Identification of Anonymous Endogenous Interactions

In theoretical studies of social interactions, we hypothesize a process and seek to deduce the implied outcomes. In inferential studies, we face an inverse logical problem. Given observations of outcomes and maintained assumptions, we seek to deduce the actual process generating the observations. Throughout the modern development of the social sciences, analysis of the problems of empirical inference on social interaction processes has lagged far behind our willingness and ability to theorize about these processes. This asymmetry is unfortunate. The theoretical studies hypothesizing alternative realities are ultimately sterile if we do not also ask how these alternative realities are empirically distinguishable. The term "ananymous endogenous interactions" describes the class of social processes in which the behavior of an individual varies with the distribution of behavior in a group containing the individual. The interactions are endogenous because the outcome of each group member varies with the outcomes of the other group members, not with other attributes of the group. The interactions are anonymous because they may be described without naming the members of the group or otherwise specifying the iternal structure of the group. Despite the large body of theory on anonymous endogenous interactions, little attention has been given to the corresponding problem of empirical inference from observations of outcomes. The present paper exposits and extends my recent work on this subject. Key words. identification, social interactions