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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

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

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  1. 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.
  2. In-Koo Cho & Kenneth Kasa, 2003. "Learning Dynamics and Endogenous Currency Crises," Computing in Economics and Finance 2003 132, Society for Computational Economics.
  3. Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-60, September.
  4. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
  5. Bullard, James & Cho, In-Koo, 2003. "Escapist policy rules," CFS Working Paper Series 2003/38, Center for Financial Studies (CFS).
  6. N. Williams, 2002. "Stability and Long Run Equilibrium in Stochastic Fictitious Play," Princeton Economic Theory Working Papers cbeeeb49cc8afc83f125df5a8, David K. Levine.
  7. Cho, In-Koo & Sargent, Thomas J., 2000. "Escaping Nash inflation," Working Paper Series 0023, European Central Bank.
  8. Robert J. Barro & David B. Gordon, 1983. "Rules, Discretion and Reputation in a Model of Monetary Policy," NBER Working Papers 1079, National Bureau of Economic Research, Inc.
  9. Bruce McGough, 2003. "Shocking Escapes," Computing in Economics and Finance 2003 294, Society for Computational Economics.
  10. George W. Evans & Seppo Honkapohja, 2004. "Adaptive learning and monetary policy design," Macroeconomics 0405008, EconWPA.
  11. Bullard, James & Mitra, Kaushik, 2002. "Learning about monetary policy rules," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1105-1129, September.
  12. Thomas J. Sargent & Noah Williams, 2003. "Impacts of priors on convergence and escapes from Nash inflation," Working Paper 2003-14, Federal Reserve Bank of Atlanta.
  13. Binmore, Ken & Samuelson, Larry, 1997. "Muddling Through: Noisy Equilibrium Selection," Journal of Economic Theory, Elsevier, vol. 74(2), pages 235-265, June.
  14. 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 473-91, June.
  15. Martin Ellison & Tony Yates, 2007. "Escaping Nash and volatile inflation," Bank of England working papers 330, Bank of England.
  16. 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.
  17. Martin Ellison & Martin Ellison & Alina Barnett, 2011. "Learning by Disinflating," Economics Series Working Papers 579, University of Oxford, Department of Economics.
  18. Noah Williams, 2003. "Small Noise Asymptotics for a Stochastic Growth Model," NBER Working Papers 10194, National Bureau of Economic Research, Inc.
  19. 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, 02.
  20. 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.
  21. Martin Ellison & Tony Yates, 2007. "Escaping Volatile Inflation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 39(4), pages 981-993, 06.
  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. Michele Berardi, 2009. "Escape Dynamics and Policy Specification," Centre for Growth and Business Cycle Research Discussion Paper Series 117, Economics, The Univeristy of Manchester.
  24. Fourgeaud Claude & Gourieroux Christian & Pradel J, 1984. "Learning procedure and convergence to rationality," CEPREMAP Working Papers (Couverture Orange) 8411, CEPREMAP.
  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. 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.
  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. In-Koo Cho & Kenneth Kasa, 2013. "An Escape Time Interpretation of Robust Control," Discussion Papers dp13-07, Department of Economics, Simon Fraser University.
  4. 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.

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