Synthetic Parallel Trends

TL;DR

This paper introduces a unified framework for policy evaluation in panel data that encompasses existing methods like DID and synthetic control, providing robustness against assumption violations and valid confidence sets.

Contribution

It develops a general identification framework for synthetic parallel trends, unifying and extending existing methods with robustness and valid inference.

Findings

The framework includes DID and synthetic control as special cases.

The proposed confidence set maintains coverage under assumption violations.

Simulations show improved robustness over existing methods.

Abstract

Popular empirical strategies for policy evaluation in the panel data literature -- including difference-in-differences (DID), synthetic control (SC) methods, and their variants -- rely on key identifying assumptions that can be expressed through a specific choice of weights $\omega$ relating pre-treatment trends to the counterfactual outcome. While each choice of $\omega$ may be defensible in empirical contexts that motivate a particular method, it relies on fundamentally untestable and often fragile assumptions. I develop an identification framework that allows for all weights satisfying a Synthetic Parallel Trends assumption: the treated unit's trend is parallel to a weighted combination of control units' trends for a general class of weights. The framework nests these existing methods as special cases and is by construction robust to violations of their respective assumptions. I construct a valid confidence set for the identified set of the treatment effect, which admits a linear programming representation with estimated coefficients and nuisance parameters that are profiled out. In simulations where the assumptions underlying DID or SC-based methods are violated, the proposed confidence set remains robust and attains nominal coverage, while existing methods suffer severe undercoverage.