# Nonparametric identification is not enough, but randomized controlled trials are

arXiv: https://arxiv.org/abs/2108.11342 · HTML: https://mlsanity.com/paper/2108.11342/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Aug 2021.

## Built on by (most cited first, 6 of 6)

- [Causal Effect Variational Autoencoder with Uniform Treatment](https://mlsanity.com/paper/2111.08656/) (2021)
- [Constructing Confidence Intervals for Average Treatment Effects from Multiple Datasets](https://mlsanity.com/paper/2412.11511/) (2024)
- [The Hardness of Validating Observational Studies with Experimental Data](https://mlsanity.com/paper/2503.14795/) (2025)
- [PrivATE: Differentially Private Confidence Intervals for Average Treatment Effects](https://mlsanity.com/paper/2505.21641/) (2025)
- [Active and Passive Causal Inference Learning](https://mlsanity.com/paper/2308.09248/) (2023)
- [Two Layers of Instability in Causal Estimation](https://mlsanity.com/paper/2606.21185/) (2026)

## Abstract (arXiv)

We argue that randomized controlled trials (RCTs) are special even among settings where average treatment effects are identified by a nonparametric unconfoundedness assumption. This claim follows from two results of Robins and Ritov (1997): (1) with at least one continuous covariate control, no estimator of the average treatment effect exists which is uniformly consistent without further assumptions, (2) knowledge of the propensity score yields a uniformly consistent estimator and honest confidence intervals that shrink at parametric rates with increasing sample size, regardless of how complicated the propensity score function is. We emphasize the latter point, and note that successfully-conducted RCTs provide knowledge of the propensity score to the researcher. We discuss modern developments in covariate adjustment for RCTs, noting that statistical models and machine learning methods can be used to improve efficiency while preserving finite sample unbiasedness. We conclude that statistical inference has the potential to be fundamentally more difficult in observational settings than it is in RCTs, even when all confounders are measured.