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In the presence of sample selection, Lee's (2009) nonparametric bounds are apopular tool for estimating a treatment effect. However, the Lee bounds rely onthe monotonicity assumption, whose empirical validity is sometimes unclear.Furthermore, the bounds are often regarded to be wide and less informative evenunder monotonicity. To address these issues, this study introduces a stochasticversion of the monotonicity assumption alongside a nonparametric distributionalshape constraint. The former enhances the robustness of the Lee bounds withrespect to monotonicity, while the latter helps tighten these bounds. Theobtained bounds do not rely on the exclusion restriction and can be root-$n$consistently estimable, making them practically viable. The potentialusefulness of the proposed methods is illustrated by their application onexperimental data from the after-school instruction programme studied byMuralidharan, Singh, and Ganimian (2019).

Robustify and Tighten the Lee Bounds: A Sample Selection Model under Stochastic Monotonicity and Symmetry Assumptions