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Escape Dynamics: A Continuous Time Approximation

  • Dmitri Kolyuzhnov
  • Anna Bogomolova
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    In this paper we provide explicit characterization of the escape dynamics for the Phellps problem of government controlling inflation with adaptive learning of the approximate Phillips curve, alternative to the one considered by Cho, Williams and Sargent (2002). Our approach is based on approximating the discrete-time stochastic recursive algorithm, which describes dynamics with learning in this problem, by the limiting diffusion. We characterize the escape dynamics (escape time and dominant escape path) for this limit process. CWS derive the characteristics of the escape dynamics for the original discrete time stochastic recursive algorithm using extension of the Freidlin and Wentzell (1998) large deviations theory by Dupuis and Kushner (1989). This theory allows one to derive the escape time and the dominant escape path for discrete time models with bounded shocks, but not unbounded (Gaussian) shocks. In the latter case only the upper bound of probability of large deviations can be derived, while both upper and lower bounds on this probability are necessary to derive the escape times and dominant escape path. Switching to continuous time approximation allows us to avoid the problem of unboundedness of shocks in discrete time. It allows us to use well-developed theory of large deviations for continuous time processes to characterize fully the escape dynamics with unbounded continuous-time shocks by using Euler and Hamilton-Jacobi differential equations.

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    Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2004 with number 190.

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    Date of creation: 11 Aug 2004
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    Handle: RePEc:sce:scecf4:190
    Contact details of provider: Web page: http://comp-econ.org/
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    1. Barro, Robert J & Gordon, David B, 1983. "A Positive Theory of Monetary Policy in a Natural Rate Model," Journal of Political Economy, University of Chicago Press, vol. 91(4), pages 589-610, August.
    2. Woodford, Michael, 1990. "Learning to Believe in Sunspots," Econometrica, Econometric Society, vol. 58(2), pages 277-307, March.
    3. Lawrence J. Christiano & Sharon G. Harrison, 1996. "Chaos, Sunspots, and Automatic Stabilizers," NBER Working Papers 5703, National Bureau of Economic Research, Inc.
    4. 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.
    5. Jess Benhabib & Roger E.A. Farmer, 1992. "Indeterminacy and Increasing Returns," UCLA Economics Working Papers 646, UCLA Department of Economics.
    6. Philippe Aghion & Philippe Bacchetta & Abhijit Banerjee, 2000. "Currency Crises and Monetary Policy in an Economy with Credit Constraints," Working Papers 00.07, Swiss National Bank, Study Center Gerzensee.
    7. Azariadis, Costas, 1981. "Self-fulfilling prophecies," Journal of Economic Theory, Elsevier, vol. 25(3), pages 380-396, December.
    8. 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.
    9. Jean-Michel Grandmont, 1998. "Expectations Formation and Stability of Large Socioeconomic Systems," Econometrica, Econometric Society, vol. 66(4), pages 741-782, July.
    10. Cho, In-Koo & Kasa, Kenneth, 2008. "Learning Dynamics And Endogenous Currency Crises," Macroeconomic Dynamics, Cambridge University Press, vol. 12(02), pages 257-285, April.
    11. Alfred Greiner & Willi Semmler, 1996. "Multiple steady states, indeterminacy, and cycles in a basic model of endogenous growth," Journal of Economics, Springer, vol. 63(1), pages 79-99, February.
    12. Paul M Romer, 1999. "Increasing Returns and Long-Run Growth," Levine's Working Paper Archive 2232, David K. Levine.
    13. Fourgeaud Claude & Gourieroux Christian & Pradel J, 1984. "Learning procedure and convergence to rationality," CEPREMAP Working Papers (Couverture Orange) 8411, CEPREMAP.
    14. Benhabib, Jess & Farmer, Roger E.A., 1996. "Indeterminacy and Sector-Specific Externalities," Working Papers 96-12, C.V. Starr Center for Applied Economics, New York University.
    15. Benhabib, Jess & Schmitt-Grohe, Stephanie & Uribe, Martin, 1998. "The Perils of Taylor Rules," Working Papers 98-37, C.V. Starr Center for Applied Economics, New York University.
    16. 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.
    17. Bray, Margaret M & Savin, Nathan E, 1986. "Rational Expectations Equilibria, Learning, and Model Specification," Econometrica, Econometric Society, vol. 54(5), pages 1129-60, September.
    18. Benhabib, Jess & Farmer, Roger E.A., 1999. "Indeterminacy and sunspots in macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 6, pages 387-448 Elsevier.
    19. Noah Williams, 2003. "Small Noise Asymptotics for a Stochastic Growth Model," Computing in Economics and Finance 2003 262, Society for Computational Economics.
    20. 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.
    21. James B. Bullard & In-Koo Cho, 2003. "Escapist policy rules," Working Papers 2002-002, Federal Reserve Bank of St. Louis.
    22. 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.
    23. Benhabib, Jess & Perli, Roberto & Xie, Danyang, 1994. "Monopolistic competition, indeterminacy and growth," MPRA Paper 37411, University Library of Munich, Germany, revised 1994.
    24. Evans, George W. & Honkapohja, Seppo, 1999. "Learning dynamics," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 7, pages 449-542 Elsevier.
    25. N. Williams, 2002. "Stability and Long Run Equilibrium in Stochastic Fictitious Play," Princeton Economic Theory Working Papers cbeeeb49cc8afc83f125df5a8, David K. Levine.
    26. Chiappori, P.A. & Geoffard, P.Y. & Guesnerie, R., 1990. "Sunspot Fluctuations around a Steady State: The Case of Multidimensional One-Step forward Looking Economic Models," DELTA Working Papers 90-02, DELTA (Ecole normale supérieure).
    27. 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.
    28. William Poole & Robert H. Rasche, 2002. "Flation," Review, Federal Reserve Bank of St. Louis, issue Nov, pages 1-6.
      • William Poole, 2002. "Flation," Speech 49, Federal Reserve Bank of St. Louis.
    29. Woodford, Michael, 1986. "Stationary sunspot equilibria in a finance constrained economy," Journal of Economic Theory, Elsevier, vol. 40(1), pages 128-137, October.
    30. M. Kandori & G. Mailath & R. Rob, 1999. "Learning, Mutation and Long Run Equilibria in Games," Levine's Working Paper Archive 500, David K. Levine.
    31. 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.
    32. 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.
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