880 Macroeconometric Modeling for Policy
Equation (17.47) represents the equilibrium in the market for foreign exchange in
a floating exchange rate regime. The central bank’s foreign currency reserves are
exogenous in the floating exchange rate regime that we are modeling, and therefore
are not specified in (17.47). The nominal exchange ratevequilibrates the market
in each time period, specifically in the hypothetical steady state represented in
(17.47). The relationship follows from the definition of the risk premium,rp:
rpt=Rt−R∗t−(vte+ 1 −vt),where(vte+ 1 −vt)denotes expected depreciation. In real terms, using the definition
rex=v+p∗−p, the relationship can be written as:
(
vet+ 1 +p∗t+e 1 −pet+ 1
)
−(
vt+p∗t−pt)
=[
Rt−(
pet+ 1 −pt)]
−[
R∗t−(
p∗te+ 1 −p∗t)]
−rptrexet=(
Rt−πte+ 1)
−(
R∗t−πt∗+e 1)
−rpt.If expected depreciation of the real exchange rate is assumed to react to deviations
from the equilibrium real exchange raterex,
rexet=α(
rext−rex)
,the solution for the realized real exchange rate becomes:
rext=
1
α[(
Rt−πet+ 1)
−(
R∗t−π∗t+e 1)]
+rex−
1
αrpt.Finally, replacing expected with realized inflation and assuming a constant risk
premium, the steady-state real exchange rate relationship becomes:
rex=−.12[
(R−π)−(
R∗−π∗)]
+μv,The sign ofαshows whether expectations are regressive (α<0) or extrapolative
(α>0), so in our case, since real interest rates are in percentage points,αis given
as:
1
α
=−.12×100,implying that expected depreciation is regressive with approximately 8% adjust-
ment per period:
rexet=−0.083(
rext−rex)
.The long-run pass-through from the exchange rate and foreign prices onto import
prices in domestic currencypiis represented by equation (17.48). It is a homo-
geneous function ofv and foreign producer pricespi∗, but the import price also
increases if the real exchange rate (in terms of consumer prices) appreciates. This is
due to pricing-to-markets in import price-setting. Equation (17.48) is written in a
way that shows the long-run relationship between the two operational definitions