  We present an alternate formula for calculating gravitational time delay. We
use this formula to reduce geodetic Very Long Baseline Interferometry (VLBI)
data, taking into account gravitational effects within the solar system, and to
test general relativity. The alternate formula was obtained by expanding the
conventional formula in a Taylor series. We show that the gravitational delay
can be split into several terms including a term due to the coordinate
transformation and terms that are explicitly linked to the light deflection
angle. Our formula is compared numerically with the conventional formula, and
difference in arrival times within 1 ps are found at 1$^\circ$ from the Sun for
a full range of baseline lengths. We conclude that the standard reduction of
geodetic VLBI data for the effects of general relativity is equivalent to
displacing the reference radio sources from their original catalogue positions
in accordance with the classical light deflection formula across the whole sky.
