The quadrupolarity of carbon dioxide has been studied with higher level ab initio methods. Carbon dioxide exhibits {- + -} quadrupolarity in all directions and an explanation is provided of the origin of the sign of the diagonal elements Qii. The quadrupole moment tensor has been computed using restricted Hartree-Fock theory, second-order Møller-Plesset perturbation theory and quadratic configuration interaction theory. A variety of basis sets have been employed up to basis sets of the type [5s, 4p, 2d, 1f] (23s, 8p, 2d, 1f). The quadrupole moment tensor component Q∥ of carbon dioxide falls in the range between -18.5 and -20.5 Debye Å. The quadrupole moment tensor components Q⊥ of carbon dioxide are smaller, ranging from -14.5 to -15 Debye Å, and they are less sensitive to the choice of the theoretical model. The correlated methods consistently predict an increase of Q∥ while they predict a more modest reduction of Q⊥. It is for the opposing electron correlation effects on Q∥ and Q⊥ that the average values of the diagonal elements, 〈Qii〉, are essentially independent of the method and exhibit only a small variation depending on the basis set. On the other hand, the anisotropy of the quadrupolarity, the quadrupole moment Θ, is affected most by the opposing electron correlation effects on Q∥ and Q⊥. The accurate reproduction of the measured quadrupolarity Θ = -4.3 Debye Å requires a theoretical model that employs both a good method and a good basis set. The results suggest that the use of second-order Møller-Plesset perturbation theory in conjunction with well-polarized triple-ζ basis sets provides a cost-effective and quite accurate method for the estimation of correlation effects on quadrupole moments.