Quantitative calculations of phonon lifetimes due to anharmonic three-phonon processes require knowledge of cubic anharmonic coupling coefficients. In order to determine the temperature dependence of phonon frequencies, anharmonic force constants of up to fourth order are needed. In polar crystals, the macroscopic electric field gives rise to nonanalytic terms in these coefficients. It is shown how these non-analytic terms can be determined from other physical quantities including higher-order dipole moments, Raman coefficients, and nonlinear susceptibilities. The contribution of these terms to the intrinsic damping of the long-wavelength optical phonon modes in GaAs has been determined by an ab initio calculation.