3.4.1 Diagnostic results
Explaining the dynamics of trade growth the employed single equation models (8) yield
degrees of explanation of 0.60 on average with an empirical standard error of 0.18. Diagnostic
results for the single equation (error correction) models are shown in the left hand side panels
of Table IV. The homoskedasticity assumption of error terms is tested by means of Lagrange
Multiplier (LM) tests against an ARCH(1)-specification (A1), and against various forms of
unconditional heteroskedasticity:36 A shift in the error variance occurring in the second half
of the sample period (H2), heteroskedasticity governed by the level of FX uncertainty, vtk,
(H3) or a trending error variance (H4). Note that particulary two types of heteroskedasticity
(A1 and H2) are of specific importance for the present investigation. On the one hand, one
may conjecture that the error terms in (8) have different unconditional variances in the sequel
of changing macroeconomic policies or the introduction of sophisticated financial innovations
to hedge FX rate risk. On the other hand, since the seminal article by Engle18 there is little
doubt about the finding that variables measured on financial markets as e.g. FX rates show
patterns of conditional heteroskedasticity. Moreover, we test for structural stability (ST)
via an F-type test comparing the accuracy of fit offered by the empirical model (8) with
a corresponding measure obtained after splitting the sample in two subsamples of almost
equal size. To provide a test against (higher order) serial error correlation Table IV also gives
results for the LM-test36,37 against joint autocorrelation up to order I (ARI). Alternative
values I = 1,12 are selected which are natural when analyzing monthly data. Aggregating
over 10 economic sectors Table IV provides absolute rejection frequencies of the respective
null hypotheses obtained at the 5% significance level by country for exports (upper panel) and
imports (lower panel), respectively. Since the analysis of exports (imports) covers 150 (140)
data sets one would expect on an aggregated level about 7 to 8 rejections of the respective
null hypotheses even if the data meet standard assumptions of econometric modelling.
Apparently the homoskedasticity assumption is violated for numerous empirical models.
In particular, the unconditional error variance is not stable over the first and second half of
the sample period for 57 (out of 150 export) or 44 (out of 140 import) equations. The re-
sults on testing the homoskedastic model against a trending variance mirror the latter results
since the corresponding test statistic (H4) obtains 56 or 46 rejections, respectively. When
testing the homoskedastic model against an ARCH(1) alternative or against heteroskedas-
ticity driven by our measure of FX uncertainty the absolute frequencies of rejecting the null
hypothesis are somewhat smaller. Summarizing these diagnostic results it is evident that for
reliable inference in models like (8) or (12) one should apply heteroskedasticity consistent
techniques.
With respect to testing on structural stability we obtain 35 and 23 rejections of the
respective null hypothesis when analyzing export and import dynamics, respectively. Some
rejections of structural invariance coincide with strong evidence in favor of heteroskedasticity
(e.g. Italian exports or imports), such that the applied F-distribution is hardly suitable
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