This paper examines the effects of Pell Grant eligibility on student outcomes. Using a regression discontinuity (RD) design and a partial identification approach, the study provides bounds on the treatment effects that account for selection bias arising from the loss of grant eligibility. While initial eligibility is determined by financial need alone, students must achieve Satisfactory Academic Progress (SAP) to retain the grant. Students eligible for the maximum grant aid are 26 percentage points less likely to persist in the year they lose grant eligibility than those with less aid. This negative effect on persistence extends to graduation; these students are 8 percentage points less likely to graduate within 4 years. Furthermore, these two groups of students differ in their underlying characteristics, which introduces attrition bias into the estimates. Finally, to address this selection bias, I provide bounds on the effects of Pell Grant on student outcomes. While naive RD estimates find no effect on completion rates, bounding estimates reveal that students eligible for the maximum grant aid are up to 4, 2, and 2 percentage points more likely to graduate from a 4-year institution within 4, 5, and 6 years compared to those with less aid, respectively. Furthermore, these eligible students graduate with a higher GPA than previously estimated. These positive effects are larger than those found in earlier studies.