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.
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- 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.
- M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
- Kandori, M. & Mailath, G.J., 1991. "Learning, Mutation, And Long Run Equilibria In Games," Papers 71, Princeton, Woodrow Wilson School - John M. Olin Program.
- 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.
- James Bullard & Kaushik Mitra, 2002.
"Learning about monetary policy rules,"
2000-001, Federal Reserve Bank of St. Louis.
- Bullard, James & Cho, In-Koo, 2003.
"Escapist policy rules,"
CFS Working Paper Series
2003/38, Center for Financial Studies (CFS).
- 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.
- Thomas J. Sargent & Noah Williams, 2003. "Impacts of priors on convergence and escapes from Nash inflation," Working Paper 2003-14, Federal Reserve Bank of Atlanta.
- Bruce McGough, 2006.
Royal Economic Society, vol. 116(511), pages 507-528, 04.
- 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, 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.
- 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.
- 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.
- Cho, In-Koo & Williams, Noah & Sargent, Thomas J, 2002.
"Escaping Nash Inflation,"
Review of Economic Studies,
Wiley Blackwell, vol. 69(1), pages 1-40, January.
- 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.
- In-Koo Cho & Kenneth Kasa, 2003.
"Learning Dynamics and Endogenous Currency Crises,"
Computing in Economics and Finance 2003
132, Society for Computational Economics.
- 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.
- Martin Ellison & Martin Ellison & Alina Barnett, 2011.
"Learning by Disinflating,"
Economics Series Working Papers
579, University of Oxford, Department of Economics.
- Kolyuzhnov, Dmitri & Bogomolova, Anna & Slobodyan, Sergey, 2014.
"Escape dynamics: A continuous-time approximation,"
Journal of Economic Dynamics and Control,
Elsevier, vol. 38(C), pages 161-183.
- Martin Ellison & Tony Yates, 2007. "Escaping Volatile Inflation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(4), pages 981-993, 06.
- Martin Ellison & Tony Yates, 2007.
"Escaping Nash and volatile inflation,"
Bank of England working papers
330, Bank of England.
- Fourgeaud, Claude & Gourieroux, Christian & Pradel, Jacqueline, 1986.
"Learning Procedures and Convergence to Rationality,"
Econometric Society, vol. 54(4), pages 845-68, July.
- Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-60, September.
- N. Williams, 2002. "Stability and Long Run Equilibrium in Stochastic Fictitious Play," Princeton Economic Theory Working Papers cbeeeb49cc8afc83f125df5a8, David K. Levine.
- 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.
- Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
- Michele Berardi, 2009.
"Escape Dynamics and Policy Specification,"
Centre for Growth and Business Cycle Research Discussion Paper Series
117, Economics, The Univeristy of Manchester.
- 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.
- Kenneth Kasa, 2000.
"Learning, large deviations, and recurrent currency crises,"
Working Paper Series
2000-10, Federal Reserve Bank of San Francisco.
- 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.
- 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.
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