Identification of Endogenous Social Effects: The Reflection Problem

An endogenous social effect exists if the propensity of an individual to behave in some way varies with the prevalence of that behavior in some reference group containing the individual. This paper investigates aspects of the problem of identifying endogenous effects from data on actual behavior. Empirical researchers have long been sensitive to the problem of distinguishing social effects from reference-group fixed effects. The present analysis reveals that the identification of endogenous effects is tenuous even in the absence of reference-group fixed effects. There are two main findings. First, a researcher who does not a priori know how individuals form their reference groups cannot infer this from data on actual behavior and cannot determine whether social effects really are present. Second, suppose that individual behavior is known to be affected directly by specified variables z ·and that an individual's reference group is known to be the sub-population having specified attributes x. Then the effect of reference-group behavior on individual behavior is not identified if x and z are either functionally dependent or statistically independent.