle: RePEc:eee:jetheo:v:64:y:1994:i:2:p:468-485. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu)
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.