To see how the exchange rate and the price level adjust to longrun equilibrium after a monetary disturbance, it is necessary to incorporate the price adjustment mechanism in (3). In order to do this, start with de…ning the expected change of the exchange rate as

(35)

and, then, substitute market expectations in (22) into the de…nition in (35):

(36)

(36) means that the market expect that the exchange rate will adjust to longrun equilibrium, if

(37)

which reduces to (27), i.e., if it is expected that the exchange rate will adjust to longrun equilibrium after a change in money supply, the exchange rate will also overshoot its longrun equilibrium level in the shortrun. Then, combine the equations that describe the money and the international asset markets in equilibrium, i.e., (1)( 2), and use the de…nition in (35):

(38)

Thereafter, substitute the longrun equilibrium price level in (15) into (38):

(39)

or, if (36) is substituted into (39),

(40)

By using the relationship between the exchange rate and the price level in (40), its longrun counterpart in (19), and the price adjustment mechanism in (3), we can derive an equation that describes the adjustment path for the price level to longrun equilibrium. In order to do this, start with de…ning the change of the price lev el as

(41)

and, then, substitute the de…nition in (41) into the price adjustment mechanism in (3):

(42)

Thereafter, substitute the relationship between the exchange rate and the price level in (40), and its longrun counterpart in (19), into (42):

(43)

(43) means that the price level will adjust to longrun equilibrium, if

(44)

or

(45)

where the weight function in (5) is utilized in the derivation. The second equation in (45) is the same as (27). Moreover, the …rst equation in (45) implies that the market does not expect that the price level (nor the exchange rate) will adjust to longrun equilibrium, because (37) is not satis…ed, even if the price level (and the exchange rate) will do that[10]. Consequently, this case is ruled out when market expectations are characterized by perfect foresight. The di¤erence equation in (43) can be written as

(46)

if the de…nition in (41) is utilized. Then, the solution of the di¤erence equation in (46) is

(47)

and, after twice substituting the relationship between the exchange rate and the price level in (40)[11] into (47), the exchange rate’s adjustment path is derived:

(48)

Thus, the exchange rate and the price level will adjust to longrun equilibrium after a monetary disturbance, if

(49)

Moreover, the adjustment process is oscillating, if

(50)

and nonoscillating, if

(51)

where the weight function in (5) is utilized in the derivations. For example, since the expression within the inequalities in (50)( 51) is larger when the planning horizon is longer, the adjustment process of the exchange rate (and the price level) to longrun equilibrium after a monetary disturbance is more likely to be oscillating for shorter than for longer planning horizons. Also recall that the magnitude of exchange rate overshooting depends inversely on the planning horizon. Thus, which is an interesting characteristic of the model, a comparably short planning horizon in currency trade is consistent with a highly variable and oscillating exchange rate.

---

10 There is no exchange rate overshooting after a monetary disturbance in this case. See (25) and note that -1 < o(τ) < 0 since the …rst equation in (45) implies that α(ω (τ) (γ + δ) - γ ) < - ¡1.

11 (40) at time t is substituted …rst into (47), and then is (40) at time 0 substituted. Note that since (40) holds at any point in time, it also holds at time 0.

By Mikael Bask and Carina Selander

Next: Perfect foresight path

Summary: Index