Increases in the minimum wage can substantially reduce earnings inequality. To demonstrate this, we combine administrative and survey data with an equilibrium model of the Brazilian labor market. We find that a 128 percent increase in the real minimum wage in Brazil between 1996 and 2018 had far-reaching spillover effects on wages higher up in the distribution. The increased minimum wage accounts for 45 percent of a large fall in earnings inequality over this period. At the same time, the effects of the minimum wage on employment and output are muted by reallocation of workers toward more productive firms..

This paper integrates the classic theory of firm boundaries, through span of control or taste for variety, into a model of the labor market with random matching and on‐the‐job search. Firms choose when to enter and exit, whether to create vacancies or destroy jobs in response to shocks, and Bertrand‐compete to hire and retain workers. Tractability is obtained by proving that, under a parsimonious set of assumptions, all worker and firm decisions are characterized by their joint surplus, which in turn only depends on firm productivity and size. The job ladder in marginal surplus that emerges in equilibrium determines net poaching patterns by firm characteristics that are in line with the data. As frictions vanish, the model converges to a standard competitive model of firm dynamics. The combination of firm dynamics and search frictions allows the model to: (i) quantify the misallocation cost of frictions; (ii) replicate elusive life‐cycle growth profiles of superstar firms; and (iii) make sense of the failure of the job ladder around the Great Recession as a result of the collapse of firm entry.