Heterogeneous Agents, Social Interactions, and Causal Inference

Abstract

Most causal analyses in the social sciences depend on the assumption that each participant possesses a single potential outcome under each possible treatment assignment. Rubin (J Am Stat Assoc 81:961–962, 1986) labeled this the “stable unit treatment value assumption” (SUTVA). Under SUTVA, the individual-specific impact of a treatment depends neither on the mechanism by which the treatment is assigned nor on the treatment assignments of other individuals. However, in the social world, heterogeneous agents enact most interventions of interest: Teachers implement curricula, psychologists enact family therapy, and precinct captains supervise community policing. Moreover, the potential outcomes of one participant will often depend on the treatment assignment of other participants (classmates, family members, neighbors). This chapter presents a model that relaxes the conventional SUTVA by incorporating agents and social interactions. We define a treatment setting for an individual participant as a local environment constituted by a set of agents and participants along with their treatment assignments. Our model assigns a single potential outcome to each participant in each of such treatment settings. In a cluster-randomized trial, if no interference exists between clusters and if cluster composition remains intact, the treatment setting is fixed for all participants in a cluster and SUTVA becomes reasonable. However, when participants are assigned to treatments within clusters, we need a model for within-cluster interference among participants. When clusters are spatially contiguous, social interactions generate interference between clusters. We also incorporate new models for interference as a part of the meditation mechanism. In general, when SUTVA is relaxed, new causal questions come to light. We illustrate these ideas using studies of grade retention in elementary school, community policing in cities, school-wide interventions for behavioral improvement, and system-wide curricular changes for promoting math learning.