The first chapter of this dissertation examines the effects of trade liberalization on local labor market outcomes and workers;; migration patterns.I develop a model of local labor markets that describes how tariff changes across industries affect wages in local labor markets within the liberalizing country.I then use these theoretical results to measure how Brazil;;s 1987-1995 trade liberalization affected wages and interstate migration within the country. I find that wages fell most in regions facing larger liberalization-induced price declines and that liberalization resulted in a substantial shift in migration patterns. These results demonstrate the empirical value of the theoretical framework and represent the first systematic evaluation of the effects of liberalization on internal migration.The second essay focuses on capital-skill complementarity, a potentially important driver of increased income inequality. I argue that standard cost function estimates assuming quasi-fixed capital systematically overestimate the effect of capital-skill complementarity when subject to skill-biased technological change.I show that the bias results directly from cost minimizing behavior.I also develop a novel instrumental variables strategy based on the tax treatment of capital to accurately measure the effect of complementarity, confirming the model;;s prediction that the standard approach overestimates the effect of complementarity.The third essay, written with David Byrne and Ryan Michaels, examines the implications of global production sharing for measuring the price of semiconductors, a critical input to high-end domestic manufacturing and U.S. productivity growth.Our primary finding is that international shifts in the location of semiconductor wafer production toward lower-cost countries can result in unmeasured price declines of up to 0.8 percent per year.This finding has important implications for productivity measurement, since unmeasured price declines are likely to result in overstated productivity measurements in industries using semiconductor wafers as inputs to production.