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Learning, large deviations, and recurrent currency crises

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  • Kenneth Kasa

Abstract

This paper studies a version of Obstfeld's (1997) "escape clause" model. The model is calibrated to produce three rational expectations equilibria. Two of these equilibria are E-stable in the sense of Evans (1985), and one is unstable. Dynamics are introduced by assuming that agents must learn about the government's decision rule. It is assumed they do this using a stochastic approximation algorithm. It turns out that as a certain parameter describing the sensitivity of beliefs to new information gets small, the algorithm converges weakly to a small noise diffusion process. The dynamics of exchange rate changes are then characterized using large deviation techniques from Freidlin and Wentzell (1998). These methods describe the sense in which the limiting distribution of exchange rate changes is approximated by a two-state Markov-switching process, where the two states correspond to the two E-stable equilibria of the algorithm's mean dynamics. The analysis relates the parameters of this process to assumptions about learning and the stochastic properties of the underlying shocks. ; The model is applied to the exchange rate histories of Argentina, Brazil, and Mexico. Although two-state Markov-switching models describe these countries' exchange rate histories quite well, they have little ex ante predictive power. Of more interest to this paper, however, is the finding that observed currency crises look a lot like the predicted 'escape routes' of the calibrated escape clause model, augmented with an adaptive learning rule. A key feature of these escape routes is that expectations of a devaluation erupt suddenly, without any large contemporaneous shocks. This is consistent with evidence showing that crises are often poorly anticipated by financial markets.

Suggested Citation

  • Kenneth Kasa, 2000. "Learning, large deviations, and recurrent currency crises," Working Paper Series 2000-10, Federal Reserve Bank of San Francisco.
  • Handle: RePEc:fip:fedfwp:2000-10
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    Cited by:

    1. William Branch & George W. Evans, 2007. "Model Uncertainty and Endogenous Volatility," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 10(2), pages 207-237, April.
    2. Thomas Sargent & Noah Williams & Tao Zha, 2009. "The Conquest of South American Inflation," Journal of Political Economy, University of Chicago Press, vol. 117(2), pages 211-256, April.
    3. KevinX.D. Huang & Zheng Liu & Tao Zha, 2009. "Learning, Adaptive Expectations and Technology Shocks," Economic Journal, Royal Economic Society, vol. 119(536), pages 377-405, March.
    4. Robert Tetlow & Peter von zur Muehlen, 2004. "Avoiding Nash Inflation: Bayesian and Robus Responses to Model Uncertainty," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 7(4), pages 869-899, October.
    5. Ellison, Martin & Scott, Andrew, 2013. "Learning and price volatility in duopoly models of resource depletion," Journal of Monetary Economics, Elsevier, vol. 60(7), pages 806-820.
    6. Dmitri Kolyuzhnov & Anna Bogomolova, 2004. "Escape Dynamics: A Continuous Time Approximation," Econometric Society 2004 Latin American Meetings 27, Econometric Society.
    7. Hansen, Lars Peter & Sargent, Thomas J., 2007. "Recursive robust estimation and control without commitment," Journal of Economic Theory, Elsevier, vol. 136(1), pages 1-27, September.
    8. Martin Ellison & Liam Graham & Jouko Vilmunen, 2006. "Strong Contagion with Weak Spillovers," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 9(2), pages 263-283, April.
    9. 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.
    10. Konstantinos Angelopoulos & Bernardo X. Fernandez & James Malley, 2010. "The distributional consequences of supply-side reforms in general equilibrium," Working Papers 2010_26, Business School - Economics, University of Glasgow, revised Jun 2012.
    11. Dmitri Kolyuzhnov & Anna Bogomolova, 2004. "Escape Dynamics: A Continuous Time Approximation," Econometric Society 2004 Far Eastern Meetings 557, Econometric Society.
    12. Chakraborty, Avik & Evans, George W., 2008. "Can perpetual learning explain the forward-premium puzzle?," Journal of Monetary Economics, Elsevier, vol. 55(3), pages 477-490, April.
    13. Williams, Noah, 2004. "Small noise asymptotics for a stochastic growth model," Journal of Economic Theory, Elsevier, vol. 119(2), pages 271-298, December.
    14. Davies, Ronald B. & Shea, Paul, 2010. "Adaptive learning with a unit root: An application to the current account," Journal of Economic Dynamics and Control, Elsevier, vol. 34(2), pages 179-190, February.
    15. Branch, William A. & Evans, George W., 2006. "A simple recursive forecasting model," Economics Letters, Elsevier, vol. 91(2), pages 158-166, May.
    16. Dmitri Kolyuzhnov & Anna Bogomolova, 2007. "Optimal Monetary Policy Rules: The Problem of Stability under Heterogeneous Learning," 2007 Meeting Papers 713, Society for Economic Dynamics.
    17. Dmitri Kolyuzhnov & Anna Bogomolova, 2004. "Escape Dynamics: A Continuous Time Approximation," Computing in Economics and Finance 2004 190, Society for Computational Economics.

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    Keywords

    Money ; Financial crises;

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