This dissertation analyzes the effects of the educational programs for students who need special care in secondary and postsecondary school. These educational programs present serious endogeneity problems to a researcher estimating their causal effects, because most of students tried to avoid these programs. I extend the current literature in the context of applied econometrics. First, I search for valid instruments based on exogenous policy changes when either appropriate proxy variables for ability or traditional instrumental variables are unavailable, and I look at the validity of instrumental variable estimation results. Second, I address the missing outcome problem in regression discontinuity design without invoking the additional assumption, after which it is possible to obtain the bounds for the estimates when the missing outcome problem presents in regression discontinuity design. Chapter 1 evaluates evaluates the impact of vocational high school on labor-market success in Korea. As a measure of the efficacy of the vocational high school, I use the wage data from the Korean Labor and Income Panel Study (KLIPS). Restricting the dataset to high-school graduates only, the comparison of general high schools and vocational high schools is made. To address the endogeneity problem in the choice of school type, the preset capacity of each school is used as an instrumental variable for the choice of school. I find that vocational high school gives greater returns to graduates in the sense of local average treatment effects. I find that enrollment in vocational high school gives about 30 percent higher wages than enrollment in general high school. This study also shows that the usual OLS estimates underestimate the effect of vocational high school on the wages while the IV estimates eliminate the downward bias generated by the selection problem. The result of this chapter is contrary to the previous studies showing that vocational high school scarcely affects wages. Chapter 2 investigates the effects of developmental math course offered at community colleges, addressing the missing outcome problem in the quasi-experimental studies. Many students are unprepared for college-level math in spite of many attempts to improve the math skills of high-school students. In community colleges, developmental mathematics courses are designed to help those students make up for the gaps in high-school math. However, there are few studies on the effect of developmental mathematics on mathematics achievement despite the vast quantity of research on the courses' effects on various outcomes. Developmental mathematics consists of various courses in a tight sequence where course assignments are determined by a rigid placement rule based on students' test scores, and in which students must master the assigned course before taking the next level of math. A course's effectiveness can be measured by the letter grade or other test scores in its subsequent course. However, such an effect is difficult to investigate because of missing outcome problems; achievement in the subsequent course is only observed for those who enrolled and finished it. Enrollment may be affected by assignment to a prerequisite course since those assigned to the prerequisite are less likely to enroll in the subsequent course compared to those assigned directly to the subsequent course. In regression discontinuity design (RDD), usual methods such as the control function approach cannot address these missing outcome problems as the outcome's propensity to be observable is also discontinuous. Applying a bounding approach in RDD, this study partially identifies the causal effects of developmental mathematics, and computes their bounds. Using the data from a community college in California, I find that assignment to developmental courses would increase achievement and learning efficiency in the subsequent math courses. [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.bibliotheek.ehb.be/en-US/products/dissertations/individuals.shtml.]