Identifying treatment effects and counterfactual distributions using data combination with unobserved heterogeneity

Abstract

This paper considers identification of treatment effects when the outcome variables and covari-ates are not observed in the same data sets. Ecological inference models, where aggregate out-come information is combined with individual demographic information, are a common example of these situations. In this context, the counterfactual distributions and the treatment effects are not point identified. However, recent results provide bounds to partially identify causal effects. Unlike previous works, this paper adopts the selection on unobservables assumption, which means that randomization of treatment assignments is not achieved until time fixed unobserved heterogeneity is controlled for. Panel data models linear in the unobserved components are con-sidered to achieve identification. To assess the performance of these bounds, this paper provides a simulation exercise.