We construct and estimate an equilibrium search model with on–the–job–search. Firms make take–it–or–leave–it wage offers to workers conditional on their characteristics and they can respond to the outside job offers received by their employees. Unobserved worker productive heterogeneity is introduced in the form of cross–worker differences in a “competence” parameter. On the other side of the market, firms also are heterogeneous with respect to their marginal productivity of labor. The model delivers a theory of steady–state wage dispersion driven by heterogenous worker abilities and firm productivities, as well as by matching frictions. The structural model is estimated using matched employer and employee French panel data. The exogenous distributions of worker and firm heterogeneity components are nonparametrically estimated. We use this structural estimation to provide a decomposition of cross–employee wage variance. We find that the share of the cross–sectional wage variance that is explained by person effects varies across skill groups. Specifically, this share lies close to 40% for high–skilled white collars, and quickly decreases to 0% as the observed skill level decreases. The contribution of market imperfections to wage dispersion is typically around 50%.

Most applications of Nash bargaining over wages ignore between-employer competition for labor services and attribute all of the workers' rent to their bargaining power. In this paper, we write and estimate an equilibrium model with strategic wage bargaining and on-the-job search and use it to take another look at the determinants of wages in France. There are three essential determinants of wages in our model: productivity, competition between employers resulting from on-the-job search, and the workers' bargaining power. We find that between-firm competition matters a lot in the determination of wages, because it is quantitatively more important than wage bargaining à la Nash in raising wages above the workers' “reservation wages,” defined as out-of-work income. In particular, we detect no significant bargaining power for intermediate- and low-skilled workers, and a modestly positive bargaining power for high-skilled workers.

We develop and estimate an equilibrium job search model of worker careers, allowing for human capital accumulation, employer heterogeneity, and individual-level shocks. Wage growth is decomposed into contributions of human capital and job search, within and between jobs. Human capital accumulation is largest for highly educated workers. The contribution from job search to wage growth, both within and between jobs, declines over the first ten years of a career—the “job-shopping” phase of a working life—after which workers settle into high-quality jobs using outside offers to generate gradual wage increases, thus reaping the benefits from competition between employers.