Cluster randomized trials (CRTs) are popular in public health and in the social sciences to evaluate a new treatment or policy where the new policy is randomly allocated to clusters of units rather than individual units. CRTs often feature both noncompliance, when individuals within a cluster are not exposed to the intervention, and individuals within a cluster may influence each other through treatment spillovers where those who comply with the new policy may affect the outcomes of those who do not. Here, we study the identification of causal effects in CRTs when both noncompliance and treatment spillovers are present. We prove that the standard analysis of CRT data with noncompliance using instrumental variables does not identify the usual complier average causal effect when treatment spillovers are present. We extend this result and show that no analysis of CRT data can unbiasedly estimate local network causal effects. Finally, we develop bounds for these causal effects under the assumption that the treatment is not harmful compared to the control. We demonstrate these results with an empirical study of a deworming intervention in Kenya.
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