Difference-in-Differences Meets Synthetic Control: Doubly Robust Identification and Estimation

2025-03-14

AI Summary

This paper addresses robust estimation of the average treatment effect on the treated (ATT) in panel data. We propose a doubly robust identification strategy that integrates difference-in-differences (DiD) and synthetic control (SC), ensuring consistent ATT estimation under either the parallel trends assumption or the group-level synthetic control assumption—thus inheriting the identifying strengths of both canonical approaches. Innovatively, we formulate a unified semiparametric framework, impose Neyman orthogonality to enhance estimation stability, and develop a multiplier bootstrap procedure tailored to the dual assumptions for asymptotic distributional inference. The method is further extended to staggered treatment adoption and repeated cross-section settings. We establish √N-consistency and asymptotic normality theoretically; simulations demonstrate superior finite-sample performance relative to either DiD or SC alone. Empirical application to Alaska’s minimum wage policy confirms its robustness and practical utility.

Technology Category

• Intelligent Robots: State Estimation
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Causality

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Difference-in-Differences (DiD) and Synthetic Control (SC) are widely used methods for causal inference in panel data, each with its own strengths and limitations. In this paper, we propose a novel methodology that integrates the advantages of both DiD and SC approaches. Our integrated approach provides a doubly robust identification strategy for causal effects in panel data with a group structure, identifying the average treatment effect on the treated (ATT) under either the parallel trends assumption or the group-level SC assumption. Building on this identification result, we develop a unified semiparametric framework for estimating the ATT. Notably, while the identification-robust moment function satisfies Neyman orthogonality under the parallel trends assumption, it does not under the SC assumption, leading to different asymptotic variances under these two identification strategies. To address this challenge, we propose a multiplier bootstrap method that consistently approximates the asymptotic distribution, regardless of which identification assumption holds. Furthermore, we extend our methodology to accommodate repeated cross-sectional data and staggered treatment designs. As an empirical application, we apply our method to evaluate the impact of the 2003 minimum wage increase in Alaska on family income.

Problem

• Integrates Difference-in-Differences and Synthetic Control methods
• Provides doubly robust identification for treatment effects
• Develops unified framework for estimation and valid inference

Innovation

• Doubly robust identification strategy for ATT
• Unified semiparametric framework for estimation
• Multiplier bootstrap method for valid inference