# Causal Inference with Invalid Instruments: Post-selection Problems and A Solution Using Searching and Sampling

arXiv: https://arxiv.org/abs/2104.06911 · HTML: https://mlsanity.com/paper/2104.06911/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Apr 2021.

## Built on by (most cited first, 3 of 3)

- [A Heteroskedasticity-Robust Overidentifying Restriction Test with High-Dimensional Covariates](https://mlsanity.com/paper/2205.00171/) (2022)
- [TSCI: two stage curvature identification for causal inference with invalid instruments](https://mlsanity.com/paper/2304.00513/) (2023)
- [Causal Discovery Should Embrace the Wisdom of the Crowd](https://mlsanity.com/paper/2603.02678/) (2026)

## Abstract (arXiv)

Instrumental variable methods are among the most commonly used causal inference approaches to deal with unmeasured confounders in observational studies. The presence of invalid instruments is the primary concern for practical applications, and a fast-growing area of research is inference for the causal effect with possibly invalid instruments. This paper illustrates that the existing confidence intervals may undercover when the valid and invalid instruments are hard to separate in a data-dependent way. To address this, we construct uniformly valid confidence intervals that are robust to the mistakes in separating valid and invalid instruments. We propose to search for a range of treatment effect values that lead to sufficiently many valid instruments. We further devise a novel sampling method, which, together with searching, leads to a more precise confidence interval. Our proposed searching and sampling confidence intervals are uniformly valid and achieve the parametric length under the finite-sample majority and plurality rules. We apply our proposal to examine the effect of education on earnings. The proposed method is implemented in the R package RobustIV available from CRAN.