Exchange Rate Economics: Theories and Evidence

132 The sticky-price monetary model
where z is ratio of money held by the representative agent for asset market purposes,
as proportion of total money held (i.e. z = Z /M ). This expression indicates that the
equilibrium price depends on the money supply,income,as in a standard quantity
theory relationship,but also the share of money used for asset purposes (this comes
from the second cash in advance constraint for assets). Using this measure of
the equilibrium price in (5.57) produces the following measure of the equilibrium
exchange rate:
s = 1 − z yt
∗ u ∗ c t
M κ
1 − z ∗ y t u ct M ∗ κ ∗ . (5.59)
Grilli and Roubini (1992) decompose (5.59) into two components. The first is
labelled the ‘fundamental’ Fisherian component:
1 − z
1 − z ∗ y ∗ t
y t
u ∗ c t
u ct
,(5.60)
and is the component which prevails absent any liquidity effects. It is referred to as
Fisherian because it consists of expected inflation and the ratio of time preferences.
The second component is the ratio of bond prices and this is referred to as the ‘nonfundamental’
equilibrium component. The latter is the liquidity effect and is driven
by government operations in the bond markets. In particular,the only role for
government in this model is to engage in open market operations with government
bonds. More specifically,the government in the home (foreign) country issues
bonds equal to a proportion, x t ,of the period-t money supply: that is, B t = x t M t .It
is assumed that the proportion x is a serially uncorrelated random variable and is
the only source of uncertainty in the model. Bond prices,in turn,are determined
by the equilibrium conditions for security markets,that is:
and
z t = x t κ t ,(5.61)
z ∗ t = x ∗ t κ∗ t ,(5.61′ )
which,in turn,implies that the ratio of securities prices is given by:
κ
κ ∗ = z x ∗
x z ∗ . (5.62)
The stochastic nature of x makes the relative bond prices stochastic as well.
The ‘liquidity’ model has the following implications,additional to those discussed
earlier for equation (5.59). First,the equilibrium exchange rate (and prices)
depend upon the share of money used in asset transactions, z. Since the price of
goods is driven by the amount of money available for goods transactions,a decrease
in this quantity through an open market operation will reduce the equilibirum price
in home country and appreciate the exchange rate currency.