The Interest Rate-Exchange Rate Link in the Mexican Float

Carlos A. Ibarra

short-term deviation from equilibrium as a regressor.¹⁰ The resulting
ECM is:

(5) ∆irdt = D υ_t + h₀ + Σ h_j ∆ird_t-j + ∑ n_i ∆lns_t-i + Σ p_i ∆lnm_t-i + Σ w_i ∆fed_t-i + ut,

where D is the coefficient of the short-run deviation from equilibrium.
The dynamic response of the interest differential to a permanent rise
in the log exchange rate was derived from the estimated coefficients
of Equation (5). In particular, the points on the impulse response
function correspond to the (total) derivative of ∆ird_t+r with respect to
∆lns_t, for r = 1, 2, ... (see Enders 1995, chapter 1). For instance, the
first three points were calculated as:

d∆ird_t∕d∆lns_t = n₀

d∆ird_t+1∕d∆lns_t = n₀ + n₁ +h₁ (d∆ird_t∕d∆lns_t)

d∆ird_t+2∕d∆lns_t = n₀ + n₁ + n₂ + h₁ (d∆ird_t+1∕d∆lns_t) + h₂ (d∆ird_t∕d∆lns_t)

where it is assumed that the variation in the exchange rate is
permanent (i.e., d∆lns_t+r = d∆lns_t, for r = 1, 2, .).

c) Estimation results

The interest rate differential used in the analysis was calculated from
the weekly auctions of 91-day Mexican Cetes and 3-month US Treasury
bills. As noted before, these rates are particularly suitable for our
purposes, because during the sample period they were not central bank
policy instruments, but market-determined variables. The exchange
rate is the weekly average of closing, interbank bid and ask rates. The
inflation rate is the 24 half-month variation in the consumer price
index (CPI) published by Banco de Mexico. Since interest rate
observations are weekly, but the CPI is available only twice a month,
it was necessary to roughly assign one inflation observation to two
interest rate observations. Given that the inflation rate appears to
determine mainly the differential’s long-run level, this does not seem
to pose a serious problem. The real money base index equals the

¹⁰ The inflation rate was excluded under the assumption that it does not affect variations in
interest rate differentials in the very short run. This intuition was confirmed in statistical terms:
inclusion of inflation in the estimated ECM yielded very poor results for the entire model.

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