Speculative attacks and defenses as wars of attrition

This paper extends the currency crisis models in Obstfeld [Obstfeld, M., 1994. The logic of currency crises. Cahiers Economiques et Monetaries], [Obstfeld, M., 1996. Models of currency crises with self-fulfilling features. European Economic Review 40, 1037-1047] by modeling both the government's side and speculators' side and introducing uncertainty about each party's payoff. We argue that a speculative attack (defense) can be well modeled as a war of attrition between the government and speculators under asymmetric information. We then solve for a pure strategy, weakly perfect, Bayesian rational expectation equilibrium in which each party's time until concession depends on her benefits from winning and her costs of fighting. Using this model, we are able to explain important facts of currency crises. First, the model shows that failed defenses (attacks) can be ex-ante rational for governments (speculators). Second, the model predicts systematic variations in the durations of defenses. Finally, we also show that currency crises can be self-fulfilling in the sense that there exist multiple rational expectation equilibria in our model.