Standard search models are unreliable for structural inference of the underlying sources of wage inequality because they are inconsistent with observed residual wage dispersion. We address this issue by modeling skill development and duration dependence in unemployment benefits in a random on the job search model featuring two-sided heterogeneity. General human capital and search on the job are the main drivers behind our model's empirical success in replicating wage dispersion (residual and overall). A realistic quantitative appraisal of search efficiencies needs to account for one third of job to job transitions resulting in wage losses. Controlling for them has important implications for the inferred sources of wage inequality. We find that the search friction accounts for around 18 percent of observed wage inequality.