Analyzing two-stage experiments in the presence of interference

Two-stage randomization is a powerful design for estimating treatment effects in the presence of interference; that is, when one individual's treatment assignment affects another individual's outcomes. Our motivating example is a two-stage randomized trial evaluating an intervention to reduce student absenteeism in the School District of Philadelphia. In that experiment, households with multiple students were first assigned to treatment or control; then, in treated households, one student was randomly assigned to treatment. Using this example, we highlight key considerations for analyzing two-stage experiments in practice. Our first contribution is to address additional complexities that arise when household sizes vary; in this case, researchers must decide between assigning equal weight to households or equal weight to individuals. We propose unbiased estimators for a broad class of individual- and household-weighted estimands, with corresponding theoretical and estimated variances. Our second contribution is to connect two common approaches for analyzing two-stage designs: linear regression and randomization inference. We show that, with suitably chosen standard errors, these two approaches yield identical point and variance estimates, which is somewhat surprising given the complex randomization scheme. Finally, we explore options for incorporating covariates to improve precision. We confirm our analytic results via simulation studies and apply these methods to the attendance study, finding substantively meaningful spillover effects.Comment: Accepted for publication in the Journal of the American Statistical Associatio

The Augmented Synthetic Control Method

The synthetic control method (SCM) is a popular approach for estimating the impact of a treatment on a single unit in panel data settings. The "synthetic control" is a weighted average of control units that balances the treated unit's pre-treatment outcomes as closely as possible. A critical feature of the original proposal is to use SCM only when the fit on pre-treatment outcomes is excellent. We propose Augmented SCM as an extension of SCM to settings where such pre-treatment fit is infeasible. Analogous to bias correction for inexact matching, Augmented SCM uses an outcome model to estimate the bias due to imperfect pre-treatment fit and then de-biases the original SCM estimate. Our main proposal, which uses ridge regression as the outcome model, directly controls pre-treatment fit while minimizing extrapolation from the convex hull. This estimator can also be expressed as a solution to a modified synthetic controls problem that allows negative weights on some donor units. We bound the estimation error of this approach under different data generating processes, including a linear factor model, and show how regularization helps to avoid over-fitting to noise. We demonstrate gains from Augmented SCM with extensive simulation studies and apply this framework to estimate the impact of the 2012 Kansas tax cuts on economic growth. We implement the proposed method in the new augsynth R package

Randomization tests for peer effects in group formation experiments

Measuring the effect of peers on individual outcomes is a challenging problem, in part because individuals often select peers who are similar in both observable and unobservable ways. Group formation experiments avoid this problem by randomly assigning individuals to groups and observing their responses; for example, do first-year students have better grades when they are randomly assigned roommates who have stronger academic backgrounds? Standard approaches for analyzing these experiments, however, are heavily model-dependent and generally fail to exploit the randomized design. In this paper, we extend methods from randomization-based testing under interference to group formation experiments. The proposed tests are justified by the randomization itself, require relatively few assumptions, and are exact in finite samples. First, we develop procedures that yield valid tests for arbitrary group formation designs. Second, we derive sufficient conditions on the design such that the randomization test can be implemented via simple random permutations. We apply this approach to two recent group formation experiments