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"A Graph-Theoretic Approach to Randomization Tests of Causal Effects Under General Interference"
In causal inference, interference exists when a unit’s outcome depends on the treatment assignments of other units. For example, intensive policing on one street could have a spillover effect on neighboring streets. Classical randomization tests typically break down in this setting because many null hypotheses of interest are no longer sharp under interference. A promising alternative is to instead construct a conditional randomization test on a subset of units and assignments for which a given null hypothesis is sharp. Finding these subsets is challenging, however, and existing methods either have low power or are limited to special cases. In this paper, we propose valid, powerful, and easy-to-implement randomization tests for a general class of null hypotheses that allow for arbitrary interference between units. Our key idea is to represent the hypothesis of interest as a bipartite graph between units and assignments, and to find a clique of this graph. Importantly, the null hypothesis is sharp for the units and assignments in this clique, enabling randomization-based tests conditional on the clique. We can apply off-the-shelf graph clustering methods to find such cliques efficiently and at scale. We illustrate this approach in settings with clustered interference and show advantages over methods designed specifically for that setting. We then apply our method to a large-scale policing experiment in Medellín, Colombia, where interference has a spatial structure.
Panos Toulis is an Assistant Professor of Econometrics and Statistics at the University of Chicago, Booth School of Business. He got his Ph.D. in Statistics, and MS in Computer Science, from Harvard University. His research interests include ausal inference: randomization inference, networks, interference, spillovers and machine learning: large-scale inference, stochastic gradient descent.