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On the Properties of the Synthetic Control Estimator with Many Periods and Many Controls

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arxiv 1906.06665 v5 pith:F3JEZ5OO submitted 2019-06-16 econ.EM

classification econ.EM
keywords controlfactorloadingsnumberunitswhenestimatorperiods
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We consider the asymptotic properties of the Synthetic Control (SC) estimator when both the number of pre-treatment periods and control units are large. If potential outcomes follow a linear factor model, we provide conditions under which the factor loadings of the SC unit converge in probability to the factor loadings of the treated unit. This happens when there are weights diluted among an increasing number of control units such that a weighted average of the factor loadings of the control units asymptotically reconstructs the factor loadings of the treated unit. In this case, the SC estimator is asymptotically unbiased even when treatment assignment is correlated with time-varying unobservables. This result can be valid even when the number of control units is larger than the number of pre-treatment periods.

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  1. Correlated Synthetic Controls

    econ.EM 2025-07 conditional novelty 6.0 of 10

    Correlated Synthetic Controls, a weight-sharing synthetic control estimator for many treated units, is proposed and shown to have smaller estimation error than difference-in-differences under selection on unobservable...

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