  It is shown that the Coulomb drag between two identical layers in the
Anderson insulting state indicates a striking difference between the Mott and
Efros-Shklovskii (ES) insulators. In the former, the trans-resistance $\rho_t$
is monotonically increasing with the localization length $\xi$; in the latter,
the presence of a Coulomb gap leads to an opposite result: $\rho_t$ is enhanced
with a decreasing $\xi$, with the same exponential factor as the single layer
resistivity. This distinction reflects the relatively pronounced role of
excited density fluctuations in the ES state, implied by the enhancement in the
rate of hopping processes at low frequencies. The magnitude of drag is
estimated for typical experimental parameters in the different cases. It is
concluded that a measurement of drag can be used to distinguish between
interacting and non-interacting insulating state.
