A Graph-Theoretic Approach to Randomization Tests of Causal Effects Under General Interference

Abstract

Interference exists when a unit's outcome depends on another unit's treatment assignment. 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 easyto-implement randomization tests for a general class of null hypotheses under 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.

Dynamic treatment regimes with interference

“…On the other hand, in explorations of interference structures, clustered interference, spatial interference and network interference are commonly considered three of the main structures (Puelz et al [2019]). First, clustered interference, analogous to the above-mentioned allocational interference, refers to individuals who can be divided into well-defined clusters or groups and may be affected by the treatments of others within the same cluster.…”

“…Second, spatial interference assumes that interactions pass through neighbouring individuals, and it is a more complicated structure than the structure of clusters. For example, an experiment in Medellin, Colombia was conducted to investigate the effects of "hot-spot policing" on crime (Collazos et al [2021]), and the corresponding spillover effects were investigated by Puelz et al [2019]. Third, network interference refers to interference between individuals in a network of influence (Kao [2017]), and its structure can be represented by an adjacency matrix with ( , ) entry for , ∈ {1, ..., }.…”

Testing for Differences in Stochastic Network Structure

“…A literature on random dot product graph models (see Tang et al 2017;Nielsen and Witten 2018) relies on a particular low-dimensional dot-product structure that often fails to characterize social and economic networks. Another application of randomization-based inference includes tests for network interference (see recently Aronow 2012;Athey et al 2018;Leung 2016;Song 2018;Puelz et al 2019). Rather than study the influence of a treatment on network structure, this literature studies the influence of a network on agents' exposure to treatment.…”

Robust inference for geographic regression discontinuity designs: assessing the impact of police precincts

“…Therefore, we have to isolate the effect of the police precincts themselves. Randomization is the gold standard for drawing causal conclusions, but while these are occasionally available in the criminology literature to evaluate policies like hot spots policing (Puelz et al, 2019), in many scenarios they are not available or feasible. When evaluating the impact of police precincts, we can not randomize individuals to a police precinct by forcing them to live or work in certain areas of a city.…”