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Escape Dynamics: A Continuous—Time Approximation

  • Dmitri Kolyuzhnov
  • Anna Bogomolova
  • Sergey Slobodyan

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.

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Paper provided by The Center for Economic Research and Graduate Education - Economic Institute, Prague in its series CERGE-EI Working Papers with number wp285.

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Date of creation: Jan 2006
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Handle: RePEc:cer:papers:wp285
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  1. George W. Evans & Seppo Honkapohja, 2004. "Adaptive learning and monetary policy design," Macroeconomics 0405008, EconWPA.
  2. Martin Ellison & Tony Yates, 2007. "Escaping Nash and volatile inflation," Bank of England working papers 330, Bank of England.
  3. 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.
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  5. Michele Berardi, 2009. "Escape Dynamics and Policy Specification," Centre for Growth and Business Cycle Research Discussion Paper Series 117, Economics, The Univeristy of Manchester.
  6. 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 - Economic Institute, Prague.
  7. Kaushik Mitra & James Bullard, . "Learning About Monetary Policy Rules," Discussion Papers 00/41, Department of Economics, University of York.
  8. 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.
  9. Barnett, Alina & Ellison, Martin, 2012. "Learning by disinflating," Research Discussion Papers 10/2012, Bank of Finland.
  10. Bruce McGough, 2003. "Shocking Escapes," Computing in Economics and Finance 2003 294, Society for Computational Economics.
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  12. 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.
  13. Cho, In-Koo & Kasa, Kenneth, 2008. "Learning Dynamics And Endogenous Currency Crises," Macroeconomic Dynamics, Cambridge University Press, vol. 12(02), pages 257-285, April.
  14. 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.
  15. 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.
  16. 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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  18. 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.
  19. James Bullard & In-Koo Cho, 2003. "Escapist policy rules," Working Papers 2002-002, Federal Reserve Bank of St. Louis.
  20. Martin Ellison & Tony Yates, 2007. "Escaping Volatile Inflation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(4), pages 981-993, 06.
  21. 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.
  22. N. Williams, 2002. "Stability and Long Run Equilibrium in Stochastic Fictitious Play," Princeton Economic Theory Working Papers cbeeeb49cc8afc83f125df5a8, David K. Levine.
  23. Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-60, September.
  24. Fourgeaud, Claude & Gourieroux, Christian & Pradel, Jacqueline, 1986. "Learning Procedures and Convergence to Rationality," Econometrica, Econometric Society, vol. 54(4), pages 845-68, July.
  25. 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.
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