Exchange Rate Economics: Theories and Evidence

Currency substitution and portfolio balance models 191
One of the first empirical studies of CS was conducted by Miles (1978). Out of a
total portfolio of assets (money and non-money) the private sector decides to hold
M 0 cash balances. Since the CS literature predicts that both domestic and foreign
money provide money services,the problem is to decide the proportion of M 0 to be
held in M and M ∗ . The choice between domestic and foreign money is captured
by Miles (1978) in the following way. Following the functional form used by Chetty
(1969) in his study of the nearness of near-moneys,Miles assumes that domestic
and foreign real money balances are inputs into a constant elasticity of substitution
(CES) production function for money services. This production function is then
maximised subject to an ‘asset constraint’ of the form
M 0
P
= M M
∗
(1 + i) +
P P ∗ (1 + i∗ ),(7.53)
which reflects the assumption that there is an opportunity cost to holding real
balances, i,and that this opportunity cost may differ between two types of balances,
i ∗ . By maximising the money services production function subject to the asset
constraint and assuming that PPP holds,Miles obtains:
log(M /M ∗ S) = a + σ ln(1 + i ∗ /1 + i),(7.54)
where σ is a measure of the elasticity of substitution between the home and foreign
money balances. Equation (7.54) has been estimated by Miles (1978) for the
Canadian dollar–US dollar,and in Miles (1981) for US dollar and German mark
holdings relative to foreign currency holdings (the interest rates being treasury bill
rates). The results are reported in Table 7.1 for the fixed and floating period.
Notice that for the three countries considered,the elasticity of substitution term
is large and statistically significant (marginally so for Canada–US) in the floating
period,but relatively small and insignificant in the fixed rate period. Miles
concludes from this that in periods of fixed exchange rates central banks make
currencies perfect substitutes on the supply side,and thus agents do not need to
substitute on the demand side,but that in periods of floating exchange rates and
little or no government intervention agents have to undertake the substitution
mechanism themselves.
But Miles has been taken to task over his implementation of the CS model by
a number of researchers. For example,Bordo and Choudri (1982) argue that the
same problem with interpreting the coefficient in monetary approach equations
as an elasticity of substitution applies to equation (7.54). Thus,for example,if the
foreign rate of interest rises we would expect domestic residents to substitute away
from both domestic and foreign currency towards foreign bonds. The significant
positive coefficient in the estimated version of equation (7.54) may simply reflect a
greater elasticity in the demand for foreign currency with respect to foreign interest
rates. By respecifying equation (7.54),in an attempt to capture the separate effects
of currency substitution and currency bond substitution,Bordo and Choudri (1982)
show that σ becomes insignificant and wrongly signed for the Canadian dollar–US
dollar. Laney et al. (1984) criticise Mile’s results from a slightly different perspective.