The Identification Power of Combining Experimental and Observational Data for Distributional Treatment Effect Parameters

Abstract

This study investigates whether and how combining experimental data, in which treatment is randomized, with observational data, in which treatment is self-selected, improves identification of distributional treatment effect (DTE) parameters. Many DTE parameters remain partially identified even under randomized treatment assignment. We show that the combined data reveal how potential-outcome distributions vary across latent self-selection types and that this information fully characterizes the identified set under the combined data. Building on this characterization, we derive sharp bounds for broad classes of DTE parameters and establish necessary and sufficient conditions under which data combination strictly tightens the identified set. We also develop a linear programming approach that accommodates additional structural restrictions, including positive dependence between potential outcomes and generalized Roy model selection. An empirical application using data on negative campaign advertisements in the 2008 U.S. presidential election illustrates the practical value of combining the two data sources.