Identification of the Average Treatment Effect when SUTVA is violated

Abstract

In order to identify the Average Treatment Effect (ATE) of a binary treatment on an outcome of interest, we need to impose, often implicitly, the so called Stable Unit Treatment Value Assumption (SUTVA). In fact only under SUTVA we can observe at least one potential outcome for each individual. If SUTVA is violated, the ATE is not point identified even if the treatment has been randomly assigned. This paper derives sharp bounds on the ATE of an exogenous binary treatment on a binary outcome as a function of the share of the units a for which SUTVA is potentially violated. We also show how to derive the maximum value of a such that 0 (or any other value) is an extreme point of the bounds (i.e., the sign of the ATE is identified). Furthermore, after decomposing SUTVA in two separate assumptions, following the epidemiology literature, we provide weaker assumptions which might help sharpening our bounds. Furthermore, we show how some of our results can be extended to continuous outcomes. Finally we apply our bounds to two well known experiments, the US Job Corps training program and randomly assigned voucher for private schools in Colombia.