# Falsification of Internal and External Validity in Observational Studies via Conditional Moment Restrictions

arXiv: https://arxiv.org/abs/2301.13133 · HTML: https://mlsanity.com/paper/2301.13133/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 47 references that are in the map.
- First posted on arXiv 30 Jan 2023.

## Builds on (most cited first, 19 of 19)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Deep Generalized Method of Moments for Instrumental Variable Analysis](https://mlsanity.com/paper/1905.12495/) (2019)
- [Minimax Estimation of Conditional Moment Models](https://mlsanity.com/paper/2006.07201/) (2020)
- [External Validity: From Do-Calculus to Transportability Across Populations](https://mlsanity.com/paper/1503.01603/) (2015)
- [Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approach](https://mlsanity.com/paper/2103.14029/) (2021)
- [A Review of Generalizability and Transportability](https://mlsanity.com/paper/2102.11904/) (2021)
- [Adversarial Generalized Method of Moments](https://mlsanity.com/paper/1803.07164/) (2018)
- [Combining Observational and Experimental Datasets Using Shrinkage Estimators](https://mlsanity.com/paper/2002.06708/) (2020)
- [Generalizing causal inferences from individuals in randomized trials to all trial-eligible individuals](https://mlsanity.com/paper/1709.04589/) (2017)
- [The Variational Method of Moments](https://mlsanity.com/paper/2012.09422/) (2020)
- [Adaptive Combination of Randomized and Observational Data](https://mlsanity.com/paper/2111.15012/) (2021)
- [Extending inferences from a randomized trial to a new target population](https://mlsanity.com/paper/1805.00550/) (2018)
- [Kernel Conditional Moment Test via Maximum Moment Restriction](https://mlsanity.com/paper/2002.09225/) (2020)
- [Elastic Integrative Analysis of Randomized Trial and Real-World Data for Treatment Heterogeneity Estimation](https://mlsanity.com/paper/2005.10579/) (2020)
- [Inference on Strongly Identified Functionals of Weakly Identified Functions](https://mlsanity.com/paper/2208.08291/) (2022)
- [Falsification before Extrapolation in Causal Effect Estimation](https://mlsanity.com/paper/2209.13708/) (2022)
- [Minimax Rates and Adaptivity in Combining Experimental and Observational Data](https://mlsanity.com/paper/2109.10522/) (2021)
- [Adversarial Estimators](https://mlsanity.com/paper/2204.10495/) (2022)

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

- [Prediction-powered Generalization of Causal Inferences](https://mlsanity.com/paper/2406.02873/) (2024)
- [Efficient Randomized Experiments Using Foundation Models](https://mlsanity.com/paper/2502.04262/) (2025)
- [Hidden yet quantifiable: A lower bound for confounding strength using randomized trials](https://mlsanity.com/paper/2312.03871/) (2023)
- [Benchmarking Observational Studies with Experimental Data under Right-Censoring](https://mlsanity.com/paper/2402.15137/) (2024)
- [The Hardness of Validating Observational Studies with Experimental Data](https://mlsanity.com/paper/2503.14795/) (2025)
- [Falsification of Unconfoundedness by Testing Independence of Causal Mechanisms](https://mlsanity.com/paper/2502.06231/) (2025)
- [Robust estimation of heterogeneous treatment effects in randomized trials leveraging external data](https://mlsanity.com/paper/2507.03681/) (2025)
- [Transportability without Graphs: A Bayesian Approach to Identifying s-Admissible Backdoor Sets](https://mlsanity.com/paper/2505.12801/) (2025)
- [Uncovering Bias Mechanisms in Observational Studies](https://mlsanity.com/paper/2506.01191/) (2025)
- [A Sensitivity Approach to Causal Inference Under Limited Overlap](https://mlsanity.com/paper/2511.22003/) (2025)

## Abstract (arXiv)

Randomized Controlled Trials (RCT)s are relied upon to assess new treatments, but suffer from limited power to guide personalized treatment decisions. On the other hand, observational (i.e., non-experimental) studies have large and diverse populations, but are prone to various biases (e.g. residual confounding). To safely leverage the strengths of observational studies, we focus on the problem of falsification, whereby RCTs are used to validate causal effect estimates learned from observational data. In particular, we show that, given data from both an RCT and an observational study, assumptions on internal and external validity have an observable, testable implication in the form of a set of Conditional Moment Restrictions (CMRs). Further, we show that expressing these CMRs with respect to the causal effect, or "causal contrast", as opposed to individual counterfactual means, provides a more reliable falsification test. In addition to giving guarantees on the asymptotic properties of our test, we demonstrate superior power and type I error of our approach on semi-synthetic and real world datasets. Our approach is interpretable, allowing a practitioner to visualize which subgroups in the population lead to falsification of an observational study.