Equilibrium search models generalize the one-sided models used earlier
by endogenizing the wage offer distribution. Attempts to estimate ver
sions of these equilibrium n search models have been unsuccessful, iro
nically because the predicted wage distribution did not fit the wage d
ata. In this paper we extend the applicability of search models by int
roducing firm heterogeneity to account for the shape of the wage densi
ty. The resulting estimation problem is difficult, but we propose a so
lution and illustrate its feasibility and performance with a Monte Car
lo study and an application to US labour market data.