to non-dormitory students. Model 1 requires only that the equal trends assumption holds conditional on student covariates and dormitory fixed effects. I also estimate model 1 with inverse probability weights that reweight each group of students to have the same distribution of covariates as the tracked dormitory students.<sup>17</sup> _β_ 3 does not equal the average treatment effect of tracking on the tracked students if dormitory and non-dormitory students have different counterfactual GPA time trends. If the assignment policy change affects students through channels other than peer effects, _β_ 3 recovers the correct treatment effect but its interpretation changes. I discuss these concerns in section 8.

The data on students’ demographic characteristics and high school test scores (reported in table 1) are broadly consistent with the assumption of equal time trends. Dormitory students have on average slightly higher and more dispersed scores than non-dormitory students on high school graduation tests (panel A).<sup>18</sup> They are more likely to be black, less likely to speak English as a home language, and more likely to be international students (panel B). However, the time changes between the tracking and random assignment periods are small and not significantly different between dormitory and non-dormitory students. The notable exception is that the proportion of English-speaking students moves in different directions. The proportion of students who graduated from high school early enough to enroll in university during the tracking period (2004 or earlier) but did not enroll until random assignment was introduced (2006 or later) is very small and not significantly different between dormitory and non-dormitory students (panel C). I interpret this as evidence that students did not strategically delay their entrance to university in order to avoid the tracking policy. Finally,

> 17Unlike the regression-adjusted model 1, reweighting estimators permit the treatment effect of tracking to vary across student covariates. This is potentially important in this study, where tracking is likely to have heterogeneous effects. However, the regression-adjusted and reweighted results in section 3 are very similar. DiNardo, Fortin, and Lemiuex (1996) and Hirano, Imbens, and Ridder (2003) discuss reweighting estimators with binary treatments. Reweighted difference-in-differences models are discussed in Abadie (2005) and Cattaneo (2010), who also derive appropriate weights for treatment-on-the-treated parameters. The reweighted and regression-adjusted model is robust to misspecification of either the regression or the propensity score model.

> 18I construct students’ high school graduation test scores from subject-specific letter grades, following the university’s admissions algorithm. I observe grades for all six tested subjects for 85% of the sample, for five subjects for 6% of the sample, and for four or fewer subjects for 9% of the sample. I treat the third group of students as having missing scores. I assign the second group of students the average of their five observed grades but omit them from analyses that sub-divide students by their grades.

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