A theory of electron correlations based on a generalized random-phase approximation is presented. An expression for the local-field correction is obtained using the third frequency moment of the spectral function of the electron-density response function. The local field is a functional of the structure factor S(q) which in turn is related to the imaginary part of the dielectric function via the fluctuation-dissipation theorem. The equations are self-consistently solved to determined S(q) as originally suggested by Singwi et al. The pair-correlation function, compressibility, plasma dispersion, and correlation energy of electron liquid at metallic densities have been calculated. © 1973 The American Physical Society.