Intervenir en public - z

~Grant eligibility in year t and all students with E 0 are ineligible for Pell Grants. 16 FigureFC it3 displays the empirical distribution of Pell Grant aid by standardized EFC. 17Consider the following first stage and reduced form equations:~~(3) Pellit 1EFCit 0EFCit1EFCit 0 [ EFCit ] jtijty(4) ijtit it ititj t ijt~~~ ~~ 1EFC 0 EFC 1EFC 0 [ EFC] Here, i indexes students, j indexes institutions, and t indexes years. Pell is the Pell Grant awardreceived by student i in year t with an expected family contribution of EFC it , and y ijt is the~outcome of interest, institutional aid. The term1EFC it 0is an indicator for Pell Granteligibility and ρ indexes the degree of polynomial in the assignment variable, E ~~itFCit. I includeyear and school fixed effects to reduce residual variation; these terms are not necessary foridentification. I also include a vector of student characteristics for this reason. 18 The ratio of the~reduced form and first-stage coefficients for the interaction between 1 EFC it 0and the linearterm in E ~ , ˆ FCitRKˆ , represents the RK estimate of the impact of Pell Grant aid onˆ institutional aid (i.e., the change in the slope of the conditional expectation at the cut-off servesas an instrument for Pell generosity). Likewise, the ratio of the reduced form and first-stageˆ coefficients for Pell Grant eligibility, ˆ RD , represents the RD estimate of the impact of Pellˆ Grant aid on institutional aid.To further illustrate the mechanics of this framework, Figures 4A and 4B illustratepotential behavior of the relationship between institutional aid and EFC near the eligibility16 For the years I examine, efc 0t equals $2140 (1996), $2925 (2000), $3850 (2004), and $4110 (2008).17 In a given year, the kink and discontinuity in the relationship between Pell Grant aid and EFC occur at slightlydifferent values of EFC. However, the distance between these points is quite small and only a small fraction ofstudents have an EFC falling on this “plateau” (Figures 3). For the remainder of the paper, I treat both the slope andthe level of Pell Grant funding changes as occurring at the eligibility cut-off. My results are robust to removingstudents whose EFC falls on the plateau (forcing the discontinuity and kink to occur at the same value of EFC).18 Student characteristics include gender, race, citizenship, level (e.g., whether the student is a first year, secondyear, etc.), a quadratic in age, indicators for full time and full year enrollment, and whether the student qualified asin jurisdiction for tuition purposes.11