  The Hipparcos catalog provides the first epoch of the celestial reference
frame (CRF) in the optical domain and serves as an indispensable tool to verify
and improve the Gaia CRF for the brighter stars ($V<11$ mag) and to identify
the elusive astrometric binary stars with dim or invisible companions,
including long-period exoplanets. The systems of positions in Hipparcos and
Gaia cannot be directly compared, because they refer to two different mean
epochs. It is shown that the proper motion systems for carefully filtered
common stars are not statistically consistent within the given formal errors.
The vector field of proper motion differences is fitted with 126 vector
spherical harmonics up to degree 7 revealing a global pattern at high
signal-to-noise ratios, including the three terms of rigid rotation. The origin
of the differential spin and other large harmonic terms is investigated by
producing a similar decomposition of the Gaia$-$HG proper motion field, where
HG stands for the long-term proper motions derived from the Hipparcos and Gaia
DR3 positions, for the same sample of stars. Hipparcos proper motions emerge as
the largest source of sky-correlated distortions of the multi-epoch optical CRF
with a median value of $\sim 190$ $\mu$as yr$^{-1}$ and a global spin of $\sim
226$ $\mu$as yr$^{-1}$, while the Hipparcos positions and Gaia EDR3 proper
motions are explicitly consistent by construction at a level of $\sim 10$
$\mu$as yr$^{-1}$. The latter, however, include multiple distortions of higher
degree, which should be taken into account in astrometric applications using
the HG field.
