The Empirical Content of Models with Social Interactions

Empirical models with social interactions or peer effects allow the outcome of an individual to depend on the outcomes, choices, treatments, and/or characteristics of the other individuals in the group. We document the subtle relationship between the data and the objects of interest in models with interactions in small groups, and show that some econometric assumptions, that are direct extensions from models of individualistic treatment response, implicitly entail strong behavioral assumptions. We point out two such econometric assumptions, EITR, or empirical individual treatment response, and EGTR, or empirical group treatment response. In some cases EITR and/or EGTR are inconsistent with a class of plausible economic models for the interaction under consideration; in other cases these econometric assumptions imply significant assumptions on behavior that are not necessarily implied by economic theory. We illustrate this using relevant examples of interaction in immunization and disease, and in educational achievement. We conclude that it is important for applications in this class of models with small group interactions to recognize the restrictions some assumptions impose on behavior.