We set up a framework to conduct experiments for estimating spillover effects when units are grouped into mutually exclusive clusters. We improve upon existing methods by allowing for heteroskedasticity, intra-cluster correlation and cluster size heterogeneity, which are typically ignored when designing experiments. We show that ignoring these factors can severely overestimate power and underestimate minimum detectable effects. We derive formulas for optimal group-level assignment probabilities and the power function used to calculate power, sample size, and minimum detectable effects. We apply our methods to the design of a largescale randomized communication campaign in a municipality of Argentina to estimate total and neighborhood spillover effects on property tax compliance. Besides the increase in tax compliance of individuals directly targeted with our mailing, we find evidence of spillover effects on untreated individuals in street blocks where a high proportion of taxpayers were notified.
We develop a framework to conduct experiments for estimating direct and spillover effects when units are grouped into mutually exclusive clusters. Crucially, our framework accounts for heterogeneous treatment effects across clusters and heterogeneous cluster sizes, which are pervasive in empirical settings but typically ignored in experimental design. We show that failing to account for cluster heterogeneity in experimental design can severely overestimate power and underestimate minimum detectable effects. We study the large-sample behavior of OLS estimators for direct and spillover effects with heterogeneous clusters and use our results to derive simple formulas to calculate power, minimum detectable effects and optimal cluster assignment probabilities. We also set up a potential outcomes framework that justifies interpreting OLS estimands as causal effects. We apply our methods to design a large-scale experiment to estimate the 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 street blocks with a high proportion of treated taxpayers.
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