Escape Dynamics: A Continuous—Time Approximation
We extend a continuous—time approach to the analysis of escape dynamics in economic models with adaptive learning with constant gain. This approach is based on applying results of continuous—time version of large deviations theory to the diffusion approximation of the original discrete—time dynamics under learning. We characterize escape dynamics by analytically deriving the most probable escape point and mean escape time. The continuous—time approach is tested on the Phelps problem of a government controlling inflation while adaptively learning the approximate Phillips curve, studied previously by Sargent (1999) and Cho, Williams and Sargent (2002) (henceforth, CWS). We compare the results with simulations and the results obtained by CWS. We express reservations regarding applicability of escape dynamics theory to characterization of mean escape time for economically plausible values of constant gain in the model of CWS.We show that for these values of the gain simple considerations and formulae generate much better mean escape time results than the large deviations theory. We explain it by insufficient averaging near the point of self—confirming equilibrium for relatively large gains and suggest two changes which might help the approaches based on large deviation theory to work better in this gain interval.
|Date of creation:||Jan 2006|
|Contact details of provider:|| Postal: P.O. Box 882, Politickych veznu 7, 111 21 Praha 1|
Phone: (+420) 224 005 123
Fax: (+420) 224 005 333
Web page: http://www.cerge-ei.cz
More information through EDIRC
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.:
- Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993.
"Learning, Mutation, and Long Run Equilibria in Games,"
Econometric Society, vol. 61(1), pages 29-56, January.
- Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
- M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
- James B. Bullard & In-Koo Cho, 2003.
"Escapist policy rules,"
2002-002, Federal Reserve Bank of St. Louis.
- Kenneth Kasa, 2004.
"Learning, Large Deviations, And Recurrent Currency Crises,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(1), pages 141-173, 02.
- Kenneth Kasa, 2000. "Learning, large deviations, and recurrent currency crises," Working Paper Series 2000-10, Federal Reserve Bank of San Francisco.
- James B. Bullard & Kaushik Mitra, 2002.
"Learning about monetary policy rules,"
2000-001, Federal Reserve Bank of St. Louis.
- Ellison, Martin & Yates, Tony, 2007.
"Escaping Nash and Volatile Inflation,"
CEPR Discussion Papers
6483, C.E.P.R. Discussion Papers.
- Robert J. Barro & David B. Gordon, 1983.
"Rules, Discretion and Reputation in a Model of Monetary Policy,"
NBER Working Papers
1079, National Bureau of Economic Research, Inc.
- Barro, Robert J. & Gordon, David B., 1983. "Rules, discretion and reputation in a model of monetary policy," Journal of Monetary Economics, Elsevier, vol. 12(1), pages 101-121.
- George W. Evans & Seppo Honkapohja, 2003.
"Adaptive learning and monetary policy design,"
Federal Reserve Bank of Cleveland, pages 1045-1084.
- George W. Evans & Seppo Honkapohja, 2002. "Adaptive Learning and Monetary Policy Design," University of Oregon Economics Department Working Papers 2002-18, University of Oregon Economics Department, revised 04 Mar 2004.
- George W. Evans & Seppo Honkapohja, 2004. "Adaptive learning and monetary policy design," Macroeconomics 0405008, EconWPA.
- Evans, George W. & Honkapohja, Seppo, 2002. "Adaptive learning and monetary policy design," Research Discussion Papers 29/2002, Bank of Finland.
- Evans, George W. & Honkapohja, Seppo, 2003. "Adaptive Learning and Monetary Policy Design," CEPR Discussion Papers 3962, C.E.P.R. Discussion Papers.
- Williams, Noah, 2004.
"Small noise asymptotics for a stochastic growth model,"
Journal of Economic Theory,
Elsevier, vol. 119(2), pages 271-298, December.
- Noah Williams, 2003. "Small Noise Asymptotics for a Stochastic Growth Model," NBER Working Papers 10194, National Bureau of Economic Research, Inc.
- Noah Williams, 2003. "Small Noise Asymptotics for a Stochastic Growth Model," Computing in Economics and Finance 2003 262, Society for Computational Economics.
- Evans, George W & Honkapohja, Seppo, 1995. "Local Convergence of Recursive Learning to Steady States and Cycles in Stochastic Nonlinear Models," Econometrica, Econometric Society, vol. 63(1), pages 195-206, January.
- Martin Ellison & Tony Yates, 2007. "Escaping Volatile Inflation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(4), pages 981-993, 06.
- Barnett, Alina & Ellison, Martin, 2012.
"Learning by disinflating,"
Research Discussion Papers
10/2012, Bank of Finland.
- Evans George W. & Honkapohja Seppo, 1994. "On the Local Stability of Sunspot Equilibria under Adaptive Learning Rules," Journal of Economic Theory, Elsevier, vol. 64(1), pages 142-161, October.
- Dmitri Kolyuzhnov & Anna Bogomolova & Sergey Slobodyan, 2006.
"Escape Dynamics: A Continuous—Time Approximation,"
CERGE-EI Working Papers
wp285, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
- Fourgeaud, Claude & Gourieroux, Christian & Pradel, Jacqueline, 1986.
"Learning Procedures and Convergence to Rationality,"
Econometric Society, vol. 54(4), pages 845-868, July.
- Evans, George W. & Honkapohja, Seppo & Honkapohja, Seppo, 1994. "Learning, convergence, and stability with multiple rational expectations equilibria," European Economic Review, Elsevier, vol. 38(5), pages 1071-1098, May.
- Bruce McGough, 2006.
Royal Economic Society, vol. 116(511), pages 507-528, 04.
- 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.
- N. Williams, 2002. "Stability and Long Run Equilibrium in Stochastic Fictitious Play," Princeton Economic Theory Working Papers cbeeeb49cc8afc83f125df5a8, David K. Levine.
- Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
- Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-1160, September.
- In-Koo Cho & Kenneth Kasa, 2003.
"Learning Dynamics and Endogenous Currency Crises,"
Computing in Economics and Finance 2003
132, Society for Computational Economics.
- Kydland, Finn E & Prescott, Edward C, 1977. "Rules Rather Than Discretion: The Inconsistency of Optimal Plans," Journal of Political Economy, University of Chicago Press, vol. 85(3), pages 473-491, June.
- In-Koo Cho & Noah Williams & Thomas J. Sargent, 2002.
"Escaping Nash Inflation,"
Review of Economic Studies,
Oxford University Press, vol. 69(1), pages 1-40.
- Thomas J. Sargent & Noah Williams, 2005.
"Impacts of Priors on Convergence and Escapes from Nash Inflation,"
Review of Economic Dynamics,
Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 360-391, April.
- Thomas J. Sargent & Noah Williams, 2003. "Impacts of priors on convergence and escapes from Nash inflation," FRB Atlanta Working Paper 2003-14, Federal Reserve Bank of Atlanta.
- Michele Berardi, 2009.
"Escape Dynamics and Policy Specification,"
Centre for Growth and Business Cycle Research Discussion Paper Series
117, Economics, The Univeristy of Manchester.
When requesting a correction, please mention this item's handle: RePEc:cer:papers:wp285. 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: (Jana Koudelkova)
If references are entirely missing, you can add them using this form.