Detecting Latent Heterogeneity

Abstract

We ask whether it is possible to determine, from statistical averages alone, whether a population under study consists of several subpopulations, unknown to the investigator, each responding differently to a given treatment? We show that such determination is feasible in three cases: (1) randomized trials with binary treatments, (2) models where treatment effects can be identified by adjustment for covariates, and (3) models in which treatment effects can be identified by mediating instruments. In each of these cases we provide an explicit condition which, if observed empirically, proves that treatment-effect is not uniform, but varies across individuals.