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

nineteen partner countries account for roughly 75% of total exports (73% of total imports).
A noteworthy exception is JP with a coverage of approximately 46% for exports (40% for
imports) since our set of partner countries omits some of JP’s important trading partners
(Singapore, Thailand, Malaysia, Korea, Hong Kong, and Chinese Taipei). Taking these
countries into account, however, would not correspond with our focus on industrialized
economies. On the other hand, excluding JP would substantially lower the coverage for a
number of industrialized countries in our cross section.

Sector j real exports (imports) of a country k are the USD denominated nominal sectoral
exports (imports) converted via the FX spot rate into national currency and deflated with
national export (import) prices. Strictly speaking, the use of the latter price indices for
realizing sectoral trade flows is particularly justified in the (unlikely) case that sectoral
prices are perfectly correlated. Sector specific prices series, however, are not available for
the considered cross section, sample period and sectoral classification. Trade figures enter
the empirical analysis after taking natural logarithms and are denoted as x⁽_k^j_t⁾ (exports) and
m⁽_k^j_t⁾ (imports), respectively.

As a natural measure of economic activity GDP figures are not available at the monthly
frequency in general. Therefore we approximate domestic economic activity by the (natural
logarithm of) industrial production for each country k, ip_kt . The quantity for foreign eco-
nomic activity is a weighted average of the industrial production (in logs) in the respective
partner countries, ip*_kt. The real effective FX rate faced by traders in country k, e_kt, is a
weighted average of the bilateral (log) real FX rates of country k and its trading partners.
Bilateral nominal FX rates are mostly deflated using national wholesale prices. Note, that
country specific weights are constant over time and among sectors but differ between the
case of exports and imports. This implies that e_kt and ip*_kt do not coincide for the analysis of
exports and imports. To simplify notation, however, we do not explicitly discriminate these
two cases in the following.

2.2.2 Modelling FX uncertainty

Being latent in nature numerous approximations of FX uncertainty are offered in the em-
pirical literature. Absolute percentage changes of FX rates,²⁵ moving averages of historical
FX rate variations measured in some past window of time,^16,22 or various measures based
on the monthly sum of daily FX rate changes^9,10 have been considered. Reviewing the lit-
erature on applications of so-called autoregressive conditionally heteroskedastic time series
processes^18,19 it turns out that the GARCH framework has been successful in a battery of em-
pirical studies to capture stylized features of FX processes such as the martingale property,
volatility clustering and leptokurtosis. In favor of the GARCH approach, moreover, Asseery
and Peel²⁶ point out that GARCH based risk measures directly concentrate on ”economically
relevant” conditional second order moments. Finally, the GARCH model provides an unbi-
ased estimator of the conditional expectation E[(∆e_kt)21Ω_t- 1] thereby mitigating problems

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