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

This paper presents the first rigorous evaluation of school-based interventions aimed at reducing LGBTphobia. We focus on a classroom intervention that addresses the issue of LGBT harassment through perspective-taking and narrative exchange. Using a field experiment in France with more than 10,000 middle and high school students, we find robust evidence of strong positive effects, with variations across gender, age, and socio-economic status. We argue that changing perceptions of group norms is a key channel driving these heterogeneous effects.

We propose a formal test to check the heterogeneity of average treatment effects when these are estimated by machine learning methods. Our test statistic involves standard matrix computations and is easy to obtain. We propose a simple bootstrap procedure to obtain the critical values. Such a bootstrap procedure is fast, as it does not require computing the machine learning estimator at each bootstrap iteration.

The ability to distinguish between facts and faith is crucial for social cohesion. In the realm of knowledge, this skill facilitates constructive dialogue by focusing on evidence rather than opinions. In the realm of belief, it promotes support for freedom of thought, conscience, and religion, recognized as a fundamental right in the Universal Declaration of Human Rights. This paper presents the results of an experiment conducted in France from December 2022 to June 2023, involving approximately 1,800 primary school students. The findings confirm that the benefits of learning the difference between facts and faith are manifold. In particular, this teaching enhances students’ support for freedom of conscience, thus fostering tolerance towards diverse beliefs. It also strengthens their willingness to intervene to prevent a peer from imposing their religious practice. In doing so, this instruction contributes to improving the school climate.