# Bounding, an accessible method for estimating principal causal effects, examined and explained

arXiv: https://arxiv.org/abs/1701.03139 · HTML: https://mlsanity.com/paper/1701.03139/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jan 2017.

## Built on by (most cited first, 1 of 1)

- [Pragmatic Fairness: Developing Policies with Outcome Disparity Control](https://mlsanity.com/paper/2301.12278/) (2023)

## Abstract (arXiv)

Estimating treatment effects for subgroups defined by post-treatment behavior (i.e., estimating causal effects in a principal stratification framework) can be technically challenging and heavily reliant on strong assumptions. We investigate an alternative path: using bounds to identify ranges of possible effects that are consistent with the data. This simple approach relies on fewer assumptions and yet can result in policy-relevant findings. As we show, covariates can be used to substantially tighten bounds in a straightforward manner. Via simulation, we demonstrate which types of covariates are maximally beneficial. We conclude with an analysis of a multi-site experimental study of Early College High Schools. When examining the program's impact on students completing the ninth grade "on-track" for college, we find little impact for ECHS students who would otherwise attend a high quality high school, but substantial effects for those who would not. This suggests potential benefit in expanding these programs in areas primarily served by lower quality schools.