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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.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:dyncon:v:38:y:2014:i:c:p:161-183 DOI: 10.1016/j.jedc.2013.10.006
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    1. Kolyuzhnov, Dmitri & Bogomolova, Anna & Slobodyan, Sergey, 2014. "Escape dynamics: A continuous-time approximation," Journal of Economic Dynamics and Control, Elsevier, pages 161-183.
    2. Thomas J. Sargent & Noah Williams, 2005. "Impacts of Priors on Convergence and Escapes from Nash Inflation," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 8(2), pages 360-391, April.
    3. Williams, Noah, 2004. "Small noise asymptotics for a stochastic growth model," Journal of Economic Theory, Elsevier, pages 271-298.
    4. Barro, Robert J. & Gordon, David B., 1983. "Rules, discretion and reputation in a model of monetary policy," Journal of Monetary Economics, Elsevier, vol. 12(1), pages 101-121.
    5. Marcet, Albert & Sargent, Thomas J., 1989. "Convergence of least squares learning mechanisms in self-referential linear stochastic models," Journal of Economic Theory, Elsevier, vol. 48(2), pages 337-368, August.
    6. Bullard, James & Cho, In-Koo, 2005. "Escapist policy rules," Journal of Economic Dynamics and Control, Elsevier, vol. 29(11), pages 1841-1865, November.
    7. Ellison, Martin & Yates, Tony, 2007. "Escaping Nash and Volatile Inflation," CEPR Discussion Papers 6483, C.E.P.R. Discussion Papers.
    8. Evans, George W & Honkapohja, Seppo, 1995. "Local Convergence of Recursive Learning to Steady States and Cycles in Stochastic Nonlinear Models," Econometrica, Econometric Society, vol. 63(1), pages 195-206, January.
    9. Bullard, James & Mitra, Kaushik, 2002. "Learning about monetary policy rules," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1105-1129, September.
    10. Bruce McGough, 2006. "Shocking Escapes," Economic Journal, Royal Economic Society, vol. 116(511), pages 507-528, April.
    11. Fourgeaud, Claude & Gourieroux, Christian & Pradel, Jacqueline, 1986. "Learning Procedures and Convergence to Rationality," Econometrica, Econometric Society, vol. 54(4), pages 845-868, July.
    12. Alina Barnett & Martin Ellison, 2013. "Learning by Disinflating," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 45(4), pages 731-746, June.
    13. Kandori, Michihiro & Mailath, George J & Rob, Rafael, 1993. "Learning, Mutation, and Long Run Equilibria in Games," Econometrica, Econometric Society, pages 29-56.
    14. George W. Evans & Seppo Honkapohja, 2003. "Adaptive learning and monetary policy design," Proceedings, Federal Reserve Bank of Cleveland, pages 1045-1084.
    15. Martin Ellison & Tony Yates, 2007. "Escaping Volatile Inflation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(4), pages 981-993, June.
    16. N. Williams, 2002. "Stability and Long Run Equilibrium in Stochastic Fictitious Play," Princeton Economic Theory Working Papers cbeeeb49cc8afc83f125df5a8, David K. Levine.
    17. Kenneth Kasa, 2004. "Learning, Large Deviations, And Recurrent Currency Crises," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 45(1), pages 141-173, February.
    18. Berardi, Michele, 2013. "Escape Dynamics And Policy Specification," Macroeconomic Dynamics, Cambridge University Press, vol. 17(01), pages 123-142, January.
    19. Cho, In-Koo & Kasa, Kenneth, 2008. "Learning Dynamics And Endogenous Currency Crises," Macroeconomic Dynamics, Cambridge University Press, pages 257-285.
    20. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
    21. In-Koo Cho & Noah Williams & Thomas J. Sargent, 2002. "Escaping Nash Inflation," Review of Economic Studies, Oxford University Press, vol. 69(1), pages 1-40.
    22. 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.
    23. Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-1160, September.
    24. 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 473-491, June.
    25. 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.
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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 - Economics Institute, Prague.
    2. 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.
    3. Kolyuzhnov, Dmitri & Bogomolova, Anna & Slobodyan, Sergey, 2014. "Escape dynamics: A continuous-time approximation," Journal of Economic Dynamics and Control, Elsevier, 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 - Economics Institute, Prague.

    More about this item

    Keywords

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

    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; Information and Knowledge; Communication; Belief; Unawareness
    • E10 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - General
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications

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