Exchange Rate Economics: Theories and Evidence

276 The new open economy macroeconomics part 2
With sticky prices it is straightforward to show that home and foreign price indices,
log linearised around the initial steady state,are:
ˆP = (1 − n)(1 − v)ŝ,(11.6)
ˆP ∗ =−n(1 − v)ŝ. (11.7)
These relationships indicate that with sticky prices the response of aggregate
price indices to an exchange rate depreciation is lower the greater the share of
goods subject to PTM,and as v →1, P and P ∗ are entirely unaffected by an
exchange rate depreciation. Using these pricing relationships,and assuming real
money balances enter the utility function with an isoelastic form as in (10.58),the
following variant of (10.33) may be obtained:
Ŝ(1 − v) = ˆM − ˆM ∗ − 1 ε
(Ĉ − Ĉ ∗) ,(11.8)
where,in contrast to (10.33) the size of v determines the magnitude of the deviations
from PPP. Using the remaining equations of the sticky-price solution of the model
(i.e. the demand and current account equations) the following relationship may be
derived:
ŝ =
Ĉ − Ĉ ∗
(1 − v)(θ − 1) + v . (11.9)
The intuition for this relationship may be seen by assuming complete PTM
(i.e. v = 1). In this instance,a positive depreciation of the exchange rate allows
domestic consumption to be above foreign consumption because the depreciation,
although having no effect on relative prices,increases the home currency earnings
of home firms and reduces the foreign currency earnings of foreign firms. This
income redistribution allows the home country to consume more relative to its
trading partner. Combining the last two equations yields the following exchange
rate relationship:
ŝ =
( ˆM − ˆM ∗ )
(1 − v)(ε + θ − 1) + v . (11.10)
In this relationship a rise in v will increase the response of the exchange rate
so long as ε>2 − θ. Since θ > 1 this condition implies that the existence of
PTM will increase the volatility of the exchange rate so long as the consumption
elasticity of money demand, ε,is ‘not too high’. Furthermore,if in addition the
consumption elasticity of demand is below unity the presence of PTM not only
increases exchange rate volatility,it also generates exchange rate overshooting.
Bergin and Feenstra (2000) also study pricing to market in the context of a
NOEM model,but in contrast to Betts and Devereux they model demand using
translog preferences,rather than the standard constant elasticity of demand schedules.
The main difference this makes is to generate variable mark-ups over marginal