  Understanding the interplay between black-hole accretion and star formation,
and how to disentangle the two, is crucial to our understanding of galaxy
formation and evolution. To investigate, we use a combination of optical and
near-infrared photometry to select a sample of 74 quasars from the VISTA Deep
Extragalactic Observations (VIDEO) Survey, over 1 deg$^2$. The depth of VIDEO
allows us to study very low accretion rates and/or lower-mass black holes, and
26 per cent of the candidate quasar sample has been spectroscopically
confirmed. We use a radio-stacking technique to sample below the nominal
flux-density threshold using data from the Very Large Array at 1.4 GHz and
find, in agreement with other work, that a power-law fit to the quasar-related
radio source counts is inadequate at low flux density. By comparing with a
control sample of galaxies (where we match in terms of stellar mass), and by
estimating the star formation rate, we suggest that this radio emission is
predominantly caused by accretion activity rather than star-formation activity.
