The Interest Rate-Exchange Rate Link in the Mexican Float
term.9 The long-run equilibrium, or cointegration, version of Equation
(2) is obtained by imposing the condition that each variable has
converged to a constant value, i. e., irdt= irdt-j for all j, etc.
Equation (2) was estimated in the following transformed, fully-
equivalent version:
(3) irdt = a0 + α irdt-1 - Σ ak (irdt-1 - irdt-k) + β lnst - Σ bj (lnst - lnst-j) + χ lnmt
- Σ c (lnmt - lnmt-j) + Φ ∏t - ∑ f (∏t - ∏t-j) + Y fedt - ∑ gj (fedt - fedt-j) + vt>
where k = 2, ..., L. It is easy to verify that estimation of this transformed
version necessarily satisfies: α = Σaj, β = Σbi, χ = Σci, φ = Σfi, and γ= Σgi.
One advantage of estimating Equation (3) instead of the original
version is that it immediately yields the coefficients forming the long-
run relationship (another is that it generates the p-values for the
long-run coefficients; see Davidson and McKinnon 1993, chapter 19).
In particular, the cointegration equation will be given by:
(4) irdtc = a0∕ω + (β∕ω) lnst + (χ∕ω) lnmt + (φ∕ω) πt + (γ∕ω) fedt,
where ω= 1-α. In any given period, the deviation from long-run
equilibrium will simply be: υt = irdt - irdtc. According to the so-called
residual-based test, if Equation (4) is indeed a cointegration equation,
then we should be able to reject the null hypothesis of a unit root in
the υt series (see Enders 1995, chapter 6).
The dynamic response of the interest rate differential to an
exchange rate change was obtained by means of an impulse response
function. The starting point was again an ADL model for the interest
differential, but this time specified in differences and including the
9 Equation (1) is mainly a theoretical relationship stating that under free capital mobility
similar assets must offer similar rates of return, up to a risk premium. Equation (2), in
contrast, is a specification intended for empirical examination. In moving from Equation (1)
to (2), there are two features that must be considered: first, in time series analysis it is
common practice to include lagged values of both the dependent variable and the regressors,
in order to account for the purely statistical properties of the data (so as to avoid, for instance,
a potential problem of serial correlation in the residuals) and the probable protracted impact
of the regressors on the variable under study. The second feature is that it surely would be
an unrealistic assumption to posit that there is perfect capital mobility between the US and
Mexico; under imperfect mobility, the interest parity condition does not hold exactly, and
there can be a risk premium affected by variables such as those included in the right side of
Equation (2), namely, the local money supply, the inflation rate, and the foreign interest
rate.
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