We present a theory of the linear and nonlinear optical characteristic
s of the insulating phase of the Falicov-Kimball model within the self
-consistent mean-field approximation. The Coulomb attraction between t
he itinerant d electrons and the localized f holes gives rise to a bui
lt-in coherence between the d and f states, which breaks the inversion
symmetry of the underlying crystal, leading to (1) electronic ferroel
ectricity, (2) ferroelectric resonance, and (3) a nonvanishing suscept
ibility for second-harmonic generation. As experimental tests of such
a built-in coherence in mixed-valent compounds, we propose measurement
s of the static dielectric constant, the microwave absorption spectrum
, and the dynamic second-order susceptibility.