Identifying Marginal Treatment Effects in the Presence of Sample Selection
80 Pages Posted: 19 Jul 2019 Last revised: 3 Apr 2020
Date Written: July 18, 2019
This article presents identification results for the marginal treatment effect (MTE) when there is sample selection. We show that the MTE is partially identified for individuals who are always observed regardless of treatment, and derive uniformly sharp bounds on this parameter under four increasingly restrictive sets of assumptions. The first result imposes standard MTE assumptions with an unrestricted sample selection mechanism. The second set of conditions imposes monotonicity of the sample selection variable with respect to the treatment, considerably shrinking the identified set. Third, we incorporate a stochastic dominance assumption which tightens the lower bound for the MTE. Finally, we provide a set of conditions that allows point identification for completeness. Our analysis extends to discrete instruments and distributional MTE. All the results rely on a mixture reformulation of the problem where the mixture weights are identified. This extends Lee (2009) trimming procedure to the MTE context. We propose nonparametric estimators for the bounds derived, provide a numerical example and simulations that corroborate the bounds feasibility and usefulness as an empirical tool. We highlight the practical relevance of the results by analyzing the impacts of managed health care options on health expenditures, following Deb, Munkin, and Trivedi (2006).
Keywords: Sample Selection, Instrumental Variable, Marginal Treatment Effect, Partial Identification, Principal Stratification, Program Evaluation, Mixture Models
JEL Classification: C14, C31, C35
Suggested Citation: Suggested Citation