  The synthetic control estimator (Abadie et al., 2010) is asymptotically
unbiased assuming that the outcome is a linear function of the underlying
predictors and that the treated unit can be well approximated by the synthetic
control before the treatment. When the outcome is nonlinear, the bias of the
synthetic control estimator can be severe. In this paper, we provide conditions
for the synthetic control estimator to be asymptotically unbiased when the
outcome is nonlinear, and propose a flexible and data-driven method to choose
the synthetic control weights. Monte Carlo simulations show that compared with
the competing methods, the nonlinear synthetic control method has similar or
better performance when the outcome is linear, and better performance when the
outcome is nonlinear, and that the confidence intervals have good coverage
probabilities across settings. In the empirical application, we illustrate the
method by estimating the impact of the 2019 anti-extradition law amendments
bill protests on Hong Kong's economy, and find that the year-long protests
reduced real GDP per capita in Hong Kong by 11.27% in the first quarter of
2020, which was larger in magnitude than the economic decline during the 1997
Asian financial crisis or the 2008 global financial crisis.
