The standard approach to calculating the dielectric constant from molecular dynamics (MD) simulations employs a variant of the Kirkwood-Frohlich methodology. Many popular nonpolarizable models of water, such as TIPnP, give a reasonable agreement with the experimental value of 78. However, it has been argued in the literature that the dipole moments of these models are effective, being smaller than the real dipole of a liquid water molecule by about a factor of root epsilon(el), or roughly root 2. If the total or corrected dipole moment is used in calculations, the dielectric constant comes out nearly twice as large, i.e., in the range of 160, which is twice as high as the experimental value. Here we discuss possible reasons for such a discrepancy. One approach takes into account dynamic corrections due to the dependence of the dielectric response of the medium producing the reaction field on the time scale of dipole fluctuations computed in the Kirkwood-Frohlich method. When dynamic corrections are incorporated into the computational scheme, a much better agreement with the experimental value of the dielectric constant is found when the corrected (real) dipole moment of liquid water is used. However, a formal analysis indicates that the static properties, such as dielectric constant, should not depend on dynamics. We discuss the resulting conundrum and related issues of simulations of electrostatic interactions using periodic boundary conditions in the context of our findings.