In my first chapter, I explore the relationship between school size and student achievement where, conditional on observable educational inputs, school size is a proxy for factors that are difficult to measure directly ( e.g., school climate and organization). Using data from the NELS:88, I estimate a series of value-added education production functions by including a different combination of educational inputs in each specification, and each series is estimated separately for urban, suburban, and rural locations. I find that the relationship between school size and student achievement in suburban areas is largely due to observable inputs (e.g., teacher characteristics and course offerings). In urban and rural areas, I find a U-shaped relationship between school size and achievement that is primarily due to unobservable inputs. The findings suggest that one size does "not" fit all, but that relatively small and relatively large schools in urban and rural areas may benefit students due to factors such as community involvement and engaging school climate associated with smaller schools, and teacher specialization and school organization associated with larger schools. In my second chapter, I use alternative measures of class size to illustrate that inherent differences in these measures can partially explain the inconclusive evidence found in prior studies of the effect of class size on student outcomes. With data from the NELS:88 and ELS:2002, I use teacher-student ratios that vary in the level of aggregation (i.e., student, school, and state-level data) and in the types of teachers included (i.e., all teachers versus only teachers in specific subjects). I estimate multiple value-added education production functions of math achievement, each using an alternative class size measure, for two cohorts of public high school students to illustrate that identically constructed teacher-student ratios yield substantially different results over time. Overall, my findings show that the composition of teachers in the school varies substantially across schools and over time, indicating that the most commonly used measure of class size--the school's teacher-student ratio--may be a poor indicator of school quality, and that the core teacher-student ratio is likely to provide richer information about school quality than other class size measures. In my third chapter, I estimate the effect of extracurricular participation on the high school dropout decision with a particular focus on at-risk students (i.e., those in economically disadvantaged families or schools in 8th grade). Using a sample of 10th grade public school students from the NELS:88, I estimate a bivariate probit model of the dropout and participation decisions, including extracurricular offerings per student and eligibility requirements as instruments in the extracurricular participation equation. A novel feature of this paper is the interaction between the participation and at-risk indicators in the dropout equation, where past disadvantages may affect the amount of skill and social capital acquired from extracurricular participation, yielding differences in the expected value of additional schooling between at-risk students and their peers. I find that all else equal, extracurricular participants, and especially athletic and "other" club participants, are significantly less likely to drop out of high school than non-participants, though at-risk participants are more likely to drop out relative to not-at-risk participants. These findings suggest that skills and peer networks developed through extracurricular activities are especially important determinants of school completion for at-risk youth. [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.]