# Covariate-assisted bounds on causal effects with instrumental variables

arXiv: https://arxiv.org/abs/2301.12106 · HTML: https://mlsanity.com/paper/2301.12106/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2023.

## Built on by (most cited first, 10 of 10)

- [Meta-Learners for Partially-Identified Treatment Effects Across Multiple Environments](https://mlsanity.com/paper/2406.02464/) (2024)
- [Partial Identification of Causal Effects Using Proxy Variables](https://mlsanity.com/paper/2304.04374/) (2023)
- [Auditing Fairness under Unobserved Confounding](https://mlsanity.com/paper/2403.14713/) (2024)
- [Learning Representations of Instruments for Partial Identification of Treatment Effects](https://mlsanity.com/paper/2410.08976/) (2024)
- [Causal K-Means Clustering](https://mlsanity.com/paper/2405.03083/) (2024)
- [IV-ICL: Bounding Causal Effects with Instrumental Variables via In-Context Learning](https://mlsanity.com/paper/2605.12924/) (2026)
- [Information-Theoretic Causal Bounds under Unmeasured Confounding](https://mlsanity.com/paper/2601.17160/) (2026)
- [Continuous Treatment Effects with Surrogate Outcomes](https://mlsanity.com/paper/2402.00168/) (2024)
- [Statistical Inference and Learning for Shapley Additive Explanations (SHAP)](https://mlsanity.com/paper/2602.10532/) (2026)
- [Bounding Causal Effects with Leaky Instruments](https://mlsanity.com/paper/2404.04446/) (2024)

## Abstract (arXiv)

When an exposure of interest is confounded by unmeasured factors, an instrumental variable (IV) can be used to identify and estimate certain causal contrasts. Identification of the marginal average treatment effect (ATE) from IVs relies on strong untestable structural assumptions. When one is unwilling to assert such structure, IVs can nonetheless be used to construct bounds on the ATE. Famously, Balke and Pearl (1997) proved tight bounds on the ATE for a binary outcome, in a randomized trial with noncompliance and no covariate information. We demonstrate how these bounds remain useful in observational settings with baseline confounders of the IV, as well as randomized trials with measured baseline covariates. The resulting bounds on the ATE are non-smooth functionals, and thus standard nonparametric efficiency theory is not immediately applicable. To remedy this, we propose (1) under a novel margin condition, influence function-based estimators of the bounds that can attain parametric convergence rates when the nuisance functions are modeled flexibly, and (2) estimators of smooth approximations of these bounds. We propose extensions to continuous outcomes, explore finite sample properties in simulations, and illustrate the proposed estimators in an observational study targeting the effect of higher education on wages.