On the Properties of the Synthetic Control Estimator with Many Periods and Many Controls
By Bruno Ferman. 2019
63 citations recorded by the source corpus.
Abstract We consider the asymptotic properties of the synthetic control (SC) estimator when both the number of pretreatment periods and control units are large. If potential outcomes follow a linear factor model, we provide conditions under which the SC unit asymptotically recovers the factor structure of the treated unit, even when the pretreatment fit is imperfect. This happens when there are weights diluted among an increasing number of control units such that a weighted average of the factor structure of the control units asymptotically reconstructs the factor structure of the treated unit. In this case, the SC estimator is asymptotically unbiased even when treatment assignment is correlated with time-varying unobservables. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.
Subfields: Control and Systems Engineering, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/36a942d87c4524f163a5ffbc0c44cad33489575e
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In Control and Systems Engineering
In Statistics and Probability
- Bruno Ferman
- Cristine Pinto
- Avi Feller
- Eli Ben-Michael
- Jesse M. Rothstein
- Alberto Abadie
- Guido W. Imbens
- Stefan Wager
Citations in the corpus
- The Augmented Synthetic Control Method (2018, methodology): “See Arkhangelsky et al. (2019) and Ferman (2019) for asymptotic analogues of this finite sample bound.”
- Synthetic controls with imperfect pretreatment fit (2016, methodology): “Importantly, if the conditions considered by Abadie, Diamond, and Hainmueller (2010) or Ferman (2019) hold in a specific application, then the demeaned SC estimator would be asymptotically unbiased, while the DID estimator may be biased.”
- Using Synthetic Controls: Feasibility, Data Requirements, and Methodological Aspects (2021, background): “(2016), Abadie and L’Hour (2019), and Dube and Zipperer (2015).”