CURRENCY CRISES WITH SELF-FULFILLING EXPECTATIONS Maurice Obstfeld and Morris and Shin

Speculative Attacks: Non- Uniqueness Government commits a finite stock of reserves— R—to defend the domestic currency. Two private traders play; each one has initially a domestic money endowment = 6. A fixed cost (=1) of selling the money endowments and purchasing foreign currency. A depreciation of 50% if attack successful. If both individuals successfully attack, they split R evenly between them. (a) A high-Reserve Game, (b) A Low-Reserve Game, (c) An Intermediate-reserve game.

A High-Reserve Game: R=20: The Payoff Matrix 0,0 Nash Equilibrium 0, -1 -1, 0-1, -1 (note: private-sector speculative buying power is 6+6=12) Hold Sell HoldSell

A Low-Reserve Game: R=6 Payoff Matrix 0,0 0, 2 2, 0 1/2, ½ Nash Equilibrium (Note: speculative buying power =6+6=12) Hold Sell HoldSell

An Intermediate-Reserve Game: R=10: Payoff Matrix 0,0 First Nash Equilibrium 0, -1 -1, 0 3/2, 3/2 Second Nash Equilibrium Note: the speculative buying power = 6+6=12) Hold Sell HoldSell

I. Common Knowledge Needs two to successfully attack. Agent’s strategy: Attack, A, or Not Attack, N. Attack involves fixed cost=1 Post-attack exchange-rate depreciation=X. If X 1, there are multiple equilibria.

Agent 2 AN Agent 1AX-1, X-1-1, 0 N0, -10,0 Payoff matrix:

Estimating Fundamentals and Second Guessing of Others Imagine that a large population of agents have access to public or private information on the underlying fundamentals. Each one aims to take action appropriate to the underlying State. But they also engage in race to second-guess the actions of other individuals. Thus decision makers are interested Parties in the actions of others. Public information has attributes that make It a double-edged instrument. On the one hand it conveys information on the underlying fundamentals; on the other hand it serves as a focal point for the beliefs of the group as a whole. Public information serves as a coordinating device. Morris and Shin (AER 2003).

X is random: each agent receives some private information (noisy signal) Signal Z is distributed uniformly around the true value of X. Z is the best estimate of the true value of X. Z lies between And.

Both the distributions of X and Z are common knowledge. Each agent’s expected payoff when using Attack strategy is Z-1, IF the other agent attacks, as well; or -1, if the other agent does not attack. Probability{other agent attacks}{Z-1}+ (1- Probability{other agent attacks){-1} = Probability{other agent attacks}{Z}-1 If A is chosen, expected payoff : For this payoff to be positive we need two elements: (1)The signal Z must be sufficiently high; (2)The probability that the other agent attacks must be sufficiently high.

Estimating probabilities If one agent receives a signal Z=1+y, y small, she will attack if she believes that the other agent attacks with a probability close to 100%. BUT: If agent receives a signal Z=1+y, she estimate the true X=1+y. This implies that she believes that the other agent receives signal below 1 with a probability of 50% and above 1 with 50% she will decide not to attack.

Cut Off Z* Since the expected payoff of attacking is prob(other attacks)*Z - 1 at Z* you are indifferent between attacking or not attacking, This implies prob(other attacks | Z*) times (Z*) = 1 But symmetry implies other party only attacks if his Z (call Z2) is greater than or equal to Z*. so, p(other attacks|Z*) p(Z2>Z*|Z*) But knowing that your signal is Z* only tells you that it is that their signal is higher than yours so p(other attacks)=.5 implying.5Z*=1 so Z*=2

A slightly higher signal, Z=1+2y will not be enough to generate positive payoff. At some point we can find a cutoff, Z=Z* at which the agent rationally switch from N to A. Since the expected payoff of attacking is p(other attacks)*Z - 1 and we know at Z* you are indifferent between attacking and not this implies p(other attacks | Z*) times (Z*) = 1 but symmetry implies other party only attacks if his Z (call Z2)is greater than or equal to Z* so p(other attacks|Z*) p(Z2>Z*|Z*) but knowing that your signal is Z* only tells you that it is that their signal is higher than yours so p(other attacks)=.5 meaning.5Z*=1 so Z*=2 Result: Unique, fundamentals-based explanation for the for a speculative attack.

Unemployment-Depreciation Model of Currency Crisis (Barro-Gordon Type) Government Objective: =the change in the exchange rate(+ or -) =output target =natural output =domestic price setters expectations of based on lagged information =i.i.d., zero-mean shock Expectations-augmented Phillips Curve y* u Assume:Dynamic inconsistency

Government can choose after observing u; unlike price setters. Any depreciation ( )has a cost Any appreciation has a cost :c(low u) for appreciation, or c(high u) for depreciation. If u is between low u and high u the fixed rate is Maintained. Given u high u the government chooses: With an output level:

I. Values Policy loss function (Ignoring the fixed cost): 2. Solving for high u and low u:

, uniform distribution. Rational expectations of next period, given the price expectation is:

45 degrees Three Equilibria