  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.
