  Starting from the many-body Bethe-Salpeter equation we derive an
exchange-correlation kernel $f_{xc}$ that reproduces excitonic effects in bulk
materials within time-dependent density functional theory. The resulting
$f_{xc}$ accounts for both self-energy corrections and the electron-hole
interaction. It is {\em static}, {\em non-local} and has a long-range Coulomb
tail. Taking the example of bulk silicon, we show that the $- \alpha / q^2$
divergency is crucial and can, in the case of continuum excitons, even be
sufficient for reproducing the excitonic effects and yielding excellent
agreement between the calculated and the experimental absorption spectrum.
