  We examine the density-functional theory of macroscopic insulators, obtained
in the large-cluster limit or under periodic boundary conditions. For polar
crystals, we find that the two procedures are not equivalent. In a
large-cluster case, the exact exchange-correlation potential acquires a
homogeneous ``electric field'' which is absent from the usual local
approximations, and the Kohn-Sham electronic system becomes metallic. With
periodic boundary conditions, such a field is forbidden, and the polarization
deduced from Kohn-Sham wavefunctions is incorrect even if the exact functional
is used.
