This paper presents a structural equilibrium search model with on-the-job search that explains wage dispersion in the labor market. The model incorporates worker and firm heterogeneity in terms of productivity and ability, as well as search frictions. Workers differ in their ability, measured by a "competence" parameter, while firms differ in their marginal productivity of labor. The model shows that wage dispersion arises from both worker ability differences and firm productivity differences, as well as matching frictions. The model is estimated using matched employer-employee French panel data, and the exogenous distributions of worker and firm heterogeneity are nonparametrically estimated. The structural estimation allows for a decomposition of cross-employee wage variance. The results show that the share of cross-sectional wage variance explained by person effects varies across skill groups, with high-skilled workers having a share close to 40%, while lower-skilled workers have a share close to 0%. The contribution of market imperfections to wage dispersion is typically around 50%. The model also provides insights into the matching process between workers and firms, showing that more productive firms devote less effort to hiring, leading to a hump-shaped relationship between productivity and firm size. The paper concludes with a discussion of the model's implications for wage dispersion and the decomposition of log-wage variance.This paper presents a structural equilibrium search model with on-the-job search that explains wage dispersion in the labor market. The model incorporates worker and firm heterogeneity in terms of productivity and ability, as well as search frictions. Workers differ in their ability, measured by a "competence" parameter, while firms differ in their marginal productivity of labor. The model shows that wage dispersion arises from both worker ability differences and firm productivity differences, as well as matching frictions. The model is estimated using matched employer-employee French panel data, and the exogenous distributions of worker and firm heterogeneity are nonparametrically estimated. The structural estimation allows for a decomposition of cross-employee wage variance. The results show that the share of cross-sectional wage variance explained by person effects varies across skill groups, with high-skilled workers having a share close to 40%, while lower-skilled workers have a share close to 0%. The contribution of market imperfections to wage dispersion is typically around 50%. The model also provides insights into the matching process between workers and firms, showing that more productive firms devote less effort to hiring, leading to a hump-shaped relationship between productivity and firm size. The paper concludes with a discussion of the model's implications for wage dispersion and the decomposition of log-wage variance.