  It has long been believed that accretion onto supermassive black holes powers
quasars, but there has been relatively few observational constraints on the
spins of the black holes. We address this problem by estimating the average
radiative efficiencies of a large sample of quasars selected from the Sloan
Digital Sky Survey, by combining their luminosity function and their black hole
mass function. Over the redshift interval $0.4<z<2.1$, we find that quasars
have average radiative efficiencies of $\sim 30% - 35%$, strongly suggesting
that their black holes are rotating very fast, with specific angular momentum
$a \approx 1$, which stays roughly constant with redshift. The average
radiative efficiency could be reduced by a factor of $\sim$2, depending on the
adopted zeropoint for the black hole mass scale. The inferred large spins and
their lack of significant evolution are in agreement with the predictions of
recent semi-analytical models of hierarchical galaxy formation if black holes
gain most of their mass through accretion.
