spillovers or interference (Hirano and Hahn, 2010; Athey, Eckles and Imbens, 2018; Baird et al., 2018; Basse, Feller and Toulis, 2019; Jiang, Imai and Malani, 2023; Puelz et al., 2022; Viviano, 2024; Leung, 2022; Liu, 2023). More specifically, our results generalize those of Hirano and Hahn (2010), Hudgens and Halloran (2008) and Baird et al. (2018) by allowing for cluster heterogeneity, heteroskedasticity, general treatment assignment mechanisms and within-group correlation structures and alternative criteria for optimal treatment assignment.

In related work, Athey, Eckles and Imbens (2018), Basse, Feller and Toulis (2019) and Puelz et al. (2022) derive randomization inference tests for a general class of null hypotheses under interference. A closely related study is Jiang, Imai and Malani (2023), who analyze two-stage completely randomized experiments and provide randomization-based variance estimators and sample size formulas. Our results complement this literature by considering different estimands, different assignment mechanisms and by conducting super-population-based large-sample (instead of design-based) inference in a double array asymptotic framework. Our approach allows us to determine the role of cluster heterogeneity in the asymptotic behavior of the treatment effect estimators.

Our paper is also related to the literature on inference in clustered experiments, which are a particular case of partial population experiments with only two saturations and no within-cluster treatment variation. Bugni et al. (2023) study inference in clustered experiments with non-ignorable cluster sizes and derive variance estimators and valid inference procedures in a setup with random cluster sizes. We further discuss the relationship between our results and that paper in Section 3.5.

We also contribute to a large empirical literature on property taxes and a small but growing empirical literature on spillover effects in tax compliance. On property taxes, recent contributions include Brockmeyer et al. (2020) study of Mexico City, Bergeron, Tourek and Weigel (2024) and Weigel (2020) for the Democratic Republic of Congo, and Krause (2020) for Haiti, among others. The latter two are randomized controlled trials, and in both cases, the authors address the presence of spillovers, but in ex-post analysis rather than in the experimental designs. The effect of social interactions in tax compliance interventions has remained a relatively elusive issue in the broader experimental compliance literature. Some notable exceptions are Pomeranz (2015), who detects enforcement spillovers up the VAT chain in Chilean firms, Drago, Mengel and Traxler (2020) who study enforcement spillovers of TV licensing inspections on untreated households in Austria, and Boning et al. (2020) who analyze direct and network effects from in-person visits by revenue officers on visited and non-visited firms in the United States (see the review in Pomeranz and Vila-Belda, 2019, for more studies covering spillover effects). In Argentina, a recent study by Carrillo, Castro and Scartascini (2021) finds neighborhood spillover effects from a program that randomly awarded 400 taxpayers with the repair of a sidewalk. Whereas these papers find spillover effects in tax compliance, their original experiments were not designed to capture these effects. We build on these pioneering works with an intervention designed with the purpose of capturing spillovers.

The paper is organized as follows. Section 2 illustrates the practical importance of cluster heterogeneity when conducting power calculations. In Section 3, we set up our framework and derive the main results. In 4