Exchange Rate Economics: Theories and Evidence

Target zone models 291
s
S
FF
C
v 1
v
–s
Figure 12.1 The S function.
offset in the future. The closer the rate is to the edge of the band the more strongly
are such expectations held and therefore the function increases at an increasing
rate. A similar argument would apply at the bottom edge of the band and so the
relationship between f and s will be bent as it approaches the edge of the band: the
S-shaped curve describes the functional relationship between s and f ,rather than
the 45 ◦ ray.
There are two points worth noting from Figure 12.1. First,in the top half of the
figure the expected change in the exchange rate is negative,while in the bottom
half it is positive. This is possible,despite the fact that m is constant and the expected
change in v is zero,because of the curvature of the S function: the concavity of S
in the top half allows E[ds/dt] to be negative,and the convexity of S in the bottom
half allows E[ds/dt] to be positive. Second,note that the existence of the band
has a stabilising effect on the exchange rate since a given shock to velocity has a
lesser effect on the exchange rate in the band than in the free float scenario. This is
despite the fact that no effort is being made by the monetary authorities to engage
in foreign exchange market intervention. This has been referred to by Svensson as
the honeymoon effect which follows on from moving from a freely floating system
to a target zone arrangement.
12.1.1 Aformal analysis of S in the target zone
In this section we consider a more formal analysis of the S curve portrayed in Figure
12.1 (the discussion here follows Krugman 1991). The objective is to determine a
relationship for s:
s = g(m, v, ¯s, s),(12.3)
which is consistent with (12.1) and the assumed monetary behaviour. Assuming
m is constant and s lies in the band then,and as we have seen,the only source
of expected changes in s comes from the random movement of v. By the rules of