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|
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- George W. Evans & Seppo Honkapohja, 2003.
"Adaptive learning and monetary policy design,"
Federal Reserve Bank of Cleveland, pages 1045-1084.
- Evans, George W. & Honkapohja, Seppo, 2003. "Adaptive Learning and Monetary Policy Design," CEPR Discussion Papers 3962, C.E.P.R. Discussion Papers.
- 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, 2004. "Adaptive learning and monetary policy design," Macroeconomics 0405008, EconWPA.
- 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.
- N. Williams, 2002. "Stability and Long Run Equilibrium in Stochastic Fictitious Play," Princeton Economic Theory Working Papers cbeeeb49cc8afc83f125df5a8, David K. Levine.
- 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.
- 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.
- Fourgeaud, Claude & Gourieroux, Christian & Pradel, Jacqueline, 1986.
"Learning Procedures and Convergence to Rationality,"
Econometric Society, vol. 54(4), pages 845-68, July.
- James B. Bullard & In-Koo Cho, 2003.
"Escapist policy rules,"
2002-002, Federal Reserve Bank of St. Louis.
- Bullard, James & Mitra, Kaushik, 2002.
"Learning about monetary policy rules,"
Journal of Monetary Economics,
Elsevier, vol. 49(6), pages 1105-1129, September.
- Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-60, September.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
- 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.
- Bruce McGough, 2006.
Royal Economic Society, vol. 116(511), pages 507-528, 04.
- 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.
- Martin Ellison & Tony Yates, 2007.
"Escaping Nash and volatile inflation,"
Bank of England working papers
330, Bank of England.
- 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.
- Cho, In-Koo & Kasa, Kenneth, 2008.
"Learning Dynamics And Endogenous Currency Crises,"
Cambridge University Press, vol. 12(02), pages 257-285, April.
- Martin Ellison & Tony Yates, 2007. "Escaping Volatile Inflation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(4), pages 981-993, 06.
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