  The BH mass (and the related Eddington ratio) in broad line AGN is usually
evaluated by combining estimates (often indirect) of the BLR radius and of the
FWHM of the broad lines, under the assumption that the BLR clouds are in
Keplerian motion around the BH. Such an evaluation depends on the geometry of
the BLR. There are two major options for the BLR configuration: spherically
symmetric or ``flattened''. In the latter case the inclination to the line of
sight becomes a relevant parameter. This paper is devoted to evaluate the bias
on the estimate of the Eddington ratio when a spherical geometry is assumed
(more generally when inclination effects are ignored), while the actual
configuration is ``flattened'', as some evidence suggests. This is done as a
function of luminosity and redshift, on the basis of recent results which show
the existence of a correlation between the fraction of obscured AGN and these
two parameters up to at least z=2.5. The assumed BLR velocity field is akin to
the ``generalized thick disk'' proposed by Collin et al. (2006). Assuming an
isotropic orientation in the sky, the mean value of the bias is calculated as a
function of luminosity and redshift. It is demonstrated that, on average, the
Eddington ratio obtained assuming a spherical geometry is underestimated for
high luminosities, and overestimated for low luminosities. This bias converges
for all luminosities at z about 2.7, while nothing can be said on this bias at
larger redshifts due to the lack of data. The effects of the bias, averaged
over the luminosity function of broad line AGN, have been calculated. The
results imply that the bias associated with the a-sphericity of the BLR make
even worse the discrepancy between the observations and the predictions of
evolutionary models.
