Exchange Rate Economics: Theories and Evidence

Currency substitution and portfolio balance models 179
a portfolio of non-money assets,the proportions of particular assets held depending
on risk/return factors. This implies that uncovered interest parity will not hold and
should instead be replaced with a risk-adjusted version,such as:
i t − i ∗ t − s e t+k = λ t (7.36)
where λ t is a risk premium. In this context if international investors decide that a
currency has become riskier,they are likely to reallocate their bond portfolios in
favour of less risky assets.
7.3.1 The portfolio balance model
The asset sector of our small country portfolio balance model is outlined as
equations (7.37) to (7.40):
W = M + B + SF ,(7.37)
where M denotes domestic money, B,domestic bonds,and,F ,and foreign bonds.
Since the bonds are assumed to be very short term assets,rather than Consols,we
do not need to consider capital gains or losses induced by interest rate changes.
Demand for the three assets depends upon the domestic and foreign rate of
interest,which are assumed to be exogenously given,and are homogenous of
degree 1 in normal wealth: 11
M = m(i, i ∗ + s e )W , m i < 0, m i ∗ +s e < 0,(7.38)
B = b(i, i ∗ + s e )W , b i > 0, b i ∗ +s e < 0,(7.39)
SF = f (i, i ∗ + s e )W , f i < 0, f i ∗ +se > 0. (7.40)
The partial derivatives in (7.38) to (7.40) indicate that for any asset an increase in
the own rate leads to an increase in demand and an increase in a cross rate leads
to a decrease in demand. It is also assumed that the bonds are gross substitutes (i.e.
b i > f i and f i ∗ +s e > b i ∗ +s e ) and a greater proportion of any increase in domestic
wealth is held in domestic bonds rather than foreign bonds. To simplify the analysis,
the asset demand equations are not dependent upon income. As Allen and Kenen
(1980) point out,this introduces an important asymmetry into a portfolio balance
model,namely that while conditions in goods markets do not have a direct effect
on asset markets,asset market conditions directly affect goods markets since the
exchange rate, S,features in both sectors. Although domestic residents can hold
all three assets,foreign residents can only hold foreign bonds (and presumably also
foreign money which is non-traded). As in our CS models the only way residents
of the small country can accumulate F is by running a current account surplus
(which as we shall see below,equals positive savings). The supplies of both M and
B are exogenously given by the authorities.
The real sector of the model is described by equations (7.41) and (7.44) and
is identical in specification to the real sector of the CS,model 2,in the previous