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 / L _ { Edd } \gtrsim 0.02 , lifetimes can range from 140 to 750 Myr for Schwarzschild black holes .
Coupled with observed black hole masses , quasar lifetimes of \leq 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 .