Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/314589 
Year of Publication: 
2025
Series/Report no.: 
IZA Discussion Papers No. 17692
Publisher: 
Institute of Labor Economics (IZA), Bonn
Abstract: 
This paper develops a framework to analyze partial population experiments, a generalization of the cluster experimental design where clusters are assigned to different treatment intensities. The framework allows for heterogeneity in cluster sizes and outcome distributions. The paper studies the large-sample behavior of OLS estimators and cluster-robust variance estimators and shows that (i) ignoring cluster heterogeneity may result in severely underpowered experiments and (ii) the clusterrobust variance estimator may be upward-biased when clusters are heterogeneous. The paper derives formulas for power, minimum detectable effects, and optimal cluster assignment probabilities. All the results apply to cluster experiments, a particular case of the framework. The paper sets up a potential outcomes framework to interpret the OLS estimands as causal effects. It implements the methods in a large-scale experiment to estimate the direct and spillover effects of a communication campaign on property tax compliance. The analysis reveals an increase in tax compliance among individuals directly targeted with the mailing, as well as compliance spillovers on untreated individuals in clusters with a high proportion of treated taxpayers.
Subjects: 
two-stage designs
partial population experiments
spillovers
randomized controlled trials
cluster experiments
property tax
tax compliance
JEL: 
C01
C93
H71
H71
H26
H26
H21
H21
O23
Document Type: 
Working Paper

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