What Do Randomized Studies of Housing Mobility Demonstrate?: Causal Inference in the Face of Interference - Sobel, Michael E (Journal of the American Statistical Association, 2006)
During the past 20 years, social scientists using observational studies have generated a large and inconclusive literature on neighborhood effects. Recent workers have argued that estimates of neighborhood effects based on randomized studies of housing mobility, such as the "Moving to Opportunity" (MTO) demonstration, are more credible. These estimates are based on the implicit assumption of no interference between units; that is, a subject's value on the response depends only on the treatment to which that subject is assigned, not on the treatment assignments of other subjects. For the MTO studies, this assumption is not reasonable. Although little work has been done on the definition and estimation of treatment effects when interference is present, interference is common in studies of neighborhood effects and in many other social settings (e.g., schools and networks), and when data from such studies are analyzed under the "no-interference assumption," very misleading inferences can result. Furthermore, the consequences of interference (e.g., spillovers) should often be of great substantive interest, even though little attention has been paid to this. Using the MTO demonstration as a concrete context, this article develops a frame-work for causal inference when interference is present and defines a number of causal estimands of interest. The properties of the usual estimators of treatment effects, which are unbiased and/or consistent in randomized studies without interference, are also characterized. When interference is present, the difference between a treatment group mean and a control group mean (unadjusted or adjusted for covariates) estimates not an average treatment effect, but rather the difference between two effects defined on two distinct subpopulations. This result is of great importance, for a researcher who fails to recognize this could easily infer that a treatment is beneficial when in fact it is universally harmful.