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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. 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.
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  17. 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.
  18. 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.
  19. 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.
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  22. Berardi, Michele, 2013. "Escape Dynamics And Policy Specification," Macroeconomic Dynamics, Cambridge University Press, vol. 17(01), pages 123-142, January.
  23. Cho, In-Koo & Kasa, Kenneth, 2008. "Learning Dynamics And Endogenous Currency Crises," Macroeconomic Dynamics, Cambridge University Press, vol. 12(02), pages 257-285, April.
  24. Ellison, Martin & Yates, Tony, 2007. "Escaping Nash and Volatile Inflation," CEPR Discussion Papers 6483, C.E.P.R. Discussion Papers.
  25. Kenneth Kasa, 2000. "Learning, large deviations, and recurrent currency crises," Working Paper Series 2000-10, Federal Reserve Bank of San Francisco.
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