Design of Partial Population Experiments with an Application to Spillovers in Tax Compliance

Cruces, Guillermo; Tortarolo, Dario; Vazquez-Bare, Gonzalo

Abstract

We develop a framework to analyze partial population experiments, a generalization of the cluster experimental design where clusters are assigned to different treatment intensities. Our framework allows for heterogeneity in cluster sizes and outcome distributions. We study the large-sample behavior of OLS estimators and cluster-robust variance estimators and show that (i) ignoring cluster heterogeneity may result in severely underpowered experiments and (ii) the cluster-robust variance estimator may be upward-biased when clusters are heterogeneous. We derive formulas for power, minimum detectable effects, and optimal cluster assignment probabilities. All our results apply to cluster experiments, a particular case of our framework. We set up a potential outcomes framework to interpret the OLS estimands as causal effects. We implement our methods in a large-scale experiment to estimate the direct and spillover effects of a communication campaign on property tax compliance. We find an increase intax compliance among individuals directly targeted with our mailing, as well as compliance spillovers on untreated individuals in clusters with a high proportion of treated taxpayers.

Citation

Cruces, G., Tortarolo, D., & Vazquez-Bare, G. (2025). Design of Partial Population Experiments with an Application to Spillovers in Tax Compliance. Review of Economics and Statistics, https://doi.org/10.1162/rest_a_01552

• Journal Article Type: Article
• Acceptance Date: Dec 9, 2024
• Online Publication Date: Jan 28, 2025
• Publication Date: Jan 28, 2025
• Deposit Date: Aug 6, 2024
• Publicly Available Date: Jan 28, 2025
• Journal: Review of Economics and Statistics
• Print ISSN: 0034-6535
• Electronic ISSN: 1530-9142
• Publisher: Massachusetts Institute of Technology Press (MIT Press)
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1162/rest_a_01552
• Public URL: https://nottingham-repository.worktribe.com/output/38107281
• Publisher URL: https://direct.mit.edu/rest/article-abstract/doi/10.1162/rest_a_01552/127746/Design-of-Partial-Population-Experiments-with-an?redirectedFrom=fulltext