# AI-Generated Measurements for Identification and Inference with Missing Data: A Weak Shadow Variable Approach

arXiv: https://arxiv.org/abs/2602.16061 · HTML: https://mlsanity.com/paper/2602.16061/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 53 references that are in the map.
- First posted on arXiv 17 Feb 2026.

## Builds on (most cited first, 9 of 9)

- [The Challenge of Using LLMs to Simulate Human Behavior: A Causal Inference Perspective](https://mlsanity.com/paper/2312.15524/) (2023)
- [Simulating User Satisfaction for the Evaluation of Task-oriented Dialogue Systems](https://mlsanity.com/paper/2105.03748/) (2021)
- [Predictions as Surrogates: Revisiting Surrogate Outcomes in the Age of AI](https://mlsanity.com/paper/2501.09731/) (2025)
- [Large Language Models for Market Research: A Data-augmentation Approach](https://mlsanity.com/paper/2412.19363/) (2024)
- [LOLA: LLM-Assisted Online Learning Algorithm for Content Experiments](https://mlsanity.com/paper/2406.02611/) (2024)
- [Semiparametric Estimation with Data Missing Not at Random Using an Instrumental Variable](https://mlsanity.com/paper/1607.03197/) (2016)
- [Fine-Tune, Then Rectify](https://mlsanity.com/paper/2511.19486/) (2025)
- [Choosing the Better Bandit Algorithm under Data Sharing: When Do A/B Experiments Work?](https://mlsanity.com/paper/2507.11891/) (2025)
- [Program Evaluation with Remotely Sensed Outcomes](https://mlsanity.com/paper/2411.10959/) (2024)

## Abstract (arXiv)

Across business and social science applications, outcomes are often missing in ways that depend on the unobserved outcomes themselves. In service systems, for example, whether a customer submits a rating depends on the rating they would have provided. Such missing-not-at-random (MNAR) mechanisms make population quantities difficult to identify without strong assumptions on the observation process. Meanwhile, rich unstructured data, such as customer interaction histories, are increasingly available and can be used to construct structured measurements using tools such as large language models (LLMs). In this work, we develop an assumption-lean partial identification framework that uses such measurements as weak shadow variables, defined as outcome-informative proxies that are conditionally independent of missingness given the true outcome and observed covariates. Importantly, they need not accurately predict missing outcomes or satisfy the completeness requirement in the classical shadow variable literature. For identification, we characterize sharp bounds on population quantities through a pair of linear programs. For estimation and inference, we propose a localized penalized estimator that remains feasible under sampling error, and a subsampling algorithm for constructing confidence intervals. In semi-synthetic experiments using real customer-service dialogues, weak-shadow-variable intervals are about 89% narrower than those without auxiliary information, while their midpoints have around 41% lower estimation error than classical MNAR methods.