# Estimating long-term causal effects from short-term experiments and long-term observational data with unobserved confounding

arXiv: https://arxiv.org/abs/2302.10625 · HTML: https://mlsanity.com/paper/2302.10625/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 25 references that are in the map.
- First posted on arXiv 21 Feb 2023.

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

- [An Introduction to Proximal Causal Learning](https://mlsanity.com/paper/2009.10982/) (2020)
- [Double/Debiased Machine Learning for Treatment and Causal Parameters](https://mlsanity.com/paper/1608.00060/) (2016)
- [Long-term Causal Inference Under Persistent Confounding via Data Combination](https://mlsanity.com/paper/2202.07234/) (2022)
- [Long-Term Effect Estimation with Surrogate Representation](https://mlsanity.com/paper/2008.08236/) (2020)
- [Integrating overlapping datasets using bivariate causal discovery](https://mlsanity.com/paper/1910.11356/) (2019)
- [Disentangling Causal Effects from Sets of Interventions in the Presence of Unobserved Confounders](https://mlsanity.com/paper/2210.05446/) (2022)
- [Leveraging directed causal discovery to detect latent common causes](https://mlsanity.com/paper/1910.10174/) (2019)
- [Estimating Treatment Effects with Observed Confounders and Mediators](https://mlsanity.com/paper/2003.11991/) (2020)
- [Causal inference via algebraic geometry: feasibility tests for functional causal structures with two binary observed variables](https://mlsanity.com/paper/1506.03880/) (2015)

## Built on by (most cited first, 12 of 12)

- [Contrastive representations of high-dimensional, structured treatments](https://mlsanity.com/paper/2411.19245/) (2024)
- [Learning Metrics that Maximise Power for Accelerated A/B-Tests](https://mlsanity.com/paper/2402.03915/) (2024)
- [The Odyssey of Commonsense Causality: From Foundational Benchmarks to Cutting-Edge Reasoning](https://mlsanity.com/paper/2406.19307/) (2024)
- [Spillover Detection for Donor Selection in Synthetic Control Models](https://mlsanity.com/paper/2406.11399/) (2024)
- [Estimating Long-term Heterogeneous Dose-response Curve: Generalization Bound Leveraging Optimal Transport Weights](https://mlsanity.com/paper/2406.19195/) (2024)
- [The Hardness of Validating Observational Studies with Experimental Data](https://mlsanity.com/paper/2503.14795/) (2025)
- [Local Interference: Removing Interference Bias in Semi-Parametric Causal Models](https://mlsanity.com/paper/2503.18756/) (2025)
- [Identification and Estimation of Long-Term Treatment Effects with Monotone Missing](https://mlsanity.com/paper/2504.19527/) (2025)
- [Quantum oracles give an advantage for identifying classical counterfactuals](https://mlsanity.com/paper/2512.13692/) (2025)
- [Testing Effect Homogeneity and Confounding in High-Dimensional Experimental and Observational Studies](https://mlsanity.com/paper/2602.19703/) (2026)
- [Orthogonal Learner for Estimating Heterogeneous Long-Term Treatment Effects](https://mlsanity.com/paper/2604.00915/) (2026)
- [Beyond Temporal Proximity: Explanatory World Models for Credit Assignment in Reinforcement Learning](https://mlsanity.com/paper/2610.13504/) (2026)

## Abstract (arXiv)

Understanding and quantifying cause and effect is an important problem in many domains. The generally-agreed solution to this problem is to perform a randomised controlled trial. However, even when randomised controlled trials can be performed, they usually have relatively short duration's due to cost considerations. This makes learning long-term causal effects a very challenging task in practice, since the long-term outcome is only observed after a long delay. In this paper, we study the identification and estimation of long-term treatment effects when both experimental and observational data are available. Previous work provided an estimation strategy to determine long-term causal effects from such data regimes. However, this strategy only works if one assumes there are no unobserved confounders in the observational data. In this paper, we specifically address the challenging case where unmeasured confounders are present in the observational data. Our long-term causal effect estimator is obtained by combining regression residuals with short-term experimental outcomes in a specific manner to create an instrumental variable, which is then used to quantify the long-term causal effect through instrumental variable regression. We prove this estimator is unbiased, and analytically study its variance. In the context of the front-door causal structure, this provides a new causal estimator, which may be of independent interest. Finally, we empirically test our approach on synthetic-data, as well as real-data from the International Stroke Trial.