  We have observed 99 mid-infrared-bright, massive young stellar objects and
compact HII regions drawn from the Red MSX source (RMS) survey in the J=3$-$2
transition of $^{12}$CO and $^{13}$CO, using the James Clerk Maxwell Telescope.
89 targets are within 6 kpc of the Sun, covering a representative range of
luminosities and core masses. These constitute a relatively unbiased sample of
bipolar molecular outflows associated with massive star formation. Of these,
59, 17 and 13 sources (66, 19 and 15 percent) are found to have outflows, show
some evidence of outflow, and have no evidence of outflow, respectively. The
time-dependent parameters of the high-velocity molecular flows are calculated
using a spatially variable dynamic timescale. The canonical correlations
between the outflow parameters and source luminosity are recovered and shown to
scale with those of low-mass sources. For coeval star formation we find the
scaling is consistent with all the protostars in an embedded cluster providing
the outflow force, with massive stars up to $\sim$30 M$_{\odot}$ generating
outflows. Taken at face value, the results support the model of a scaled-up
version of the accretion-related outflow-generation mechanism associated with
discs and jets in low-mass objects with time-averaged accretion rates of
$\sim$10$^{-3}$ M$_{\odot}$ yr$^{-1}$ onto the cores. However, we also suggest
an alternative model, in which the molecular outflow dynamics are dominated by
the entrained mass and are unrelated to the details of the acceleration
mechanism. We find no evidence that outflows contribute significantly to the
turbulent kinetic energy of the surrounding dense cores.
