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.
Centre for microdata methods and practice