Equations of light, propagating from quasar to observer on earth, are integrated in the time-dependent gravitational field of the solar system by making use of either retarded or advanced solutions of the Einstein field equations. This technique allows to separate explicitly the effects associated with the propagation of gravity from those associated with light in the integral expression for the relativistic time delay of light. We prove that the relativistic correction to the Shapiro time delay discovered by Kopeikin (ApJ, 556, L1, 2001) changes sign if one retains direction of the light propagation but replaces retarded with advanced solution of the gravitational field equations. Hence, this correction is due to the propagation of gravity and allows to measure its speed. Relativistic VLBI experiment conducted by Fomalont and Kopeikin in September 2002 proves that the propagation of gravitational field is characterized by the retarded potentials.