The federal Pell Grant Program provides billions of dollars in subsidies to low-income college students to increase affordability and access to higher education. I estimate the economic incidence of these subsidies using regression discontinuity (RD) and regression kink (RK) designs. I show that institutions capture 17 percent of all Pell Grant aid. However, the extent and pattern of capture vary by institutional control and selectivity. While RK estimates suggest that schools capture Pell Grant aid through price discrimination, RD estimates imply the opposite result, that schools supplement Pell Grants with increases in institutional aid. I reconcile these disparate findings through a framework in which the treatment of Pell Grant aid is multidimensional: students receive an additional dollar of Pell Grant aid and are also labeled as Pell Grant recipients. RD estimates confound the effects of these dimensions, which have opposite impacts on schools’ pricing decisions. I develop a combined RD/RK approach, which allows me to separately identify schools’ willingness to pay for students categorized as needy and the pricing response to outside subsidies.