# Synthetic Difference in Differences

arXiv: https://arxiv.org/abs/1812.09970 · HTML: https://mlsanity.com/paper/1812.09970/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Dec 2018.

## Built on by (most cited first, 30 of 41)

- [Causal Matrix Completion](https://mlsanity.com/paper/2109.15154/) (2021)
- [Augmented balancing weights as linear regression](https://mlsanity.com/paper/2304.14545/) (2023)
- [Counterfactual inference in sequential experiments](https://mlsanity.com/paper/2202.06891/) (2022)
- [The Impact of Large Language Models on Open-source Innovation: Evidence from GitHub Copilot](https://mlsanity.com/paper/2409.08379/) (2024)
- [Reinforcement Learning in the Wild: Scalable RL Dispatching Algorithm Deployed in Ridehailing Marketplace](https://mlsanity.com/paper/2202.05118/) (2022)
- [On counterfactual inference with unobserved confounding](https://mlsanity.com/paper/2211.08209/) (2022)
- [Doubly robust nearest neighbors in factor models](https://mlsanity.com/paper/2211.14297/) (2022)
- [Synthetically Controlled Bandits](https://mlsanity.com/paper/2202.07079/) (2022)
- [Learning Treatment Effects in Panels with General Intervention Patterns](https://mlsanity.com/paper/2106.02780/) (2021)
- [Synthetic Control As Online Linear Regression](https://mlsanity.com/paper/2202.08426/) (2022)
- [Adaptive Principal Component Regression with Applications to Panel Data](https://mlsanity.com/paper/2307.01357/) (2023)
- [Strategyproof Decision-Making in Panel Data Settings and Beyond](https://mlsanity.com/paper/2211.14236/) (2022)
- [Doubly Robust Inference in Causal Latent Factor Models](https://mlsanity.com/paper/2402.11652/) (2024)
- [Causal Inference with Complex Treatments: A Survey](https://mlsanity.com/paper/2407.14022/) (2024)
- [Forecasting Algorithms for Causal Inference with Panel Data](https://mlsanity.com/paper/2208.03489/) (2022)
- [Network Synthetic Interventions: A Causal Framework for Panel Data Under Network Interference](https://mlsanity.com/paper/2210.11355/) (2022)
- [OpportunityFinder: A Framework for Automated Causal Inference](https://mlsanity.com/paper/2309.13103/) (2023)
- [A primer on optimal transport for causal inference with observational data](https://mlsanity.com/paper/2503.07811/) (2025)
- [Identification of Average Treatment Effects in Nonparametric Panel Models](https://mlsanity.com/paper/2503.19873/) (2025)
- [A Causal Inference Framework for Data Rich Environments](https://mlsanity.com/paper/2504.01702/) (2025)
- [Causal Inference in Possibly Nonlinear Factor Models](https://mlsanity.com/paper/2008.13651/) (2020)
- [Shapes as Product Differentiation: Neural Network Embedding in the Analysis of Markets for Fonts](https://mlsanity.com/paper/2107.02739/) (2021)
- [Downstream Fairness Caveats with Synthetic Healthcare Data](https://mlsanity.com/paper/2203.04462/) (2022)
- [Synthetic Principal Component Design: Fast Covariate Balancing with Synthetic Controls](https://mlsanity.com/paper/2211.15241/) (2022)
- [ClusterSC: Advancing Synthetic Control with Donor Selection](https://mlsanity.com/paper/2503.21629/) (2025)
- [The (Short-Term) Effects of Large Language Models on Unemployment and Earnings](https://mlsanity.com/paper/2509.15510/) (2025)
- [Dynamic covariate balancing: estimating treatment effects over time with potential local projections](https://mlsanity.com/paper/2103.01280/) (2021)
- [Predictor Selection for Synthetic Controls](https://mlsanity.com/paper/2203.11576/) (2022)
- [Dynamic Synthetic Controls vs. Panel-Aware Double Machine Learning for Geo-Level Marketing Impact Estimation](https://mlsanity.com/paper/2508.20335/) (2025)
- [Counterfactual Forecasting for Panel Data](https://mlsanity.com/paper/2511.06189/) (2025)

## Abstract (arXiv)

We present a new estimator for causal effects with panel data that builds on insights behind the widely used difference in differences and synthetic control methods. Relative to these methods we find, both theoretically and empirically, that this "synthetic difference in differences" estimator has desirable robustness properties, and that it performs well in settings where the conventional estimators are commonly used in practice. We study the asymptotic behavior of the estimator when the systematic part of the outcome model includes latent unit factors interacted with latent time factors, and we present conditions for consistency and asymptotic normality.