Learning, Large Deviations, And Recurrent Currency Crises*

Abstract

This article studies a version of Obstfeld's (Journal of International Economics 43 (1997), 61–77) “escape clause” model. The model is calibrated to produce three rational expectations equilibria. Two of these equilibria are E‐stable 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 to a small noise diffusion process. The dynamics of exchange rate changes are then characterized using large deviation techniques from Freidlin and Wentzell (Random Perturbations of Dynamical Systems, Second Edition, Berlin: Springer‐Verlag, 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. The model is calibrated to the exchange rate histories of Argentina, Brazil, and Mexico. Currency crises in these countries resemble the predicted “escape routes” of the model. A key feature of these escape routes is that expectations of a devaluation erupt suddenly, without large contemporaneous shocks. This is consistent with evidence showing that crises are often poorly anticipated by financial markets.