B0951
Title: Doubly robust proximal synthetic controls
Authors: Hongxiang Qiu - University of Pennsylvania (United States) [presenting]
Edgar Dobriban - University of Pennsylvania (United States)
Xu Shi - University of Michigan (United States)
Wang Miao - Peking University (China)
Eric Tchetgen Tchetgen - The Wharton School, University of Pennsylvania (United States)
Abstract: To infer the treatment effect for a single treated unit using panel data, one common approach is to search for a linear combination of control units' outcomes that mimics the treated unit's pre-treatment outcome trajectory. This linear combination is subsequently used to impute the counterfactual outcomes of the treated unit had it not been treated in the post-treatment period, and estimation of the treatment effect follows. Approaches following this idea have been called synthetic control methods. Existing synthetic control methods rely on correctly modeling certain aspects of the counterfactual outcome generating mechanism and may require near-perfect matching of the pre-treatment trajectory. Inspired by proximal causal inference, we obtain two novel nonparametric identifying formulae for the average treatment effect for the treated unit: one is based on weighting, and the other combines models for the counterfactual outcome and the weighting function. We develop two GMM estimators based on these two formulae. One new estimator is doubly robust: it is consistent and asymptotically normal if at least one of the outcome model and the weighting model is correctly specified in a parametric model. We demonstrate the performance of the methods via simulations and apply them to evaluate the effect of a tax cut in Kansas on GDP.
