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Escape dynamics: A continuous-time approximation

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  • Kolyuzhnov, Dmitri
  • Bogomolova, Anna
  • Slobodyan, Sergey

Abstract

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 38 (2014)
Issue (Month): C ()
Pages: 161-183

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Handle: RePEc:eee:dyncon:v:38:y:2014:i:c:p:161-183

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Web page: http://www.elsevier.com/locate/jedc

Related research

Keywords: Constant gain adaptive learning; Escape dynamics; Recursive least squares; Large deviations theory;

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  17. 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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Citations

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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. 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.
  3. 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.
  4. Cho, In-Koo & Kasa, Kenneth, 2014. "An escape time interpretation of robust control," Journal of Economic Dynamics and Control, Elsevier, vol. 42(C), pages 1-12.

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