We develop over-identification tests that use admissions lotteries to assess the predictive value of regression-based value-added models (VAMs). These tests have degrees of freedom equal to the number of quasi-experiments available to estimate school effects. By contrast, previously implemented VAM validation strategies look at a single restriction only, sometimes said to measure forecast bias. Tests of forecast bias may be misleading when the test statistic is constructed from many lotteries or quasi-experiments, some of which have weak first stage effects on school attendance. The theory developed here is applied to data from the Charlotte-Mecklenberg School district analyzed by Deming (2014).

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.

Charter takeovers are traditional public schools restarted as charter schools. We develop a grandfathering instrument for takeover attendance that compares students at schools designated for takeover with a matched sample of students attending similar schools not yet taken over. Grandfathering estimates from New Orleans show substantial gains from takeover enrollment. In Boston, grandfathered students see achievement gains at least as large as the gains for students assigned charter seats in lotteries. A non-charter Boston turnaround intervention that had much in common with the takeover strategy generated gains as large as those seen for takeovers, while other more modest turnaround interventions yielded smaller effects.