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

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.

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