Ab initio wave function-based methods are applied to the study of electron correlation effects on the band structure of oxide systems. We choose MgO as a prototype closed-shell ionic oxide. Our analysis is based on a local Hamiltonian approach and performed on finite fragments cut from the infinite solid. Localized Wannier functions and embedding potentials are obtained from prior periodic Hartree-Fock HF calculations. We investigate the role of various electron correlation effects in reducing the HF band gap and modifying the bandwidths. On-site and nearest-neighbor charge relaxation as well as long-range polarization effects are calculated. Whereas correlation effects are essential for computing accurate band gaps, we found that they produce smaller changes on the HF bandwidths, at least for this material. Surprisingly, a broadening effect is obtained for the O 2p valence bands. The ab initio data are in good agreement with the energy gap and bandwidth derived from thermoreflectance and x-ray photoemission experiments. The results show that the wave function-based approach applied here allows for well controlled approximations and a transparent identification of the microscopic processes which determine the electronic band structure.