Real Exchange Rate Misalignment: Prelude to Crisis?

Now following Montiel (1999b), and Baffes, Elbadawi, and O’Connell (1999) the
equilibrium real exchange rate, et^eq, is specified as a single equation, the reduced form solution of
a small simultaneous equation model:

log (et^eq) = β'F^pt                                                                                (3)

where Ft^p is a vector of the permanent components of macro fundamentals, and β' is a vector of
parameters to be estimated.¹⁷ We must estimate both β and Ft^p. β may be estimated from the
long run steady state relationship between the observed values of the fundamentals and the
exchange rate:

log (et) = β'Ft + εt ,                                                                      (4)

where, et is the real exchange rate and F is the vector of fundamentals. εt is assumed to be a
stationary stochastic variable with zero mean.

An important condition for the existence of the relationship given by equation (3) is that Ft is
stationary in first differences [i.e. I(1)]. Only then will equation (3) be a candidate for a
cointegrating relationship. Kaminsky (1988) showed that equation (3) is a cointegrating
relationship when the reduced form equation of the structural model expresses the equilibrium
real exchange rate as a function of current and expected permanent components of the
macroeconomic fundamentals. If the cointegrating relationship in equation (3) holds and we
have an estimate of β', B say, then there exists a dynamic error correction equation consistent
with (3), which can be written as:

D(log(et+ι)) = γo (log et - B'F t ) + γ4D(F t+ι ) + γ´2 D(X_t+ι)                           (5)

where D(.) stands for the first difference of the corresponding variable or vector; (log et - B'F t )
is the error correction (ECt) term; and X is a vector of exogenous variables that are either

¹⁷ See also Maeso-Fernandez, Osbat and Schnatz (2004) for a review of methodological issues in estimating
equilibrium real exchange rates for Central and East European countries. See Baffes, Elbadawi and O’Connell
(1999) for the rationale behind the single equation approach, which we employ here.

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