This dissertation consists of three chapters that study econometrics questions and their applications to education. Chapter 1 studies a nonparametric two-sided many-to-one matching model, where many agents on one side match one institution on the other side. Classical examples include student-college matching and firm-worker matching. In this paper, I study nonparametric identification and estimation of many-to-one matching with non-transferable utility. The existing literature either assumes that the matching algorithm and reported preferences are observed or that preferences are homogeneous. This paper assumes heterogeneous preferences on the two sides and only requires data on who matches with whom in a single large market. Under mild restrictions, I prove that both the utility functions of the students and colleges and the joint distribution of unobserved heterogeneity from the two sides are nonparametrically identified. Based on my constructive identification results, I propose nonparametric and semiparametric estimators of the model and establish their consistency and asymptotic normality. The semiparametric estimator converges at a root-n rate.
Chapter 2 analyzes the U.S. college admissions under a many-to-one matching framework. In recovering the parameters of the utility functions, I am able to demonstrate substantial welfare consequences for different groups of students, relative to a centralized matching mechanism. In estimating the model using data from High School Longitudinal Study of 2009 (HSLS:09) and the Integrated Postsecondary Education Data System (IPEDS), I show that the students who experience the largest losses are first-generation college students and low-ability students. This potential loss among these groups provides an opportunity for policy interventions to lead to substantial gains in welfare.
Chapter 3 (joint with Kathleen McGarry) studies the three generations of changing gender patterns of schooling in China. The phenomenon of son preference in China and throughout much of Asia has been well documented. However, changing economic conditions, such as increases in educational attainment and employment opportunities for women and the rise in the prevalence of one child families, have likely changed the incentives for parents to invest in daughters. In this paper, we take advantage of data spanning three generations of Chinese families to examine the evolution of educational attainment for boys and girls and importantly the relative levels of schooling of each gender. We also use variation in the timing of compulsory schooling laws and the implementation of the one child policy to assess the effect of these policy measures on the relative educational levels. We find a substantial narrowing of the gap between the schooling of boys and girls, so much so that girls now have more schooling on average than boys. In addition, public policy initiatives had a larger effect in rural than urban areas.
