Exercise 4 This exercise deals with the choice between a fixed exchange rate regime and a floating exchange rate based on a variation of the Dornbusch model seen in Section 7.2. The equilibrium relation in the goods market and the uncovered interest rate parity are given by the following equations, respectively:

mt 2 pt 5 yt 2 λit 1 vt it 5 i



t 1 Etfst11 2 stg 1 εt;

where mt is the nominal money supply, pt is the level of domestic prices, it is the nominal interest rate, vt represents a shock on the money demand, st represents the nominal exchange rate, and εt represents the risk premium. Both vt and εt are shocks i.i.d., such that Et½vt 5 0 and Et½εt 5 0. All variables used in the model are expressed in logarithmic terms.

Let wt be the nominal wage, which is predetermined (and therefore constant on date t), established on t 2 1 in such a way as to be equal to the price level expected for period t, Chapter 10 • Exchange Rate Regimes 293 based on the set of available information on t 2 1. The aggregate economic demand is given by the following equation:

yd t 5 δðst 1 p

t 2 ptÞ 1 gt;

where gt is a shock of demand i.i.d., such that Et½gt 5 0. The aggregate supply of the economy is given as:

ys t 5 θðpt 2 wtÞ:

a. Under the hypothesis that mt is fixed and that st is floating, calculate the equilibrium values of st, and yt. Further assume that i



t 5 p

t 5 0.

b. Continuing within the context of the previous item, calculate the variance of output yt, supposing that shocks vt, εt, and gt are orthogonal.

c. Solve the model while now assuming that the exchange rate is fixed, i.e., st 5 s.

d. In the context of the previous item, calculate the variance of output yt, assuming that shocks vt, εt, and gt are orthogonal.

e. Define the random variable φt  vt 2 λεt, which can be interpreted as the financial shock that acts upon the economy. Show that when the variance of financial shocks is zero, the output variance will be lower under a floating regime than under a fixed regime. Show that when the variance of the demand shock is zero, the variance of output is lower under a fixed regime.