  We couple non-magnetic, hydrodynamical simulations of collapsing protostellar
cores with radiative transfer evolutionary models to generate synthetic
observations. We then use these synthetic observations to investigate the
extent to which a simple method for measuring protostellar disc masses used in
the literature recovers the intrinsic masses of the discs formed in the
simulations. We evaluate the effects of contamination from the surrounding
core, partially resolving out the disc, optical depth, fixed assumed dust
temperatures, inclination, and the dust opacity law. We show that the
combination of these effects can lead to disc mass underestimates by up to
factors of 2-3 at millimeter wavelengths and up to an order of magnitude or
larger at submillimeter wavelengths. The optically thin portions of
protostellar discs are generally cooler in the Class I stage than the Class 0
stage since Class I discs are typically larger and more optically thick, and
thus more shielded. The observed disc mass distribution closely resembles the
intrinsic distribution if this effect is taken into account, especially at
millimeter wavelengths where optical depth effects are minimized. Approximately
50%-70% of protostellar discs observed to date with this method are consistent
with the masses of the gravitationally unstable discs formed in the
simulations, suggesting that at least some protostellar discs are likely
sufficiently massive to fragment. We emphasize key future work needed to
confirm these results, including assembling larger, less biased samples, and
using molecular line observations to distinguish between rotationally
supported, Keplerian discs and magnetically supported pseudodiscs.
