Synthetic Difference in Differences

Dmitry Arkhangelsky, Susan Athey, David A. Hirshberg (), Guido Imbens and Stefan Wager ()
Additional contact information
David A. Hirshberg: Stanford University, https://www.stanford.edu/
Stefan Wager: Stanford University, https://www.stanford.edu/

Working Papers from CEMFI

Abstract: We present a new perspective on the Synthetic Control (SC) method as a weighted least squares regression estimator with time fixed effects and unit weights. This perspective suggests a generalization with two way (both unit and time) fixed effects, and both unit and time weights, which can be interpreted as a unit and time weighted version of the standard Difference In Differences (DID) estimator. We find that this new Synthetic Difference In Differences (SDID) estimator has attractive properties compared to the SC and DID estimators. Formally we show that our approach has double robustness properties: the SDID estimator is consistent under a wide variety of weighting schemes given a well-specified fixed effects model, and SDID is consistent with appropriately penalized SC weights when the basic fixed effects model is misspecified and instead the true data generating process involves a more general low-rank structure (e.g., a latent factor model). We also present results that justify standard inference based on weighted DID regression. Further generalizations include unit and time weighted factor models.

Keywords: Synthetic control; difference in differences; low-rank matrix estimation; factor models. (search for similar items in EconPapers)
JEL-codes: C01 (search for similar items in EconPapers)
Date: 2019-03
New Economics Papers: this item is included in nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (35)

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Related works:
Journal Article: Synthetic Difference-in-Differences (2021)
Working Paper: Synthetic Difference In Differences (2019)
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