In this dissertation, I examine the importance of specific components of the skill vector in affecting outcomes across various settings. In particular, I first consider the importance of non-cognitive skills in higher education in the United States, both in explaining academic undermatch, but also showing their importance towards successful degree completion. In the Chilean context, I consider how early-life math skills affect the likelihood of reaching the top of the income distribution, partly through leading to employment in higher-quality firms. The last chapter of my dissertation presents a discrete choice model of college majors, in which I consider how non-cognitive skills contribute to the gender gap in STEM majors in the United States. In particular, I document the importance of mathematical self-efficacy as an important driver of the gender gap in STEM.

In Chapter 2, I analyze the importance of non-cognitive skills in the context of higher education. Using longitudinal data for the United States, I first find that students with higher non-cognitive skills are more likely to enroll in higher-quality four-year colleges. Furthermore, students who have been previously characterized as "under-matched" in higher education have significantly lower non-cognitive skills than students with equivalent test scores. While enrollment is the first step towards higher education completion, a burgeoning literature has documented falling completion rates among enrollees. In this context, I find that for both two-year enrollees as well as those in four-year colleges of varying qualities, non-cognitive skills are strong predictors of subsequent college completion.

Chapter 3, written in collaboration with Sergio Urzua, estimates the returns to skills in the labor market by taking advantage of three administrative data sources. We first test for non-linearities in these returns and find that the returns to mathematical skills are highly non-linear, with math skill 'superstars' far outearning other high math scorers. High math-skilled workers not only complete more years of education, but graduate from higher quality universities and earn higher-paying degrees. We further examine the role of firms as a mediator of the returns to skills, a dimension not previously explored in the literature. We find that high-skilled workers match to high-paying firms immediately upon labor market entry. We conduct a decomposition to examine the separate contribution of education and firms in mediating the returns to skills, and find that worker-firm matching explains almost half of the estimated returns.

Chapter 4 studies the relationship between pre-college skills and the gender gap in STEM majors. I expand upon the analysis in the first two chapters, by introducing structure to students' human capital investment decisions using a discrete choice model of college major choices. I implement the model using longitudinal data for the United States and consider students' initial and final major choices in a context where college students sort into majors based on observed characteristics and unobserved ability. More specifically, I distinguish observed test scores from latent ability. I find that math test scores significantly overstate gender gaps in math problem solving ability. Math problem solving ability strongly predicts STEM enrollment and completion for men and women. I further explore the importance of math self-efficacy, which captures students' beliefs about their ability to perform math-related tasks. Math self-efficacy raises both men's and women's probability of enrolling in a STEM major. Math self-efficacy also plays a critical role in explaining decisions to drop out of STEM majors for women, but not for men. The correlation between the two math ability components is higher for men than for women, indicating a relative shortfall of high-achieving women who are confident in their math ability. Lastly, I estimate the returns to STEM enrollment and completion and find large returns for high math ability women. These findings suggest that well-focused math self-efficacy interventions could boost women's STEM participation and graduation rates. Further, given the high returns to a STEM major for high math ability women, such interventions also could improve women's labor market outcomes.