This paper employs a nonparametric potential outcomes framework to study causal spillover effects in a setting where units are clustered and their potential outcomes can depend on the treatment assignment of all the units within a cluster. Using this framework, I define parameters of interest and provide conditions under which direct and spillover effects can be  identified when a treatment is randomly assigned. In addition, I characterize and discuss the causal interpretation of the estimands that are recovered by two popular estimation approaches in empirical work: a regression of an outcome on a treatment indicator (difference in means) and a regression of an outcome on a treatment indicator and the proportion of treated peers (a reduced-form linear-in-means model). It is shown that consistency and asymptotic normality of the nonparametric spillover effects estimators require a precise relationship between the number of parameters, the total sample size and the probability distribution of the treatment assignments, which has important implications for the design of experiments. The findings are illustrated with data from a conditional cash transfer pilot study and with simulations. The wild bootstrap is shown to be consistent, and simulation evidence suggests a better performance compared to the Gaussian approximation when groups are moderately large relative to the sample size.
This paper employs a potential outcomes framework to study causal spillover effects in a setting where units are clustered and their potential outcomes can depend on the treatment assignment of all the units within a cluster. Using this framework, I define parameters of interest and provide conditions under which direct and spillover effects can be nonparametrically identified when a treatment is randomly assigned. In addition, I characterize and discuss the causal interpretation of the estimands that are recovered by two popular estimation approaches in empirical work: a regression of an outcome on a treatment indicator (difference in means) and a regression of an outcome on a treatment indicator and the proportion of treated peers (a reduced-form linear-in-means model). I show consistency and asymptotic normality of the nonparametric spillover effects under a precise relationship between the number of parameters, the total sample size and the probability distribution of the treatment assignments, which has important implications for the design of experiments. The findings are illustrated with data from a conditional cash transfer program and with simulations. The wild bootstrap is shown to be consistent, and simulation evidence suggests a better performance compared to the Gaussian approximation when groups are moderately large relative to the sample size.
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nonparametric
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nonparametrically
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estimators require
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pilot study
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