Escape dynamics as a way to describe economic phenomena

Abstract
This paper presents the review of issues and approaches to the analysis of escape dynamics in economic models with constant gain adaptive learning which is used to model and describe the behavior of various (macroeconomic as well as microeconomic) variables in diverse economic phenomena such as currency crises, inflation episodes, endogenous collusion in oligopoly, and cycles of economic activity. This review considers and contrasts two currently existing approaches to the analysis of escape dynamics: the discrete-time approach employed, for example, by Cho, Williams and Sargent (2002), and the continuous-time approach proposed by Kasa (2004) and extended recently by Kolyuzhnov, Bogomolova and Slobodyan (2014), stressing the advantages of the latter. The continuous-time approach is based on the application of the results of the continuous-time version of the large deviations theory to the diffusion approximation of the original discrete-time dynamics under learning. Escape dynamics is characterized by analytically deriving the most probable escape point and mean escape time. The paper provides an example of the continuous-time approach applied to the Phelps problem of a government controlling inflation while adaptively learning the approximate Phillips curve.

Keywords
constant gain adaptive learning, escape dynamics, recursive least squares, large deviations theory



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