Escape Dynamics: A Continuous—Time Approximation
AbstractWe 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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Bibliographic InfoPaper provided by The Center for Economic Research and Graduate Education - Economic Institute, Prague in its series CERGE-EI Working Papers with number wp285.
Date of creation: Jan 2006
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Constant gain adaptive learning; E—stability; recursive least squares; large deviations theory.;
Find related papers by JEL classification:
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
- D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search, Learning, and Information
- E10 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - General
- E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-03-25 (All new papers)
- NEP-CBA-2006-03-25 (Central Banking)
- NEP-MAC-2006-03-25 (Macroeconomics)
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