This paper models decisions to apply to and attend charter schools in Boston using a generalized Roy selection framework linking preferences to the achievement gains generated by charter attendance. The model is estimated with instruments based on randomized admission lotteries and distance to charter schools. Charter schools generate larger gains for disadvantaged students, but demand for charters is stronger among more advantaged students. Similarly, gains are inversely related to unobserved preferences for charters. As a result, counterfactual simulations indicate that charter expansion is likely to be most effective when accompanied by efforts to target students who are unlikely to apply.

We use data from the Head Start Impact Study (HSIS) to evaluate the cost-effectiveness of Head Start, the largest early childhood education program in the United States. Head Start draws roughly a third of its participants from competing preschool programs, many of which receive public funds. We show that accounting for the fiscal impacts of such program substitution pushes estimates of Head Start’s benefit-cost ratio well above one under a wide range of assumptions on the structure of the market for preschool services and the dollar value of test score gains. To parse the program’s test score impacts relative to home care and competing preschools, we selection-correct test scores in each care environment using excluded interactions between experimental assignments and household characteristics. We find that Head Start generates larger test score gains for children who would not otherwise attend preschool and for children who are less likely to participate in the program.

Structural econometric methods are often criticized for being sensitive to functional form assumptions. We study parametric estimators of the local average treatment effect (LATE) derived from a widely used class of latent threshold crossing models and show they yield LATE estimates algebraically equivalent to the instrumental variables (IV) estimator. Our leading example is Heckman's (1979) two‐step (“Heckit”) control function estimator which, with two‐sided non‐compliance, can be used to compute estimates of a variety of causal parameters. Equivalence with IV is established for a semiparametric family of control function estimators and shown to hold at interior solutions for a class of maximum likelihood estimators. Our results suggest differences between structural and IV estimates often stem from disagreements about the target parameter rather than from functional form assumptions per se. In cases where equivalence fails, reporting structural estimates of LATE alongside IV provides a simple means of assessing the credibility of structural extrapolation exercises.

We study the results of a massive nationwide correspondence experiment sending more than 83,000 fictitious applications with randomized characteristics to geographically dispersed jobs posted by 108 of the largest U.S. employers. Distinctively Black names reduce the probability of employer contact by 2.1 percentage points relative to distinctively white names. The magnitude of this racial gap in contact rates differs substantially across firms, exhibiting a between-company standard deviation of 1.9 percentage points. Despite an insignificant average gap in contact rates between male and female applicants, we find a between-company standard deviation in gender contact gaps of 2.7 percentage points, revealing that some firms favor male applicants and others favor women. Company-specific racial contact gaps are temporally and spatially persistent, and negatively correlated with firm profitability, federal contractor status, and a measure of recruiting centralization. Discrimination exhibits little geographical dispersion, but two-digit industry explains roughly half of the cross-firm variation in both racial and gender contact gaps. Contact gaps are highly concentrated in particular companies, with firms in the top quintile of racial discrimination responsible for nearly half of lost contacts to Black applicants in the experiment. Controlling false discovery rates to the 5% level, 23 companies are found to discriminate against Black applicants. Our findings establish that discrimination against distinctively Black names is concentrated among a select set of large employers, many of which can be identified with high confidence using large-scale inference methods.

We develop an empirical Bayes ranking procedure that assigns ordinal grades to noisy measurements, balancing the information content of the assigned grades against the expected frequency of ranking errors. Applying the method to a massive correspondence experiment, we grade the race and gender contact gaps of 97 US employers, the identities of which we disclose for the first time. The grades are presented alongside measures of uncertainty about each firm’s contact gap in an accessible report card that is easily adaptable to other settings where ranks and levels are of simultaneous interest. (JEL C11, D22, J15, J16, J71)

We use admissions lotteries to estimate the effects of large-scale public preschool in Boston on college-going, college preparation, standardized test scores, and behavioral outcomes. Preschool enrollment boosts college attendance as well as SAT test taking and high school graduation. Preschool also decreases high school disciplinary measures including juvenile incarceration, but has no detectable effect on state achievement test scores. An analysis of subgroups shows that effects on college enrollment, SAT-taking, and disciplinary outcomes are larger for boys than for girls. Our findings illustrate possibilities for large-scale modern, public preschool and highlight the importance of measuring long-term and non–test score outcomes in evaluating the effectiveness of education programs.

We use a large-scale randomized experiment to study the impact of augmenting staffing in the world’s largest public early-childhood program: India’s Integrated Child Development Services. Adding a worker doubled net preschool instructional time and led to increases of 0.28σ and 0.46σ in math and language test scores after 18 months for children who remained enrolled in the program and 0.13σ and 0.10σ for all children enrolled at baseline. Rates of stunting and severe malnutrition were also lower in the treatment group for children who remained enrolled. A cost-benefit analysis suggests that the benefits of augmenting staffing significantly exceed its costs. These effects are likely to replicate even at larger scales of program implementation.

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.

Empirical researchers often combine multiple instrumental variables (IVs) for a single treatment using two-stage least squares (2SLS). When treatment effects are heterogeneous, a common justification for including multiple IVs is that the 2SLS estimand can be given a causal interpretation as a positively weighted average of local average treatment effects (LATEs). This justification requires the well-known monotonicity condition. However, we show that with more than one instrument, this condition can only be satisfied if choice behavior is effectively homogeneous. Based on this finding, we consider the use of multiple IVs under a weaker, partial monotonicity condition. We characterize empirically verifiable sufficient and necessary conditions for the 2SLS estimand to be a positively weighted average of LATEs under partial monotonicity. We apply these results to an empirical analysis of the returns to college with multiple instruments. We show that the standard monotonicity condition is at odds with the data. Nevertheless, our empirical checks reveal that the 2SLS estimate retains a causal interpretation as a positively weighted average of the effects of college attendance among complier groups. (JEL C26, I23, I26, J24, J31, R23)

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.