Identification of treatment response with social interactions

Abstract

This paper studies identification of potential outcome distributions when treatment response may have social interactions. Defining a person's treatment response to be a function of the entire vector of treatments received by the population, I study identification when non‐parametric shape restrictions and distributional assumptions are placed on response functions. An early key result is that the traditional assumption of individualistic treatment response is a polar case within the broad class of constant treatment response (CTR) assumptions, the other pole being unrestricted interactions. Important non‐polar cases are interactions within reference groups and anonymous interactions. I first study identification under Assumption CTR alone. I then strengthen this Assumption to semi‐monotone response. I next discuss derivation of these assumptions from models of endogenous interactions. Finally, I combine Assumption CTR with statistical independence of potential outcomes from realized effective treatments. The findings both extend and delimit the classical analysis of randomized experiments.