# Panel Experiments and Dynamic Causal Effects: A Finite Population Perspective

arXiv: https://arxiv.org/abs/2003.09915 · HTML: https://mlsanity.com/paper/2003.09915/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Mar 2020.

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

- [Counterfactual inference in sequential experiments](https://mlsanity.com/paper/2202.06891/) (2022)
- [An Experimental Design for Anytime-Valid Causal Inference on Multi-Armed Bandits](https://mlsanity.com/paper/2311.05794/) (2023)
- [Privacy Preserving Adaptive Experiment Design](https://mlsanity.com/paper/2401.08224/) (2024)
- [Dynamic covariate balancing: estimating treatment effects over time with potential local projections](https://mlsanity.com/paper/2103.01280/) (2021)
- [Causal Estimation of User Learning in Personalized Systems](https://mlsanity.com/paper/2306.00485/) (2023)
- [Beyond ATE: Multi-Criteria Design for A/B Testing](https://mlsanity.com/paper/2509.05864/) (2025)
- [Fit CATE Once: Model-Assisted Randomization Tests Without Sample Splitting](https://mlsanity.com/paper/2605.09116/) (2026)
- [Always-On Experimentation](https://mlsanity.com/paper/2609.38695/) (2026)

## Abstract (arXiv)

In panel experiments, we randomly assign units to different interventions, measuring their outcomes, and repeating the procedure in several periods. Using the potential outcomes framework, we define finite population dynamic causal effects that capture the relative effectiveness of alternative treatment paths. For a rich class of dynamic causal effects, we provide a nonparametric estimator that is unbiased over the randomization distribution and derive its finite population limiting distribution as either the sample size or the duration of the experiment increases. We develop two methods for inference: a conservative test for weak null hypotheses and an exact randomization test for sharp null hypotheses. We further analyze the finite population probability limit of linear fixed effects estimators. These commonly-used estimators do not recover a causally interpretable estimand if there are dynamic causal effects and serial correlation in the assignments, highlighting the value of our proposed estimator.