Distance Dependent Offsets between Parallaxes for Nearby Stars and Gaia   DR1 Parallaxes
  We use 612 single stars with previously published trigonometric parallaxes placing them within 25 pc to evaluate parallaxes released in Gaia's first data release (DR1). We find that the Gaia parallaxes are, on average, $0.24 \pm 0.02$ mas smaller than the weighted mean trigonometric parallax values for these stars in the solar neighborhood. We also find that the offset changes with distance out to 100 pc, in the sense that the closer the star, the larger the offset. We find no systematic trends in the parallax offsets with stellar $V$ magnitude, $V-K$ color, or proper motion. We do find that the offset is roughly twice as large for stars south of the ecliptic compared to those that are north. 
Wei-Chun Jao, Todd J. Henry, Adric R. Riedel, Jennifer G. Winters,   Kenneth J. Slatten and Douglas R. Gies
astro-ph.SR