We present evidence from nonlinear refractive index measurements, two-photon absorption measurements, and fourwave mixing measurements on semiconductors showing that the bound electronic nonlinearity can be calculated from two-photon absorption dispersion via a simple Kramers-Kronig analysis. This analysis shows n² changing from positive to negative as the photon energy approaches the band-gap energy, consistent with observations. Additionally, this simple calculation, which assumes two parabolic bands, gives good agreement with measured values of n² in wide-gap dielectrics that are 2 to 3 orders of magnitude smaller than in semiconductors.