Escape dynamics: A continuous-time approximation
We extend a continuous-time approximation approach to the analysis of escape dynamics in economic models with constant gain adaptive learning. This approach is based on the application of the results of continuous-time version of large deviations theory to the linear 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 approximation is tested on the Phelps problem of a government controlling inflation while adaptively learning a misspecified Phillips curve, studied previously by Sargent (1999) and Cho et al. (2002) (henceforth, CWS), among others. We compare our results with simulations extended to very low values of the constant gain and show that, for the lowest gains, our approach approximates simulations relatively well. We express reservations regarding the applicability of any approach based on large deviations theory to characterizing escape dynamics for economically plausible values of constant gain in the model of CWS when escapes are not rare. We show that for these values of the gain it is possible to derive first passage times for learning dynamics reduced to one dimension without resort to large deviations theory. This procedure delivers mean escape time results that fit the simulations closely. We explain inapplicability of large deviations theory by insufficient averaging near the point of self-confirming equilibrium for relatively large gains which makes escapes relatively frequent, suggest the changes which might help approaches based on the theory to work better in this gain interval, and describe a simple heuristic method for determining the range of constant gain values for which large deviations theory could be applicable.
If 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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
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.:
- Noah Williams, 2003.
"Small Noise Asymptotics for a Stochastic Growth Model,"
Computing in Economics and Finance 2003
262, Society for Computational Economics.
- 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.
- 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.
- Cho, In-Koo & Kasa, Kenneth, 2008.
"Learning Dynamics And Endogenous Currency Crises,"
Cambridge University Press, vol. 12(02), pages 257-285, April.
- Bullard, James & Cho, In-Koo, 2005.
"Escapist policy rules,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 29(11), pages 1841-1865, November.
- N. Williams, 2002. "Stability and Long Run Equilibrium in Stochastic Fictitious Play," Princeton Economic Theory Working Papers cbeeeb49cc8afc83f125df5a8, David K. Levine.
- James B. Bullard & Kaushik Mitra, 2002.
"Learning about monetary policy rules,"
2000-001, Federal Reserve Bank of St. Louis.
- Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-60, September.
- Berardi, Michele, 2013.
"Escape Dynamics And Policy Specification,"
Cambridge University Press, vol. 17(01), pages 123-142, January.
- Michele Berardi, 2009. "Escape Dynamics and Policy Specification," Centre for Growth and Business Cycle Research Discussion Paper Series 117, Economics, The Univeristy of Manchester.
- 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.
- 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.
- George W. Evans & Seppo Honkapohja, 2004.
"Adaptive learning and monetary policy design,"
- 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.
- 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.
- Cho, In-Koo & Sargent, Thomas J., 2000.
"Escaping Nash inflation,"
Working Paper Series
0023, European Central Bank.
- 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.
- Thomas J. Sargent & Noah William, 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.
- 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.
- Kandori, M. & Mailath, G.J., 1991.
"Learning, Mutation, And Long Run Equilibria In Games,"
71, Princeton, Woodrow Wilson School - John M. Olin Program.
- Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, vol. 61(1), pages 29-56, January.
- M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
- Martin Ellison & Tony Yates, 2007.
"Escaping Nash and volatile inflation,"
Bank of England working papers
330, Bank of England.
- 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.
- 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.
- Fourgeaud Claude & Gourieroux Christian & Pradel J, 1984.
"Learning procedure and convergence to rationality,"
CEPREMAP Working Papers (Couverture Orange)
- Fourgeaud, Claude & Gourieroux, Christian & Pradel, Jacqueline, 1986. "Learning Procedures and Convergence to Rationality," Econometrica, Econometric Society, vol. 54(4), pages 845-68, July.
- Martin Ellison & Tony Yates, 2007. "Escaping Volatile Inflation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(4), pages 981-993, 06.
- 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.
- Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
- 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 473-91, June.
- 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.
- Bruce McGough, 2006.
Royal Economic Society, vol. 116(511), pages 507-528, 04.
When requesting a correction, please mention this item's handle: RePEc:eee:dyncon:v:38:y:2014:i:c:p:161-183. 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: (Zhang, Lei)
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.