  We investigate the ability of hierarchical models of QSO formation and
evolution to match the observed luminosity, number counts and spatial
clustering of quasars at redshift z<2. These models assume that the QSO
emission is triggered by galaxy mergers, that the mass of the central black
hole correlates with halo properties and that quasars shine at their Eddington
luminosity except, perhaps, during the very early stages of evolution. We find
that models based on simple analytic approximations successfully reproduce the
observed B-band QSO luminosity function at all redshifts, provided that some
mechanisms is advocated to quench mass accretion within haloes larger than
about 1e13 Msun that host bright quasars. These models also match the observed
strength of QSO clustering at z~0.8. At larger redshifts, however, they
underpredict the QSO biasing which, instead, is correctly reproduced by
semi-analytic models in which the halo merger history and associated BHs are
followed by Monte Carlo realizations of the merger hierarchy. We show that the
disagreement between the luminosity function predicted by semi-analytic models
and observations can be ascribed to the use of B-band data, which are a biased
tracer of the quasar population, due to obscuration.
