Identifying Treatment Effects with Data Combination and Unobserved Heterogeneity

This paper considers identification of treatment effects when the outcome variables and covariates are not observed in the same data sets. Ecological inference models, where aggregate outcome 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 considered to achieve identification. To assess the performance of these bounds, this paper provides a simulation exercise.