I examine the role of federal loans on access to higher education and student welfare by modeling students' postsecondary investments in human capital. I develop a dynamic discrete choice model of a student's decision to apply to college, to enroll in a college in which she is admitted, and to finance education, either by borrowing or working, in the presence of borrowing constraints. I estimate the structural parameters of this forward-looking decision process using data from two cohorts of

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... dents who enter college before and after a rare increase to federal loan limits in 2007 and 2008. Analysis of counterfactual policies shows that raising loan limits increases enrollment, specifically towards four-year non-elite colleges, and improves persistence of enrollment. While providing free non-elite college encourages enrollment, sorting to community colleges and four-year colleges by income may not reduce existing gaps in the quality of college attended. Welfare gains are concentrated among high-ability students, who benefit from relaxed credit constraints across the income distribution. Relative to free college, increasing borrowing limits provides 50 percent of the average welfare gains and more than 94 percent of the welfare gains for high-ability students at a fraction of the policy cost. However, accounting for supply side college pricing responses reduces welfare gains non-trivially, specifically for low-income students. I supplement this analysis with a model of college admission and pricing decisions. Heterogeneous colleges try to attract a high-achieving student population and generate revenue while facing capacity constraints. Expansion in loans relax financial constraints and make expensive colleges more affordable, but colleges may increase tuition because they anticipate that students can borrow to pay higher tuition. I then provide a strategy to estimate the structural parameters of colleges' decision-making, which can be used to better evaluate hypothetical subsidies on student welfare.