# Sharp Bounds for the Marginal Treatment Effect with Sample Selection

## TL;DR

This paper develops sharp bounds for the marginal treatment effect in the presence of sample selection and endogenous treatment choice, providing new identification strategies and empirical estimates for a real-world program.

## Contribution

It introduces pointwise sharp bounds for the MTE under monotonicity and mean dominance assumptions, extending identification to both continuous and discrete propensity scores.

## Key findings

- Bounds for MTE are estimated for the Job Corps program.
- MTE decreases with higher likelihood of attending the program.
- Estimated ATE on the treated ranges from 0.33 to 0.99 dollars.

## Abstract

I analyze treatment effects in situations when agents endogenously select into the treatment group and into the observed sample. As a theoretical contribution, I propose pointwise sharp bounds for the marginal treatment effect (MTE) of interest within the always-observed subpopulation under monotonicity assumptions. Moreover, I impose an extra mean dominance assumption to tighten the previous bounds. I further discuss how to identify those bounds when the support of the propensity score is either continuous or discrete. Using these results, I estimate bounds for the MTE of the Job Corps Training Program on hourly wages for the always-employed subpopulation and find that it is decreasing in the likelihood of attending the program within the Non-Hispanic group. For example, the Average Treatment Effect on the Treated is between \$.33 and \$.99 while the Average Treatment Effect on the Untreated is between \$.71 and \$3.00.