  We consider a model in which the ultra-relativistic jet in a gamma-ray burst
(GRB) is cold and magnetically accelerated. We assume that the energy flux in
the outflowing material is partially thermalized via internal shocks or a
reverse shock, and we estimate the maximum amount of radiation that could be
produced in such magnetized shocks. We compare this estimate with the available
observational data on prompt gamma-ray emission in GRBs. We find that, even
with highly optimistic assumptions, the magnetized jet model is radiatively too
inefficient to be consistent with observations. One way out is to assume that
much of the magnetic energy in the post-shock, or even pre-shock, jet material
is converted to particle thermal energy by some unspecified process, and then
radiated. This can increase the radiative efficiency sufficiently to fit
observations. Alternatively, jet acceleration may be driven by thermal pressure
rather than magnetic fields. In this case, which corresponds to the traditional
fireball model, sufficient prompt GRB emission could be produced either from
shocks at a large radius or from the jet photosphere closer to the center.
