Exchange Rate Economics: Theories and Evidence

The sticky-price monetary model 133
Second,stochastic open market operations which lead to an increase in the
supply of bonds in the home country (i.e. an increase in x) will produce an appreciation
of the exchange rate through a familiar route: bond prices fall as a result,
the home interest rate rises and the currency appreciates. However,in contrast
to the standard liquidity effect in the MFD model,the liquidity effect here is ‘pure’
in the sense the rate of growth of money is held constant (by assumption,using a
tax) which means that in (5.59) the expected inflation rate is constant,as is the rate
of time preference.
Third,the model has implications for the excess volatility of nominal exchange
rates. This can be demonstrated in the following way. Write the equilibrium
exchange rate in (5.54) in logs as:
ln s = k + ln(x ∗ ) − ln(x),(5.63)
where the constant term, k,includes all non-stochastic components of the exchange
rate (i.e. relative money supplies,relative prices,the rate of time preference and
relative output levels). The constancy of the Fisherian fundamentals would,on
their own,imply a constant value of the exchange rate. However,with stochastic
interest rate shocks,due to stochastic Open Market Operations,the exchange rate
becomes excessively volatile relative to the non-stochastic fundamentals:
Var(ln s) = Var[ln(x ∗ )]+Var[ln(x)]. (5.64)
Of course this result presupposes the two shocks are uncorrelated. In the presence
of a non-zero correlation,expression (5.64) has to be modified to:
Var(ln s) = Var[ln(x)]+Var[ln(x ∗ )]−2Cov(ln(x),ln(x ∗ )),(5.65)
It is worth noting that this relationship implies that in the presence of unexpected
liquidity shocks,the variance of the exchange rate could be reduced to zero if the
monetary policies of the two countries are perfectly correlated such that (x) and
(x ∗ ) are perfectly correlated. In the presence of such liquidity shocks the model
therefore predicts that exchange rate stability can only be achieved if monetary
policies are tightly coordinated across countries.