Carlos A. Ibarra
inflation is zero): dlnq / dt = dlns / dt - π, where q is the real
exchange rate, and as before ln denotes the natural logarithm. How
the change in the nominal exchange rate is determined is a matter
of dispute in the literature. For our purposes, it seems safe to posit
that it is determined by a combination of fundamentals (represented
by the inflation rate) and monetary factors (summarized by the
interest rate): dlns/dt = σπ - μi, where σ and μ are positive
coefficients. To the extent that the rate does not fully reflect
fundamentals (or because for a country like Mexico there may be a
Balassa-Samuelson effect), σ will be less than one. If the inflation
rate depends negatively on the interest rate and positively on the
real exchange rate, the change in the real exchange rate will be
given by:
(7) dlnq/dt = - μi - (1 - σ) π (q, i).
(+, -)
After equalizing to zero, Equation (7) defines a downward sloping
schedule of stationary q values in the (q, i) space. It is easy to see that
the real exchange rate has stable dynamics in the sense that, starting
from stationarity, an exogenous rise in the interest rate and/or the
exchange rate will lead to a negative rate of change of q.
We will conventionally assume that the central bank attempts to
minimize a weighted sum of output and inflation deviations from
target:
(8) min L = ½ [y 2 + τ (π - πT)2]
where τ reflects the strength of inflation aversion and for notation
simplicity the output target is set at zero (Martmez et al., 2001, present
evidence supporting this sort of reaction function for the Banco de
Mexico, at least since November 1998).18
18 This formulation is now standard in the analysis of monetary policy rules among developed
countries (see Taylor 1999). For supporting evidence in the case of Latin America, see Corbo
(2000). Recently, a difference has been made between countries following strict inflation targeting,
where output (or the output gap, or unemployment) does not enter the central bank policy
function, and in cases of flexible targeting, where it does. According to the results in Martinez
et al. (2001), Mexico would belong to the latter category at least since late 1998. But it is important
to note that the conclusions derived below regarding the interest rate-exchange rate link do not
depend on including output in the government’s loss function. Even if they were strict targeters,
the authorities would react to a currency depreciation by tightening monetary policy, thus
producing the positive correlation discussed in the text.
20