We conducted a field experiment to study social influences on partisan political participation. We sent letters to 92,000 contributors during the 2012 presidential election campaign. We randomized features of the letters and measured the effects of these variations on the recipients’ subsequent contributions. We find that making an individual’s contributions more visible to her neighbors increases the contributions of supporters of the local majority party and decreases those of supporters of the minority party. Individuals contribute more when they perceive higher average contributions from own-party supporters in their area and contribute less if there is a higher share of own-party contributors.

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.