  Wang et al. (2006) estimated an average radiative efficiency of 30% -- 35%
for quasars at moderate redshift. We find that their method is not independent
of quasar lifetimes and thus that quasars do not necessarily have such high
efficiencies. Nonetheless, it is possible to derive interrelated constraints on
quasar lifetimes, Eddington ratios, and radiative efficiencies of supermassive
black holes. We derive such constraints using a statistically complete sample
of quasars with black hole mass estimates from broad Mg II, made both with and
without the radiation pressure correction of Marconi et al. (2008). We conclude
that for quasars with L/LEdd > 0.02, lifetimes can range from 140 to 750 Myr
for Schwarzschild black holes. Coupled with observed black hole masses, quasar
lifetimes of < 140 Myr would imply that radiatively inefficient accretion or BH
mergers must be important in the accretion history of quasars. Given reasonable
assumptions about the quasar population, if the average quasar lifetime is < 1
Gyr, and if radiatively inefficient accretion is unimportant, then not many BHs
with Eddington ratio < 0.2 can be rapidly spinning.
