# Research

**Working Papers**

**1. Do Developmental Mathematics Courses Develop the Mathematics? (Job Market Paper)** [pdf]

**Abstract**: 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.

**2. Estimating Returns to Vocational Education at High Schools in Korea** [pdf]

**Abstract**: The paper evaluates the impact of vocational high school on the labor market success in Korea. As a measure of the efficacy of the vocational high school, I use the wage data from Korean Labor and Income Panel Study (KLIPS). Restricting to the 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 instrumental variables for the choice of school. Then, I find that vocational high school had given more returns to graduates in the sense of local average treatment effects. I find that the enrollment in vocational high school gives about 30 percent higher wages than the 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 paper is contrary to the previous studies showing that the vocational high school hardly affects the wage.

**Work in Progress**

**1. Using a Regression Discontinuity Design to Estimate the Impact of Placement Decisions in Developmental Math in Los Angeles Community College District. **(with T. Melguizo, J. Bos, and G. Prather)