# Distributional synthetic controls

arXiv: https://arxiv.org/abs/2001.06118 · HTML: https://mlsanity.com/paper/2001.06118/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jan 2020.

## Built on by (most cited first, 9 of 9)

- [Tangential Wasserstein Projections](https://mlsanity.com/paper/2207.14727/) (2022)
- [Distributional Matrix Completion via Nearest Neighbors in the Wasserstein Space](https://mlsanity.com/paper/2410.13112/) (2024)
- [Asymptotically Unbiased Synthetic Control Methods by Moment Matching](https://mlsanity.com/paper/2307.11127/) (2023)
- [Interpretable Causal Inference for Analyzing Wearable, Sensor, and Distributional Data](https://mlsanity.com/paper/2312.10569/) (2023)
- [Learning Counterfactual Distributions via Kernel Nearest Neighbors](https://mlsanity.com/paper/2410.13381/) (2024)
- [A primer on optimal transport for causal inference with observational data](https://mlsanity.com/paper/2503.07811/) (2025)
- [Beyond the Average: Distributional Causal Inference under Imperfect Compliance](https://mlsanity.com/paper/2509.15594/) (2025)
- [Constructing Synthetic Treatment Groups without the Mean Exchangeability Assumption](https://mlsanity.com/paper/2309.16409/) (2023)
- [Counterexamples and Sufficient Conditions: Comments on "Optimally-Transported Generalized Method of Moments"](https://mlsanity.com/paper/2609.20260/) (2026)

## Abstract (arXiv)

This article extends the widely-used synthetic controls estimator for evaluating causal effects of policy changes to quantile functions. The proposed method provides a geometrically faithful estimate of the entire counterfactual quantile function of the treated unit. Its appeal stems from an efficient implementation via a constrained quantile-on-quantile regression. This constitutes a novel concept of independent interest. The method provides a unique counterfactual quantile function in any scenario: for continuous, discrete or mixed distributions. It operates in both repeated cross-sections and panel data with as little as a single pre-treatment period. The article also provides abstract identification results by showing that any synthetic controls method, classical or our generalization, provides the correct counterfactual for causal models that preserve distances between the outcome distributions. Working with whole quantile functions instead of aggregate values allows for tests of equality and stochastic dominance of the counterfactual- and the observed distribution. It can provide causal inference on standard outcomes like average- or quantile treatment effects, but also more general concepts such as counterfactual Lorenz curves or interquartile ranges.