Exchange Rate Economics: Theories and Evidence

The sticky-price monetary model 125
(5.29) we obtain the steady-state exchange rate as:
( ) (
1
¯s = m + − α 1 y + α 2 + γ )
3
i ∗ + α 1 µ,(5.33)
γ 1 γ 1
and on using (5.32) in (5.8) we obtain the steady-state price level as:
¯p = m − α 1 y + α 2 i ∗ + α 2 µ. (5.34)
Using expressions (5.33) and (5.34) we may define the long-run levels of competitiveness
and real balances as:
and
¯q =¯s − ¯p = 1 γ 1
y + γ 3
γ 1
i ∗ (5.35)
¯l =¯m − ¯p = α 1 y − α 2 (i ∗ + µ). (5.36)
Equation (5.35) shows that the long-run level of competitiveness is constant and
makes clear why if there is any long-run core inflation the exchange rate must
change to offset it. The SPMA II model’s dynamics,and,in particular,its adjustment
to the steady-state conditions,may be captured by two key equations. On
setting y equal to unity and using (5.31) in (5.30) we get
˙l + πd = 0,(5.37)
and by substituting (5.7) in (5.30) we obtain:
˙q + πd − i = µ − i ∗ ,(5.38)
and on using equations (5.8) and (5.29) to eliminate d and i and after some
manipulation the following expression can be obtained:
[ i˙q]
= 1 [ ]
πγ3 πα 2 γ 1 1
+
1 γ 1 (πα 2 − α 1 )][ 1 [ ][ ]
πα2 γ 3 0 µ
q α 2 − i ∗ ,(5.39)
where = β 0 (πα 2 − α 1 ) − α 2 < 0. The dynamic equations in (5.39) are illustrated
in Figure 5.12.
The locus ˙l = 0 represents combinations of l and q that satisfy a stationary level
of real money balances and we see from (5.39) that it has a negative slope. 4 The
schedule ˙q = 0 is the locus of l and q which gives a stationary level of competitiveness
and its slope can be seen to depend upon the aggregate demand adjustment
coefficient, π. 5 For low values of π, ˙q = 0 has a positive slope and for high values
(corresponding to rapid goods market adjustment) ˙q = 0 will be negatively sloped.
We assume here that ˙q = 0 has a positive slope. The horizontal arrows indicate
that from a position of equilibrium on the ˙l = 0 schedule a point to the right (left),
implies higher (lower) real money balances,a lower (higher) nominal interest rate