Conventional value-added models (VAMs) compare average test scores across schools after regression-adjusting for students’ demographic characteristics and previous scores. This article tests for VAM bias using a procedure that asks whether VAM estimates accurately predict the achievement consequences of random assignment to specific schools. Test results from admissions lotteries in Boston suggest conventional VAM estimates are biased, a finding that motivates the development of a hierarchical model describing the joint distribution of school value-added, bias, and lottery compliance. We use this model to assess the substantive importance of bias in conventional VAM estimates and to construct hybrid value-added estimates that optimally combine ordinary least squares and lottery-based estimates of VAM parameters. The hybrid estimation strategy provides a general recipe for combining nonexperimental and quasi-experimental estimates. While still biased, hybrid school value-added estimates have lower mean squared error than conventional VAM estimates. Simulations calibrated to the Boston data show that, bias notwithstanding, policy decisions based on conventional VAMs that control for lagged achievement are likely to generate substantial achievement gains. Hybrid estimates that incorporate lotteries yield further gains.

Many schools in large urban districts have more applicants than seats. Centralized school assignment algorithms ration seats at over‐subscribed schools using randomly assigned lottery numbers, non‐lottery tie‐breakers like test scores, or both. The New York City public high school match illustrates the latter, using test scores and other criteria to rank applicants at the city's screened schools, combined with lottery tie‐breaking at the rest. We show how to identify causal effects of school attendance in such settings. Our approach generalizes regression discontinuity methods to allow for multiple treatments and multiple running variables, some of which are randomly assigned. The key to this generalization is a local propensity score that quantifies the school assignment probabilities induced by lottery and non‐lottery tie‐breakers. The utility of the local propensity score is demonstrated in an assessment of the predictive value of New York City's school report cards. Schools that earn the highest report card grade indeed improve SAT math scores and increase graduation rates, though by much less than OLS estimates suggest. Selection bias in OLS estimates of grade effects is egregious for screened schools.

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. (JEL D44, H75, I21, I28)

A growing number of school districts use centralized assignment mechanisms to allocate school seats in a manner that reflects student preferences and school priorities. Many of these assignment schemes use lotteries to ration seats when schools are oversubscribed. The resulting random assignment opens the door to credible quasi-experimental research designs for the evaluation of school effectiveness. Yet the question of how best to separate the lottery-generated randomization integral to such designs from non-random preferences and priorities remains open. This paper develops easily-implemented empirical strategies that fully exploit the random assignment embedded in a wide class of mechanisms, while also revealing why seats are randomized at one school but not another. We use these methods to evaluate charter schools in Denver, one of a growing number of districts that combine charter and traditional public schools in a unified assignment system. The resulting estimates show large achievement gains from charter school attendance. Our approach generates efficiency gains over ad hoc methods, such as those that focus on schools ranked first, while also identifying a more representative average causal effect. We also show how to use centralized assignment mechanisms to identify causal effects in models with multiple school sectors.

Inputs and Impacts in Charter Schools: KIPP Lynn by Joshua D. Angrist, Susan M. Dynarski, Thomas J. Kane, Parag A. Pathak and Christopher R. Walters. Published in volume 100, issue 2, pages 239-43 of American Economic Review, May 2010

Many school and college admission systems use centralized mechanisms to allocate seats based on applicant preferences and school priorities. When tie-breaking uses non-randomly assigned criteria like distance or a test score, applicants with the same preferences and priorities are not directly comparable. The non-lottery setting does generate a kind of local random assignment that opens the door to regression discontinuity designs. This paper introduces a hybrid RD/propensity score empirical strategy that exploits quasi-experiments embedded in serial dictatorship, a mechanism widely used for college and selective K-12 school admissions. We use our approach to estimate achievement effects of Chicago's exam schools.