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

Abstract

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.