This paper studies the formation of math and verbal skills during compulsory education and their impact on educational attainment. Using longitudinal data that follow students in England from elementary school to university, we find that the production functions of math and verbal skills are inherently different, where cross effects are present only in the production of math skills. Results on long-term educational outcomes indicate that verbal skills play a substantially greater role in explaining university enrollment than math skills. This finding, combined with the large female advantage in verbal skills, has key implications for gender gaps in college enrollment.

We document measurable, lasting gains in student achievement caused by a change in teachers' evaluation incentives. A short-lived rule created a discontinuity in teachers' incentives when allocating effort across their assigned students: students who failed an initial end-of-year test were retested a few weeks later, and then only the higher of the two scores was used when calculating the teacher's evaluation score. One year later, long after the discontinuity in incentives had ended, retested students scored 0.03σ higher than nonretested students. Otherwise identical students were treated differently by teachers because of evaluation incentives, despite arguably equal returns to teacher effort.

We propose a framework for value-added models that flexibly characterizes heterogeneous teacher productivity based on multidimensional student characteristics. We show that teacher effectiveness heavily depends on the specific attributes of their students. For example, the difference in value-added between well-matched and poorlymatched students for the average teacher is approximately 0.1 standard deviations in test scores. Notably, these matching effects are particularly pronounced among lowachieving students. In language arts, the standard deviation in teacher value-added is one-third larger for low-achieving students compared to high-achieving students.

We examine differences in minority science graduation rates among University of California campuses when racial preferences were in place. Less prepared minorities at higher ranked campuses had lower persistence rates in science and took longer to graduate. We estimate a model of students' college major choice where net returns of a science major differ across campuses and student preparation. We find less prepared minority students at top ranked campuses would have higher science graduation rates had they attended lower ranked campuses. Better matching of science students to universities by preparation and providing information about students' prospects in different major-university combinations could increase minority science graduation.

We examine how informational frictions impact schooling and work outcomes by estimating a dynamic structural model where individuals face uncertainty about their academic ability and productivity, which determine their schooling utility and wages. We account for different college types, majors, occupational search frictions, and work hours. Individuals learn from grades and wages, which may affect their choices. Removing informational frictions would increase graduation by 4.4 percentage points and by an additional 2 points without search frictions. Providing students with full information about their abilities would increase the college and white-collar wage premia while reducing the graduation gap by family income.