TY  - RPRT
        AU  - Cruces, Guillermo
AU  - Tortarolo, Dario
AU  - Vazquez-Bare, Gonzalo
        TI  - Design of Partial Population Experiments with an Application to Spillovers in Tax Compliance
        PY  - 2024/Aug/
        PB  - Institute of Labor Economics (IZA)
        CY  - Bonn
        T2  - IZA Discussion Paper
        IS  - 17256
        UR  - https://www.iza.org/publications/dp17256
        AB  - 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 in tax 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.
        KW  - partial population experiments
KW  - spillovers
KW  - randomized controlled trials
KW  - cluster experiments
KW  - two-stage designs
KW  - property tax
KW  - tax compliance
        ER  -