Escape Dynamics: A Continuous—Time Approximation

Dmitri Kolyuzhnov, Anna Bogomolova and Sergey Slobodyan

CERGE-EI Working Papers from The Center for Economic Research and Graduate Education - Economics Institute, Prague

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.

Keywords: Constant gain adaptive learning; E—stability; recursive least squares; large deviations theory. (search for similar items in EconPapers)
JEL-codes: C62 C65 D83 E10 E17 (search for similar items in EconPapers)
Date: 2006-01
New Economics Papers: this item is included in nep-cba and nep-mac
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Journal Article: Escape dynamics: A continuous-time approximation (2014)
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