Unique Equilibrium in a Model of Self-Fulfilling Currency Attacks: Comment
指出Morris和Shin关于货币攻击模型的一个定理只在特殊情况下成立，并给出正确推广，证明即使投机者信息精确，资本控制仍然有效。
In a recent issue of this journal, Stephen Morris and Hyun Song Shin (1998a) prove the uniqueness of an equilibrium in a model of self-fulfilling currency attacks, when speculators face uncertainty in their signals about macroeconomic fundamentals. In Theorem 2 of their paper, Morris and Shin characterize the equilibrium as uncertainty approaches zero. They claim that the threshold of the fundamental state, up to which a currency attack will occur with probability one, is independent of the critical mass of capital needed for an attack to be successful. Hence, direct capital controls are less effective when speculators have fairly precise information about fundamentals. Yet, their Theorem 2 holds only for a special case. This Comment gives the correct generalization and proves that for small uncertainty currency crises depend on the critical mass of capital needed for success. Thus, direct capital controls are effective even when fundamentals are fairly transparent to all market participants. The reduced-game structure is given by the following assumptions: Fundamentals of the economy are characterized by some parameter u unknown to agents. There is a continuum of agents receiving independently and identically distributed (i.i.d.) signals x about the fundamentals. Each agent must decide whether or not to attack the currency, which is associated with transaction costs t . 0. If a proportion a(u ) of all traders attacks the currency, the attack is successful and each attacking agent obtains a reward R(u ) 5 e* 2 f(u ). a and R are continuous; there is a state u with a(u ) 5 0 for all u # u; a is strictly increasing above u; and a(u ) , 1 for all u. R is strictly decreasing and there is a state u# . u with R(u# ) 5 t. u is uniformly distributed over an interval, say [0, 1]. Given u, signals have a uniform distribution in [u 2 «, u 1 «]. Critical levels u and u# must be at least 2« away from the margins of the interval [0, 1]. In Section II of their paper, Morris and Shin show that a unique equilibrium switching point x* and a threshold u* exist, such that an agent attacks [does not attack] the currency if her signal x is smaller [larger] than x*, and that a successful speculative attack occurs with probability one [zero] if state u is below [above] u*. In Section III, Theorem 2 states that “In the limit as « tends to zero, u* is given by the unique solution to the equation f(u*) 5 e* 2 2t” (p. 594). As stated, this theorem holds only for the special case where a(u*) 5 1⁄2. It should therefore be generalized as follows.