fundamentals are either stationary or difference stationary. For a few variables, the results
obtained from the ADF test and that from the Phillips-Perron test differ. Since for each country
the real exchange rate along with some other macroeconomic fundamentals are found to be non-
stationary in levels and stationary in first differences, the long run equilibrium equations for each
country can be estimated, provided the real exchange rate and the fundamentals are cointegrated.
5. Estimation of the Long Run Real Equilibrium Exchange Rate Equation
Finding the long run equilibrium relation (equation (3)) involves two separate but related
tasks: testing for the existence of a cointegrating relation, and estimation of the coefficient
vector. The Engel-Granger (1987) method applies OLS to a static regression of the real
exchange rate on its fundamentals in levels (equation (4)). If the residuals from the regression are
found to be stationary, then the estimated parameters are cointegrating parameters.26 However,
in finite samples the static OLS (henceforth SLOS) estimators are biased if the regressors are not
strictly exogenous (Banerjee et al., 1986, and Stock, 1987). Strict exogeneity would be violated
if there is serial correlation (Hamilton, 1994, pp. 608 - 612, and Hayashi, 2000, pp. 650 - 655).
Yet another drawback of SOLS is that the asymptotic distributions of the t-ratios depend on
‘nuisance parameters’ (Hayashi, 2000). To correct this Saikkonen (1991), Phillips and Loretan
(1991), Stock and Watson (1993), and Wooldridge (1991) suggest dynamic OLS (henceforth
DOLS), in which the regressors would be strictly exogenous. In this case, first differences, as
well as first differences with lags and leads of the regressors are considered along with the
26 When testing for a unit root in the residuals more restrictive critical values should be employed than in the
univariate unit root tests.
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