  We calculate the $c$-axis kinetic energy difference between normal and
superconducting state for coherent and for incoherent interlayer coupling
between CuO$_{2}$ planes. For coherent coupling the ratio of the missing
conductivity spectral weight to the superfluid density is equal to one and
there is no violation of the conventional sum rule, but for the incoherent case
we find it is always greater than one whatever the nature of the impurity
potential may be. To model more explicitly YBa$_{2}$Cu$_{3}$O$_{7-x}$ around
optimum doping, which is found to obey the sum rule, we consider a plane-chain
model and show that the sum rule still applies. A violation of the sum rule of
either sign is found even for coherent coupling when the in-plane density of
electronic states depends on energy on a scale of the order of the gap.
