Econometrica: Mar, 2014, Volume 82, Issue 2

Identifying Treatment Effects Under Data Combination

https://doi.org/10.3982/ECTA10601
p. 811-822

Yanqin Fan, Robert Sherman, Matthew Shum

We consider the identification of counterfactual distributions and treatment effects when the outcome variables and conditioning covariates are observed in separate data sets. Under the standard selection on observables assumption, the counterfactual distributions and treatment effect parameters are no longer point identified. However, applying the classical monotone rearrangement inequality, we derive sharp bounds on the counterfactual distributions and policy parameters of interest.