Subsidizing the cost of education is one of the most common, and expensive, activities of governments. While primary and secondary schooling is available tuition-free in the United States, among post-secondary students the direct cost of schooling is quite heterogeneous. First, tuition prices vary widely across schools. During the 2000-2001 academic year, college tuitions varied from zero at some community colleges to over $27,000 at Ivy League institutions. Second, institutions heavily discount these sticker prices for many students, using detailed information on family finances and academic merit to engage in finely tuned price discrimination.' Third, the federal and state governments provide individual subsidies, such as the Pell Grant and low-interest Stafford loan, that are portable across institutions. The standard model of human capital clearly predicts that such cost subsidies will raise the optimal level of schooling. While the theoretical predictions are clear, it is an empirical question how much a given dollar of subsidy affects behavior. Answering this empirical question is a challenge, since eligibility for subsidies is certainly not random and, in fact, is likely to be correlated with many other determinants of schooling. As a result, estimates based on the cross-sectional correlation of aid eligibility with schooling are subject to multiple sources of bias. This paper examines work that has used quasi-experimental methodology to isolate exogenous sources of variation in schooling costs in order to determine their effect on schooling decisions.

Does Aid Matter? Measuring the Effect of Student Aid on College Attendance and Completion by Susan M. Dynarski. Published in volume 93, issue 1, pages 279-288 of American Economic Review, March 2003

We use admissions lotteries to estimate the effects of attendance at Boston's charter high schools on college preparation, college attendance, and college choice. Charter attendance increases pass rates on the high-stakes exam required for high school graduation in Massachusetts, with especially large effects on the likelihood of qualifying for a state-sponsored college scholarship. Charter attendance has little effect on the likelihood of taking the SAT, but shifts the distribution of scores rightward, moving students into higher quartiles of the state SAT score distribution. Boston's charter high schools also increase the likelihood of taking an Advanced Placement (AP) exam, the number of AP exams taken, and scores on AP Calculus tests. Finally, charter attendance induces a substantial shift from two-to four-year institutions, though the effect on overall college enrollment is modest. The increase in four-year enrollment is concentrated among four-year public institutions in Massachusetts. The large gains generated by Boston's charter high schools are unlikely to be generated by changes in peer composition or other peer effects.

High-achieving, low-income students attend selective colleges at far lower rates than upper-income students with similar achievement. Behavioral biases, intensified by complexity and uncertainty in the admissions and aid process, may explain this gap. In a large-scale experiment we test an early commitment of free tuition at a flagship university. The intervention did not increase aid: rather, students were guaranteed before application the same grant aid that they would qualify for in expectation if admitted. The offer substantially increased application (68 percent versus 26 percent) and enrollment rates (27 percent versus 12 percent). The results suggest that uncertainty, present bias, and loss aversion loom large in students’ college decisions.

Inputs and Impacts in Charter Schools: KIPP Lynn by Joshua D. Angrist, Susan M. Dynarski, Thomas J. Kane, Parag A. Pathak and Christopher R. Walters. Published in volume 100, issue 2, pages 239-43 of American Economic Review, May 2010