A1434
Title: Randomization tests in two-stage experiments
Authors: Liang Zhong - Faculty of Business and Economics, The University of Hong Kong. (Hong Kong) [presenting]
Jizhou Liu - Peking University (China)
Azeem Shaikh - University of Chicago (United States)
Abstract: Two-stage randomized experiments are widely used to study spillover effects in clustered settings. In such designs, clusters are first randomly assigned to different treatment saturation levels, and units within each cluster are then randomly assigned to treatment, with the number treated determined by the assigned saturation level. Randomization tests are developed for general two-stage experiments with multiple saturation levels and varying cluster sizes. For sharp null hypotheses, conditional randomization tests are proposed that reduce to simple cluster-level permutation procedures; the resulting tests are exactly valid in finite samples. Weak null hypotheses on average spillover effects are then studied and it is shown that studentized conditional randomization tests based on Neymanian variance estimation are asymptotically valid. The framework is further extended to bounded spillover nulls and monotone spillover nulls across ordered saturation levels. For the latter, a novel unconditional randomization test based on pairwise imputation is developed and finite-sample validity is established. This approach also extends to more general ordered-exposure settings, including network experiments. Taken together, these results provide a unified randomization-based approach to testing sharp, weak, bounded, and monotone hypotheses in two-stage experiments.
