The Interest Rate-Exchange Rate Link in the Mexican Float
To solve the problem, let us postulate linear functions for output:
y=y0 + yqq + yii, the real exchange rate: q = q0 + qii, the interest rate:
i=i0 + imm, and the inflation rate: π = π0 + πqq + πii. Output is assumed
to depend negatively on the interest rate, but the effect of variations
in the real exchange rate is uncertain: a rise in q improves the trade
balance, thus raising aggregate demand, but it also has income-
distribution and balance-sheet effects operating in the opposite
direction (see, e.g., Ocampo 2000). Following the previous discussion,
the real exchange rate is taken to be a negative function of the interest
rate; we leave aside considerations of dynamic adjustment for
simplicity. The interest rate is posited to have a market component
(i0), reflecting portfolio preferences, expectations, etc., and a policy
component. If, for instance, the central bank uses the money base as
its instrument (m), then im <0.
The inflation rate is assumed to depend negatively on the interest
rate and positively on the real exchange rate. The former effect simply
reflects the idea that a rise in the interest rate is disinflationary
because it reduces aggregate demand and, thus, upward price pressures
in the labor and goods markets; naturally, the inflation rate may in
turn affect the interest rate through the market component i0, but
such complication is not further considered here. The second
determinant of inflation may require some elaboration. Calvo (1997),
among others, has called attention to the existence of a strong negative
link between the inflation rate and the level of the real exchange rate
in Mexico. This nexus is a critical factor in the present analysis. In
particular, if an exogenous rise in the exchange rate only led to a higher
price level, but without affecting the inflation rate, then inflation-averse
authorities would not assume a tighter policy stance (except in the
unlikely case that they were targeting the price level, and not the
inflation rate).
Returning to the government’s loss function, we can set dL/dm = 0
and find that the policy rule is:
(9) m = {τ (π*-Π) Πm - OYm} / {(Ym)2 + τ (Πm)2}
where Π = π0 + πq(q0 + qii0) + πii0, Πm = im (πqqi + πi), O = y0 + yq (q0 + i0qi) +
i0yi, and Ym = im (yqqi + yi). Ym measures the output response to a monetary
expansion; it will be positive, unless the possibly negative effect of the real
exchange rate on output is very strong. Πm measures the overall impact of
a monetary expansion on the inflation rate and it is, of course, positive.
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