The generation of robust causal evidence is of paramount importance for informing policy and assessing the effect of different interventions in the educational setting. The objective of this thesis is to design and apply new methods for causal inference, particularly in observational studies, to answer pressing educational questions and provide evidence of the effect of specific events and policies. This thesis consists of three papers that use different identification strategies, such as a natural experiment, a regression discontinuity design, and a difference-in-differences approach, in combination with matching techniques, to identify the effect that specific educational interventions and a natural disaster had on students' and schools' outcomes in Chile. In the first paper, Vielma, Zubizarreta, and I present a new way of matching in observational studies that is able to (i) balance covariates directly with multiple-valued treatments, (ii) build self-weighted matched samples that are representative of a target population, and (iii) handle matching problems in large datasets in a fast and efficient way. The key insights of this new approach to matching are balancing the treatment groups relative to a target population and positing a linear-sized mixed integer formulation of the matching problem. We illustrate this method using both a simulation study and a case study. In the observational study, we estimate the effect that different intensities of the 2010 Chilean earthquake had on senior high school students' educational outcomes. We find that while increasing levels of exposure to the earthquake had a negative impact on school attendance, it had no effect on college admission test scores. In my second paper, I tackle the issue of generalization in a regression discontinuity design. Regression discontinuity designs are a commonly used approach for causal inference in observational studies. Under mild continuity assumptions, the method provides a robust estimate of the average treatment effect for observations directly at the threshold of assignment. However, it has limited external validity for populations away from the cutoff. This paper proposes a strategy to overcome this limitation by identifying a wider interval around the cutoff for estimation using a Generalization of a Regression Discontinuity Design (GRD). In this interval, predictive covariates are used to explain away the relationship between the assignment score and the outcome of interest for the pre-intervention period. Under the partially-testable assumption of conditional time-invariance in absence of the treatment, the generalization bandwidth can be applied to the post-intervention period, allowing for the estimation of average treatment effects for populations away from the cutoff. To illustrate this method, GRD is applied in the context of free higher education in Chile to estimate effects for vulnerable students. I find evidence that students at the margin of eligibility were positively affected by the policy, increasing both application and enrollment rates to university. In terms of a generalized effect, evidence is also consistent with an increasing effect as we get away from the cutoff. Finally, the third paper in this thesis addresses the question of unintended consequences in school segregation due to the introduction of a targeted voucher scheme. I use a difference-in-difference approach, in combination with matching on time-stable covariates, to estimate the effect that the 2008 Chilean voucher policy had on both average students' household income and academic performance at the school level. Results show that even though the policy had a positive effect on schools' standardized test scores, closing the gap between schools that subscribed to the policy compared to those that did not, there was also an increase in the differences between socioeconomic characteristics at the school level, such as average household income.