# Instrumentality Tests Revisited

arXiv: https://arxiv.org/abs/1301.2258 · HTML: https://mlsanity.com/paper/1301.2258/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Jan 2013.

## Built on by (most cited first, 8 of 8)

- [An Automated Approach to Causal Inference in Discrete Settings](https://mlsanity.com/paper/2109.13471/) (2021)
- [The d-separation criterion in Categorical Probability](https://mlsanity.com/paper/2207.05740/) (2022)
- [Partial Identification with Noisy Covariates: A Robust Optimization Approach](https://mlsanity.com/paper/2202.10665/) (2022)
- [The Fragility of Fairness: Causal Sensitivity Analysis for Fair Machine Learning](https://mlsanity.com/paper/2410.09600/) (2024)
- [Consistency of Neural Causal Partial Identification](https://mlsanity.com/paper/2405.15673/) (2024)
- [Causal inference with imperfect instrumental variables](https://mlsanity.com/paper/2111.03029/) (2021)
- [Revisiting the Berkeley Admissions data: Statistical Tests for Causal Hypotheses](https://mlsanity.com/paper/2502.10161/) (2025)
- [Uncertainty-aware Causal Decision Making via Effect Bound Decomposition](https://mlsanity.com/paper/2601.22736/) (2026)

## Abstract (arXiv)

An instrument is a random variable thatallows the identification of parameters inlinear models when the error terms arenot uncorrelated.It is a popular method used in economicsand the social sciences that reduces theproblem of identification to the problemof finding the appropriate instruments.Few years ago, Pearl introduced a necessarytest for instruments that allows the researcher to discard those candidatesthat fail the test.In this paper, we make a detailed study of Pearl's test and the general model forinstruments. The results of this studyinclude a novel interpretation of Pearl'stest, a general theory of instrumentaltests, and an affirmative answer to aprevious conjecture. We also presentnew instrumentality tests for the casesof discrete and continuous variables.