# Incentive-Aware Synthetic Control: Accurate Counterfactual Estimation via Incentivized Exploration

arXiv: https://arxiv.org/abs/2312.16307 · HTML: https://mlsanity.com/paper/2312.16307/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 52 references that are in the map.
- First posted on arXiv 26 Dec 2023.

## Builds on (most cited first, 21 of 21)

- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)
- [Causal Bandits: Learning Good Interventions via Causal Inference](https://mlsanity.com/paper/1606.03203/) (2016)
- [Bayesian Incentive-Compatible Bandit Exploration](https://mlsanity.com/paper/1502.04147/) (2015)
- [Bayesian Exploration: Incentivizing Exploration in Bayesian Games](https://mlsanity.com/paper/1602.07570/) (2016)
- [The Price of Incentivizing Exploration: A Characterization via Thompson Sampling and Sample Complexity](https://mlsanity.com/paper/2002.00558/) (2020)
- [Synthetic Interventions](https://mlsanity.com/paper/2006.07691/) (2020)
- [Robust Synthetic Control](https://mlsanity.com/paper/1711.06940/) (2017)
- [Incentivizing Exploration with Selective Data Disclosure](https://mlsanity.com/paper/1811.06026/) (2018)
- [Causal Bandits for Linear Structural Equation Models](https://mlsanity.com/paper/2208.12764/) (2022)
- [Counterfactual inference in sequential experiments](https://mlsanity.com/paper/2202.06891/) (2022)
- [Treatment Allocation under Uncertain Costs](https://mlsanity.com/paper/2103.11066/) (2021)
- [Incentivizing Combinatorial Bandit Exploration](https://mlsanity.com/paper/2206.00494/) (2022)
- [Synthetically Controlled Bandits](https://mlsanity.com/paper/2202.07079/) (2022)
- [Synthetic Control As Online Linear Regression](https://mlsanity.com/paper/2202.08426/) (2022)
- [Incentivizing Exploration with Linear Contexts and Combinatorial Actions](https://mlsanity.com/paper/2306.01990/) (2023)
- [Adaptive Principal Component Regression with Applications to Panel Data](https://mlsanity.com/paper/2307.01357/) (2023)
- [Incentivizing Compliance with Algorithmic Instruments](https://mlsanity.com/paper/2107.10093/) (2021)
- [Same Root Different Leaves: Time Series and Cross-Sectional Methods in Panel Data](https://mlsanity.com/paper/2207.14481/) (2022)
- [Strategyproof Decision-Making in Panel Data Settings and Beyond](https://mlsanity.com/paper/2211.14236/) (2022)
- [Individualized treatment rules under stochastic treatment cost constraints](https://mlsanity.com/paper/2201.06669/) (2022)
- [On Model Identification and Out-of-Sample Prediction of Principal Component Regression: Applications to Synthetic Controls](https://mlsanity.com/paper/2010.14449/) (2020)

## Abstract (arXiv)

Synthetic control methods (SCMs) are a canonical approach used to estimate treatment effects from panel data in the internet economy. We shed light on a frequently overlooked but ubiquitous assumption made in SCMs of "overlap": a treated unit can be written as some combination -- typically, convex or linear -- of the units that remain under control. We show that if units select their own interventions, and there is sufficiently large heterogeneity between units that prefer different interventions, overlap will not hold. We address this issue by proposing a recommender system which incentivizes units with different preferences to take interventions they would not normally consider. Specifically, leveraging tools from information design and online learning, we propose an SCM that incentivizes exploration in panel data settings by providing incentive-compatible intervention recommendations to units. We establish this estimator obtains valid counterfactual estimates without the need for an a priori overlap assumption. We extend our results to the setting of synthetic interventions, where the goal is to produce counterfactual outcomes under all interventions, not just control. Finally, we provide two hypothesis tests for determining whether unit overlap holds for a given panel dataset.