The essays of this dissertation contribute to the understanding of how public schools respond to competition in educational markets. Evidence is drawn from the Milwaukee Parental Choice Program, the longest-running and largest-scale private school voucher program in the United States. A major justification school choice programs is that they create market-based accountability for public schools. By both giving families the choice to opt out of bad public schools and tying revenue losses to their departure, a "competition effect" is hypothesized where school choice programs induce low-performing schools to improve their quality in order to retain their enrollment and thus their funding. The first essay contributes to the recent literature on school effects, using a flexible approach to measure the response of student achievement growth in schools facing nearby entry of private schools to the voucher program. The response of schools to competition is found to vary significantly by the percentage of that school's enrollment that is eligible for the voucher program. Those with the most eligible students show the least positive effect explained by the fact that, by the targeting of the voucher program, these are also the school serving the most low-income households. In general, while point estimates of the competition effect are positive, the average marginal treatment effects of facing an additional competitor are small and generally statistically insignificant. The second essay is the first to study competition effects using estimates of household demand to study how enrollment flows are affected by the entry of competing schools. Characterizations of demand find taste heterogeneity across different types of households, and that proximity, racial balance, and peer group composition are important determinants of choice in addition to school quality. The magnitude of predicted enrollment expected to leave to competitors is small, rarely exceeding 4% in any given year. This approach finds competition effects for math and reading that are statistically significant but small and, similar to Essay 1, that low-income public schools show the least positive response to competition. Overall, the findings of this work indicate a very low and poorly-distributed return to school choice programs relative to their cost. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]