4.1 Two further competitors
4.1.1 No causal relation
From the estimation results presented in the last section one may draw the conclusion that
the true (partial) relation between FX uncertainty and trade is at most weak if it exists
at all. In the latter case the best forecast of trade growth conditional on volatility is just
”Zero” after controlling for remaining explanatory variables by means of partial regression.
For this reason we will also provide forecasting results obtained under the assumption that
trade growth is unaffected by FX uncertainty.
4.1.2 A threshold model
Eyeball inspection of the semiparametric estimates in Figure 1 or Figure 2 suggests for a
few data sets that the slope of ^k (v) varies over the support of v. Preferring parametric
models relative to the semiparametric approach for the reasons of estimation and forecasting
efficiency one may therefore also employ a basically linear model allowing for a shift in the
slope coefficient or the intercept term. Since volatility clustering is a stylized feature of FX
variations one may regard the relation between trade and volatility to differ across states of
low and high volatility. Such an assumption is straightforward to implement by means of a
dummy variable model,30 i.e.
ykt = ck + vtkθk + c(k+) + vtkθk(+) I(vtk >0) + εtk .
(16)
In (16) I(.) denotes an indicator variable which is equal to 1 if vkt is positive. Owing to our
practice of adjusting volatility by means of partial regression vtk = 0 is suitable to separate
states of relatively high and low volatility. In addition, for the vast majority of analyzed
data sets the zero threshold is rather close to the empirical median of vtk . For the linear
projections in (10) it turns out that the volatility measures vkt and vkt are highly correlated,
having correlation coefficients of 0.94 on average with an empirical standard deviation of
0.04. If the relationship between volatility and trade growth is stable across alternative
states of volatility the parameters governing threshold effects c(k+) and θk(+) are not different
from zero. Vice versa, nonlinear dynamics would be indicated if forecasts based on the
threshold specification (16) outperform a linear forecasting scheme.
4.2 The forecasting design
Ex-ante forecasting exercises are performed for the linear specification (11), the semipara-
metric model (12) estimated by means of the local linear estimator (14) and the threshold
model (16). In addition to the latter specifications building on some a-priori assumed rela-
tionship between FX uncertainty and trade growth we will also compare their outcomes with
”unconditional” forecasts of zero implying that there is no relation between the two variables
13