# On the Testability of Causal Models with Latent and Instrumental Variables

arXiv: https://arxiv.org/abs/1302.4976 · HTML: https://mlsanity.com/paper/1302.4976/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2013.

## Built on by (most cited first, 26 of 26)

- [Counterfactual Identifiability of Bijective Causal Models](https://mlsanity.com/paper/2302.02228/) (2023)
- [An Automated Approach to Causal Inference in Discrete Settings](https://mlsanity.com/paper/2109.13471/) (2021)
- [Data-Driven Causal Effect Estimation Based on Graphical Causal Modelling: A Survey](https://mlsanity.com/paper/2208.09590/) (2022)
- [The d-separation criterion in Categorical Probability](https://mlsanity.com/paper/2207.05740/) (2022)
- [Training a Resilient Q-Network against Observational Interference](https://mlsanity.com/paper/2102.09677/) (2021)
- [On Testability of the Front-Door Model via Verma Constraints](https://mlsanity.com/paper/2203.00161/) (2022)
- [Discovering Ancestral Instrumental Variables for Causal Inference from Observational Data](https://mlsanity.com/paper/2206.01931/) (2022)
- [Ancestral Instrument Method for Causal Inference without Complete Knowledge](https://mlsanity.com/paper/2201.03810/) (2022)
- [Disentangled Representation Learning for Causal Inference with Instruments](https://mlsanity.com/paper/2412.04641/) (2024)
- [Parameter identification in linear non-Gaussian causal models under general confounding](https://mlsanity.com/paper/2405.20856/) (2024)
- [Causal Inference in medicine and in health policy, a summary](https://mlsanity.com/paper/2105.04655/) (2021)
- [The Causal Marginal Polytope for Bounding Treatment Effects](https://mlsanity.com/paper/2202.13851/) (2022)
- [Treatment Learning Causal Transformer for Noisy Image Classification](https://mlsanity.com/paper/2203.15529/) (2022)
- [Falsification of Unconfoundedness by Testing Independence of Causal Mechanisms](https://mlsanity.com/paper/2502.06231/) (2025)
- [Automating the Selection of Proxy Variables of Unmeasured Confounders](https://mlsanity.com/paper/2405.16130/) (2024)
- [A primer on optimal transport for causal inference with observational data](https://mlsanity.com/paper/2503.07811/) (2025)
- [Text Rationalization for Robust Causal Effect Estimation](https://mlsanity.com/paper/2512.05373/) (2025)
- [Combining Interventional and Observational Data Using Causal Reductions](https://mlsanity.com/paper/2103.04786/) (2021)
- [Causal inference with imperfect instrumental variables](https://mlsanity.com/paper/2111.03029/) (2021)
- [Classifying Causal Structures: Ascertaining when Classical Correlations are Constrained by Inequalities](https://mlsanity.com/paper/2308.02380/) (2023)
- [On the physics of nested Markov models: a generalized probabilistic theory perspective](https://mlsanity.com/paper/2411.11614/) (2024)
- [Revisiting the Berkeley Admissions data: Statistical Tests for Causal Hypotheses](https://mlsanity.com/paper/2502.10161/) (2025)
- [Differentiable Causal Discovery for Singular Linear Models under Confounding](https://mlsanity.com/paper/2601.01368/) (2026)
- [Uncertainty-aware Causal Decision Making via Effect Bound Decomposition](https://mlsanity.com/paper/2601.22736/) (2026)
- [Verifying formulas for interventional distributions](https://mlsanity.com/paper/2607.13883/) (2026)
- [Beyond Conditional Independence: Root Cause Analysis with Deep Causal Models](https://mlsanity.com/paper/2609.36771/) (2026)

## Abstract (arXiv)

Certain causal models involving unmeasured variables induce no independence constraints among the observed variables but imply, nevertheless, inequality contraints on the observed distribution. This paper derives a general formula for such instrumental variables, that is, exogenous variables that directly affect some variables but not all. With the help of this formula, it is possible to test whether a model involving instrumental variables may account for the data, or, conversely, whether a given variables can be deemed instrumental.