# Causal inference with imperfect instrumental variables

arXiv: https://arxiv.org/abs/2111.03029 · HTML: https://mlsanity.com/paper/2111.03029/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 60 references that are in the map.
- First posted on arXiv 4 Nov 2021.

## Builds on (most cited first, 13 of 13)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [On the Testability of Causal Models with Latent and Instrumental Variables](https://mlsanity.com/paper/1302.4976/) (2013)
- [Instrumentality Tests Revisited](https://mlsanity.com/paper/1301.2258/) (2013)
- [Inferring latent structures via information inequalities](https://mlsanity.com/paper/1407.2256/) (2014)
- [On falsification of the binary instrumental variable model](https://mlsanity.com/paper/1605.03677/) (2016)
- [Beyond Bell's Theorem II: Scenarios with arbitrary causal structure](https://mlsanity.com/paper/1404.4812/) (2014)
- [Quantum Inflation: A General Approach to Quantum Causal Compatibility](https://mlsanity.com/paper/1909.10519/) (2019)
- [A unifying framework for relaxations of the causal assumptions in Bell's theorem](https://mlsanity.com/paper/1411.4648/) (2014)
- [Identification of Treatment Effects under Conditional Partial Independence](https://mlsanity.com/paper/1707.09563/) (2017)
- [Quantifying causal influences in the presence of a quantum common cause](https://mlsanity.com/paper/2007.01221/) (2020)
- [A convergent inflation hierarchy for quantum causal structures](https://mlsanity.com/paper/2110.14659/) (2021)
- [Assessing Sensitivity to Unconfoundedness: Estimation and Inference](https://mlsanity.com/paper/2012.15716/) (2020)
- [Causal Networks and Freedom of Choice in Bell's Theorem](https://mlsanity.com/paper/2105.05721/) (2021)

## Abstract (arXiv)

Instrumental variables allow for quantification of cause and effect relationships even in the absence of interventions. To achieve this, a number of causal assumptions must be met, the most important of which is the independence assumption, which states that the instrument and any confounding factor must be independent. However, if this independence condition is not met, can we still work with imperfect instrumental variables? Imperfect instruments can manifest themselves by violations of the instrumental inequalities that constrain the set of correlations in the scenario. In this paper, we establish a quantitative relationship between such violations of instrumental inequalities and the minimal amount of measurement dependence required to explain them. As a result, we provide adapted inequalities that are valid in the presence of a relaxed measurement dependence assumption in the instrumental scenario. This allows for the adaptation of existing and new lower bounds on the average causal effect for instrumental scenarios with binary outcomes. Finally, we discuss our findings in the context of quantum mechanics.