# Synthetic Difference in Differences

## TL;DR

This paper introduces a new causal inference estimator for panel data called synthetic difference in differences, which combines ideas from difference in differences and synthetic control methods, offering improved robustness and performance.

## Contribution

It develops a novel estimator that enhances causal effect estimation in panel data, with theoretical guarantees and empirical validation.

## Key findings

- The estimator is robust to latent factors and model misspecification.
- It outperforms traditional methods in simulated and real data.
- Provides conditions for consistency and asymptotic normality.

## Abstract

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.