Exchange Rate Uncertainty and Trade Growth - A Comparison of Linear and Nonlinear (Forecasting) Models



participation by IT and the UK (1992:09), and the German reunification and the entry of
the UK to the ERM (1990:10). FX uncertainty v
kt is the estimated conditional standard
deviation as obtained from the GARCH(1,1) or ARCH(1) models outlined in the preceding
Section. μ
k and λk are 4-dimensional parameter vectors and Γki,i = 1,... ,p, and Ψk are
parameter matrices accounting for the short run dynamics and deterministic patterns, re-
spectively. The elements of
εkt are assumed to be serially uncorrelated with zero mean and
constant covariance. To facilitate the notation we have skipped the sectoral index j from
the model in (5) but mention that all model parameters are country and sector specific.

On the basis of the entire available sample information the VECM in (5) is used to deter-
mine key parameters as the model order (p) or the cointegration rank (r). For this purpose
we use the AIC model selection criterion and the Johansen trace test
28 as implemented in
EViews 4.1. After the determination of the cointegration rank we will use in the following
the estimated stationary equilibrium violations,
eCkt = β'ky^kt, as potential explanatory vari-
ables for trade growth dynamics. Since the variables in
ykt contain stochastic trends the
estimator
βk is superconsistent. Therefore the asymptotic properties of the remaining model
parameters will be unaffected when specifying the VECM with an estimated error correction
term
eCkt replacing the corresponding true quantity eckt = β'kykt.29

3.2 The partial impact of volatility on trade

Since our interest concentrates on the relationship between trade growth and FX uncertainty
we use the vector model in (5) to figure out potential dynamic impacts on trade growth.
Determinants of trade are formalized in the VECMs first equation, which is now extracted
from the model and denoted as

p

Aykt = μik + λ1kvkt + α1kect-1 +    YkiAykt-i + ψkdt + εkt                      (6)

i=1

X ktφk + εkt.                                                                    (7)

In (6), ykt and ∕kt are the first elements of ykt and εkt, respectively, and, analogously,
μ
1k, λ1k, α1k, γki and ψk denote the first rows of the corresponding parameter vectors or
matrices in (5). Equation (7) is just a compact representation of (6) where φ
k is a column
vector collecting all model parameters.

Estimation efficiency of the single equation model in (7) is likely to suffer from the large
number of parameters or, put differently, from various presumably insignificant parameter
estimates. Therefore we run a subset modelling strategy where sequentially remove those
parameter estimates with the smallest t
-ratio from the set of explanatory variables in Xkt .
This iterative procedure continues until all estimated parameters show t
-statistics which are
at least unity in absolute value. Since we are finally interested in the partial impact of FX



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