Fabien Postel-Vinay and Jean-Marc Robin construct and estimate an equilibrium search model with on-the-job search, where firms make take-it-or-leave-it wage offers to workers based on their characteristics and can respond to outside job offers. Unobserved worker productivity heterogeneity is introduced through a "competence" parameter, and firms are heterogeneous in their marginal productivity of labor. The model explains steady-state wage dispersion driven by worker abilities, firm productivities, and matching frictions. Using French employer-employee panel data, they estimate the structural model nonparametrically, estimating the exogenous distributions of worker and firm heterogeneity. They find that the share of cross-sectional wage variance explained by person effects varies across skill groups, with high-skilled workers having a higher share (around 40%) compared to lower-skilled workers (0%). The contribution of market imperfections to wage dispersion is typically around 50%. The paper also discusses the dynamics of wage changes and job mobility, and provides a decomposition of the variance of log wages into worker-specific, firm-specific, and friction effects.Fabien Postel-Vinay and Jean-Marc Robin construct and estimate an equilibrium search model with on-the-job search, where firms make take-it-or-leave-it wage offers to workers based on their characteristics and can respond to outside job offers. Unobserved worker productivity heterogeneity is introduced through a "competence" parameter, and firms are heterogeneous in their marginal productivity of labor. The model explains steady-state wage dispersion driven by worker abilities, firm productivities, and matching frictions. Using French employer-employee panel data, they estimate the structural model nonparametrically, estimating the exogenous distributions of worker and firm heterogeneity. They find that the share of cross-sectional wage variance explained by person effects varies across skill groups, with high-skilled workers having a higher share (around 40%) compared to lower-skilled workers (0%). The contribution of market imperfections to wage dispersion is typically around 50%. The paper also discusses the dynamics of wage changes and job mobility, and provides a decomposition of the variance of log wages into worker-specific, firm-specific, and friction effects.