  In this paper we investigate whether a misestimate of proper motions could
have been a source of substantial systematic errors in the statistical parallax
determination of the absolute magnitude of RR Lyrae stars. In an earlier paper,
we showed that the statistical parallax method is extremely robust and rather
insensitive to various systematic effects. The main potential problem with this
method would therefore arise from systematically bad observational inputs,
primarily radial velocities and proper motions. In that paper, we demonstrated
that the radial velocities have not been systematically misestimated. Here we
turn our attention to proper motions. We compare three different catalogs of
proper motions --- Lick, Hipparcos and the one compiled by Wan et al. (WMJ). We
find that the WMJ catalog is too heterogeneous to be a reliable source.
  We analyze the sample of 165 halo RR Lyrae stars with either Lick or
Hipparcos proper motions. For the stars with both Lick and Hipparcos proper
motions we use the weighted means of reported values. Various possible biases
are investigated through vigorous Monte Carlo simulations and we evaluate small
corrections due to Malmquist bias, anisotropic positions of the stars on the
sky, and non-Gaussian distribution of stellar velocities. The mean RR Lyrae
absolute magnitude is M_V = 0.74 +/- 0.12 at the mean metallicity of the sample
<[Fe/H]> = -1.60, only 0.01 mag brighter than the value obtained in the
previous study which did not incorporate Hipparcos proper motions. The faint
absolute magnitudes of RR Lyrae stars confirmed by this analysis gives strong
support to the short distance scale.
