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The synthetic control estimator (Abadie et al., 2010) is asymptoticallyunbiased assuming that the outcome is a linear function of the underlyingpredictors and that the treated unit can be well approximated by the syntheticcontrol before the treatment. When the outcome is nonlinear, the bias of thesynthetic control estimator can be severe. In this paper, we provide conditionsfor the synthetic control estimator to be asymptotically unbiased when theoutcome is nonlinear, and propose a flexible and data-driven method to choosethe synthetic control weights. Monte Carlo simulations show that compared withthe competing methods, the nonlinear synthetic control method has similar orbetter performance when the outcome is linear, and better performance when theoutcome is nonlinear, and that the confidence intervals have good coverageprobabilities across settings. In the empirical application, we illustrate themethod by estimating the impact of the 2019 anti-extradition law amendmentsbill protests on Hong Kong's economy, and find that the year-long protestsreduced real GDP per capita in Hong Kong by 11.27% in the first quarter of2020, which was larger in magnitude than the economic decline during the 1997Asian financial crisis or the 2008 global financial crisis.

The Synthetic Control Method with Nonlinear Outcomes: Estimating the  Impact of the 2019 Anti-Extradition Law Amendments Bill Protests on Hong  Kong's Economy