Research

When assigning units to treatment and control, researchers are often confronted with the sequential arrival of participants over time (e.g., jobseekers, patients). The challenge in such settings is to assign participants sequentially while maintaining covariate balance between treatment arms. This paper introduces the sequential cube method (SCM), a new design that achieves near-exact balance in covariate moments at the cost of only a short waiting period before treatment assignment. I first show that exact balance, for a given function of covariates, delivers the optimal precision of treatment effect estimators. Under general conditions, I prove that SCM attains near-exact balance. Moreover, I establish that the expected waiting time under SCM grows only in proportion to the number of covariates used for balancing, making the procedure scalable in practice. I further derive the asymptotic normality of average treatment effect estimators under SCM, ensuring valid inference. Simulation studies and empirical applications highlight the practical advantages of SCM. Relative to alternative balancing designs, SCM (i) improves covariate balance, (ii) increases the precision of treatment effect estimators, and (iii) requires substantially shorter waiting times. Finally, I discuss extensions to multiple treatments and response-adaptive randomization, encompassing multi-armed bandit settings.

We propose a novel randomization approach for randomized controlled trials (RCTs), named the cube method. The cube method allows for the selection of balanced samples across various covariate types, ensuring consistent adherence to balance tests and, whence, substantial precision gains when estimating treatment effects. We establish several statistical properties for the population and sample average treatment effects (PATE and SATE, respectively) under randomization using the cube method. The relevance of the cube method is particularly striking when comparing the behavior of prevailing methods employed for treatment allocation when the number of covariates to balance is increasing. We formally derive and compare bounds of balancing adjustments depending on the number of units n and the number of covariates p and show that our randomization approach outperforms methods proposed in the literature when p is large and p/n tends to 0. We run simulation studies to illustrate the substantial gains from the cube method for a large set of covariates

Anti-LGBT harassment remains pervasive in schools. Although advocacy organizations in many countries deliver classroom-based training to help counter bullying, rigorous evidence on effective prevention is scarce. This paper presents the first impact evaluation of a school-based intervention aimed at combating LGBTphobia. Using a large-scale randomized field experiment conducted in secondary schools in the Paris region, France, we evaluate a two-hour classroom workshop led by LGBT+ facilitators and based on non-judgemental narrative exchanges centered on empathy-building. Among more than 6,000 secondary school students, the intervention increased recep-tiveness to LGBT inclusion by 0.16 standard deviations, with effects persisting for at least three months. The intervention is particularly effective in encouraging discussion with school staff and improving understanding of LGBT identities, as well as awareness of the consequences of anti-LGBT harassment. It also shifts self-reported attitudes among high school students. We document substantial heterogeneity: girls, older students, and students in more socio-economically advantaged school environments benefit more, whereas some groups exhibit short-run backlash. The evidence suggests that changes in perceived classroom norms are a key mechanism, highlighting the importance of peer dynamics. These findings imply that scaling school-based programs should account for heterogeneity and may require repeated exposure to consolidate inclusive norms.

This study proposes a formal, computationally efficient nonparametric omnibus test for treatment-effect heterogeneity that is compatible with a broad class of estimators, including modern machine-learning methods. The test is designed for settings in which identification can rely on high-dimensional controls while heterogeneity is assessed with respect to a low-dimensional subset of covariates. We derive the test statistic’s asymptotic null distribution and develop a bootstrap procedure that is efficient because it avoids re-estimating nuisance parameters in each iteration. The testing approach applies to multiple empirical designs, including randomized experiments, selection-on-observables, difference-in-differences, and instrumental-variables settings. Monte Carlo simulations show that the test attains near-nominal size under the null and exhibits good power against heterogeneous alternatives. We further illustrate the procedure using two empirical applications on retirement savings and trade liberalization. 

We evaluate the impact of a classroom-based intervention designed to strengthen support for freedom of conscience and religion—an important step not only in reducing discrimination against religious minorities, but also in preventing the pull of radicalization that such discrimination may trigger among those who experience it. We do so through a randomized controlled trial involving approximately 1,800 primary school students in the Paris region (France). The program consists of interactive lessons delivered by trained teachers, aimed at increasing students’ familiarity with a range of convictions and helping them distinguish between facts and beliefs. We find that teacher training, which lasts four hours on average, increases by nine hours the time devoted to teaching religious facts and secularism over a given semester. Consistent with the program’s core objective, students in the treatment group demonstrate improved knowledge of various religions and are better able to distinguish between facts (“savoir") and beliefs (“croire”). This translates into greater tolerance of the peaceful expression of a wide range of religious beliefs, increased acceptance of individuals’ decisions to change or abandon their beliefs, and stronger disapproval of attempts to impose religious views on others, along with a greater willingness to act to prevent such behavior. Taken together, these changes indicate increased support for the principle of secularism. These effects are consistent across student characteristics, with limited heterogeneity. We also document improvements in teacher-reported classroom behavior, but no effects on perceived academic performance.