In structural empirical models of labor market search, the distribution of wage offers is usually assumed to be exogenous. However, because in setting their wages profit-maximizing firms should consider the reservation wages of job seekers, the wage offer distribution is essentially endogenous. We investigate whether a proposed equilibrium search model, in which the wage offer distribution is endogenous, is able to describe observed labor market histories. We find that the distributions of job and unemployment spells are consistent with the data, and that the qualitative predictions of the model for the wages set by employers are confirmed by wage regressions. The model is estimated using panel data on unemployed and employed individuals. We distinguish between separate segments of the labor market, and we show that productivity heterogeneity is important to obtain an acceptable fit to the data. The results are used to estimate the degree of monopsony power of firms. Further, the effects of changes in the mandatory minimum wage are examined.