This dissertation contains essays on three questions about the labor market. Chapter 1 considers the question: why do some firms pay so much and some so little? Firms account for a substantial portion of earnings inequality. Although the standard explanation is that there are search frictions that support an equilibrium with rents, this chapter finds that compensating differentials for nonpecuniary characteristics are at least as important. To reach this finding, this chapter develops a structural search model and estimates it on U.S. administrative data. The model analyzes the revealed preference information in the labor market: specifically, how workers move between the 1.5 million firms in the data. With on the order of 1.5 million parameters, standard estimation approaches are infeasible and so the chapter develops a new estimation approach that is feasible on such big data. Chapter 2 considers the question: why do men and women work at different firms? Men work for higher-paying firms than women. The chapter builds on chapter 1 to consider two explanations for why men and women work in different firms. First, men and women might search from different offer distributions. Second, men and women might have different rankings of firms. Estimation finds that the main explanation for why men and women are sorted is that women search from a lower-paying offer distribution than men. Indeed, men and women are estimated to have quite similar rankings of firms. Chapter 3 considers the question: what are there long-run effects of the minimum wage? An empirical consensus suggests that there are small employment effects of minimum wage increases. This chapter argues that these are short-run elasticities. Long-run elasticities, which may differ from short-run elasticities, are more policy relevant. This chapter develops a dynamic industry equilibrium model of labor demand. The model makes two points. First, long-run regressions have been misinterpreted because even if the short- and long-run employment elasticities differ, standard methods would not detect a difference using U.S. variation. Second, the model offers a reconciliation of the small estimated short-run employment effects with the commonly found pass-through of minimum wage increases to product prices.