Methods to estimate the causal effects of interventions are increasingly used in clinical medicine, public policy and social science. Using observational data, researchers can obtain causal treatment effect estimates without the ethical risks and time constraints that typically burden randomized experiments. The three studies in this dissertation estimate the effects of New York City's Gifted and Talented (G&T) program on academic outcomes using student level data collected between the years 2010 and 2019. Study one evaluates how the synthetic control method performs when estimating the impact of G&T availability on academic outcomes at the sub-district level. Study two estimates the individual average treatment effect through propensity score methods and explores how data augmentation influences the bias and precision of commonly used estimators. The final study uses difference in difference estimation to explore how a city-wide policy impacted the minority representation and academic effectiveness of the G&T program. Given a growing interest in school choice models, these applied analyses are timely. Through simulation and discussion, they also present a critical evaluation of modeling frameworks and research design for causal inference. [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://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]