Partial Identification of Population Average and Quantile Treatment Effects in Observational Data Under Sample Selection

ABSTRACT This article partially identifies population treatment effects in observational data under both non‐random treatment assignment and sample selection. Bounds are provided for both average and quantile population treatment effects, combining assumptions for the selected and the non‐selected subsamples. We show how different assumptions help narrow identification regions, and we illustrate our methods by partially identifying the effect of maternal education on the 2015 PISA math test scores in Brazil. We find that while sample selection considerably increases the uncertainty around the effect of maternal education, it is still possible to calculate informative identification regions.