diagnostic features obtained when testing for remaining heteroskedasticity in ξ^kt we keep
the ARCH(1) model for a few volatility processes (FR, GE, NL for exports and CA, FR,
and GE for imports). This may be justified from an economic point of view. According to
the ARCH-LM(I) test18 applied to the estimated GARCH(1,1) residuals ξ^kt, the estimated
volatility models do not indicate any remaining conditional heteroskedasticity.
3 Estimation
3.1 The VECM
Apart from the measures of FX uncertainty all remaining variables, real sectoral exports
(imports), domestic and foreign economic activity, and the real effective FX rate turned out
to contain stochastic trends. We refrain from providing detailed results of ADF-tests applied
to these respective series in levels and first differences but assure that with almost no excep-
tion xktt ,mktt, ipkt, ip*kt, ekt are found to be integrated of order one. Therefore we formalize a
VECM specified in first differences that captures potential cointegrating relationships linking
the stochastic trends of the nonstationary processes. Apart from separating long and short
run dynamics, the error correction approach is likely to improve the diagnostic features of
the empirical trade models owing to the rich dynamic structure. It is worthwhile to note that
poor diagnostic features of empirical trade models were mostly ignored in the literature.20
Since our volatility estimates turned out to be stationary and accounting for the seasonal
pattern of the macroeconomic variables we employ the following conditional VECM of order
p as a multivariate starting point for the empirical analysis:
p
∆ykt = μk + λkvkt + πkykt-1 + ∣'k^ykt-i + ψkdt + εkt∙ (5)
i=1
In (5) ykt collects the nonstationary variables, i.e. ykt = (xj), ipkt, ipkt, ekt) and ykt =
(mktt, ipkt, ipkt, ekt) when investigating exports and imports, respectively. In case of coin-
tegration with cointegration rank r, 0 < r < 4, the matrix Πk factorizes as Πk = αkβ'k,
where αk is a 4 × r matrix. As indicated by model selection criteria we allow for an inter-
cept term in the cointegration relationship. Therefore ykt is defined as ykt = (y'kt, 1)' and
β is a 5 × r matrix. Whereas βk parameterizes the equilibrium relationships between the
nonstationary variables the loading matrix αk governs how lagged violations of the long-run
relation(s) affect current adjustments of the components in ykt. In case the variables in ykt
fail to cointegrate, i.e. r = 0, the matrix Πk disappears and trade dynamics are modelled
via a conditional VAR specified in (stationary) first differences. Deterministic terms in dt
contain seasonal dummy variables and three event dummy variables capturing the widening
of the Exchange Rate Mechanism (ERM) margins to 15% (1993:08), the suspension of ERM