  We estimate the luminosity evolution and formation rate for over 900 GRBs by
using redshift and luminosity data calculated by Band, Norris, $&$ Bonnell
(2004) via the lag-luminosity correlation. By applying maximum likelihood
techniques, we are able to infer the true distribution of the parent GRB
population's luminosity function and density distributions in a way that
accounts for detector selection effects. We find that after accounting for data
truncation, there still exists a significant correlation between the average
luminosity and redshift, indicating that distant GRBs are on average more
luminous than nearby counterparts. This is consistent with previous studies
showing strong source evolution and also recent observations of under luminous
nearby GRBs. We find no evidence for beaming angle evolution in the current
sample of GRBs with known redshift, suggesting that this increase in luminosity
can not be due to an evolution of the collimation of gamma-ray emission. The
resulting luminosity function is well fit with a single power law of index
$L'^{-1.5}$, which is intermediate between the values predicted by the
power-law and Gaussian structured jet models. We also find that the GRB
comoving rate density rises steeply with a broad peak between $1<z<2$ followed
by a steady decline above $z> 3$. This rate density qualitatively matches the
current estimates of the cosmic star formation rate, favoring a short lived
massive star progenitor model, or a binary model with a short delay between the
formation of the compact object and the eventual merger.
