1. Dynamic Inconsistency and Self-Fulfilling Expectation Equilibrium
Maurice Obstfeld

2. Dynamic inconsistency and currency crises(Barro-Gordon Type)
Government Objective:
Expectations-augmented Phillips Curve
=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 y* u
Assume:
Dynamic inconsistency

3. 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<low u, or u> high u the government chooses:
With an output level:

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

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

6. 45 degrees
Three Equilibria