Everyday events such as hirings, layoffs, poachings, and promotions generate outcomes depending on the productivity of workers. While search frictions may attenuate the impact of pre-market worker productivity dispersion into wage inequality, the selectivity or screening of employer decisions tend to work in the opposite direction. Hence, labor market transitions may magnify the pre-market inequality effect into employment and wages. Moreover, we present some evidence showing a suggestive link between labor market flows and wage inequality. To rationalize these facts, we construct and solve an equilibrium nonsequential search model with on-the-job search, in which selection plays a potentially large role to explain how labor markets act as a catalyst for wage and employment inequality. We also show that costly screening and search frictions generate a welfare-maximizing level of inequality and unemployment.