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Escape Dynamics: A Continuous—Time Approximation

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  • Dmitri Kolyuzhnov
  • Anna Bogomolova
  • Sergey Slobodyan

Abstract

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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Keywords: Constant gain adaptive learning; E—stability; recursive least squares; large deviations theory.;

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  1. Evans, George W. & Honkapohja, Seppo, 2002. "Adaptive learning and monetary policy design," Research Discussion Papers 29/2002, Bank of Finland.
  2. 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.
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  8. Barnett, Alina & Ellison, Martin, 2012. "Learning by disinflating," Research Discussion Papers 10/2012, Bank of Finland.
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  14. Williams, Noah, 2004. "Small noise asymptotics for a stochastic growth model," Journal of Economic Theory, Elsevier, vol. 119(2), pages 271-298, December.
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  16. 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.
  17. N. Williams, 2002. "Stability and Long Run Equilibrium in Stochastic Fictitious Play," Princeton Economic Theory Working Papers cbeeeb49cc8afc83f125df5a8, David K. Levine.
  18. James Bullard & In-Koo Cho, 2003. "Escapist policy rules," Working Papers 2002-002, Federal Reserve Bank of St. Louis.
  19. 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.
  20. 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.
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Cited by:
  1. Sergey Slobodyan & Anna Bogomolova, & Dmitri Kolyuzhnov, 2006. "Stochastic Gradient versus Recursive Least Squares Learning," CERGE-EI Working Papers wp309, The Center for Economic Research and Graduate Education - Economic Institute, Prague.
  2. In-Koo Cho & Kenneth Kasa, 2013. "An Escape Time Interpretation of Robust Control," Discussion Papers dp13-07, Department of Economics, Simon Fraser University.
  3. 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.
  4. Batlome Janjgava, 2013. "Free Entry and Social Efficiency under Unknown Demand Parameters," CERGE-EI Working Papers wp495, The Center for Economic Research and Graduate Education - Economic Institute, Prague.

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