to provide critical values. The strongest case for structural instability is obtained when
modelling Japanese exports where the null hypothesis of structural invariance is rejected
for 7 out of 10 sectors and, in the same time, only weak evidence is obtained against the
assumption of homoskedasticity. Since structural stability is an important condition when it
comes to forecasting issues the latter results may call for some respecification of the employed
models or of the applied subset modelling strategy. Regarding the forecasting exercises,
however, it is worthwhile mentioning that the issue of potential structural variation will be
mitigated by running the model selection procedure for each (recursive) sample separately.
Testing against serial correlation it turns out that in particular for 30 (34) empirical
export (import) equations error terms exhibit some overall autocorrelation up to lag 12. This
might indicate some misspecification of seasonal dynamics or shortcomings of the adopted
subset model selection strategy. Given the evidence in favor of heteroskedasticity, however,
some of the reported rejections for AR12 may falsely indicate serial correlation owing to size
distortions of the LM-test. The evidence in favor of first order serial correlation is much
weaker (only 10 or 14 rejections for export and import models, respectively). Note that for
the forecasting exercises discussed in the next section higher order serial correlation is of
minor importance relative to first order correlation since we will concentrate on one step
ahead forecasting.
insert Figure 1 and Figure 2 about here
3.4.2 Estimation Results
Estimation results for selected sectors of the US and trade patterns observed for sector 7
over a subset of the cross section are shown in Figure 1 and Figure 2, respectively. Note
that sector 7 is (almost uniformly) the most active sector of international trade over the set
of economies considered in our study (see Table II).
The left (right) hand side panels of Figure 1 show both estimates of the partial relation
between FX uncertainty and export (import) growth, linear (dashed line) and semiparametric
estimates (solid curves). To indicate significance of the latter estimates 95% confidence
intervals are given that are obtained by means of a heteroskedasticity consistent bootstrap
procedure.35 To facilitate the interpretation of the estimates we also provide horizontal lines
through ykt = 0 indicating a scenario where by assumption FX uncertainty has no impact
on trade growth at all. Moreover, each graph provides the (partial) degree of explanation
(Rp) obtained from model (11) and the corresponding slope estimate θk. The (partial)
degree of explanation turns out to be low for both, the linear (being at most 0.045) and
the semiparametric estimator. Obviously, the relationship between FX uncertainty and
trade growth is not uniform over different sectors, and, moreover, may differ for a given
sector when contrasting conditional estimates of export and import growth. Some results
indicate an overall positive relationship (US-exports, sector 8, US-imports, sector 0) whereas
11