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

By assumption the error terms in (12) have conditional zero mean and finite variance,
E[βkt|v] = 0, Var[ekt∣v] = Z2(v) < ∞.                                                     (13)

Given the nonparametric nature of the regression model in (12) on the one hand and recalling
on the other hand that both variables y_kt and v_kt are obtained from linear projections the
model in (12) actually formalizes a semiparametric approach. We evaluate the (unknown)
conditional mean, ak(v), using the locally linear estimator^32,33 which is the first component
of a_k = (ak⁰) , ak¹))’ that solves the minimization problem

K(.) and h are a symmetric kernel function and the bandwidth parameter, respectively.
Obviously ^_k(v) solves locally a common least squares problem. Weights associated to sample
values ykt depend on the distance between vkt and v , the bandwidth h and the employed
kernel function. For our purposes locally linear estimation is implemented by means of the
Gaussian kernel

(^-2 ^u2) ∙

A particular problem in semiparametric regression is to select the bandwidth parameter
h.³⁴ Owing to the large number of empirical models employed for estimation and recursive

forecasting, a data driven bandwidth selection is infeasible to implement for this empirical
study. Therefore a common rule of thumb bandwidth choice is preferred, namely
where σ_v is the empirical standard deviation of v_kt and T is the sample size.

To illustrate the precision of semiparametric estimates pointwise confidence bands for
ak (v) could be obtained from quantiles of the Gaussian distribution and some variance esti-
mate Z2(v) or from resampling techniques as outlined in Neumann and Kreiss.^35,36 The latter,
applied in this study, have the advantage to account for the potential of heteroskedastic error
terms where the particular form of heteroskedasticity is left unspecified.

3.4 Results

Having introduced the basic tools employed to infer on the relationship between FX uncer-
tainty and trade growth, the partial linear model (11) and the semiparametric specification
(12), we will now provide some model diagnostics for the former and selected estimation
results for both models applied. Since we have investigated 150 export and 140 import equa-
tions we refrain from reporting test statistics in detail but will rather provide test decisions
on an aggregated level.

insert Table IV about here

<<   8   9   10   11   12   13   14   >>

More intriguing information