Before revision: We develop a method to help quantify the impact different levels of mobility restrictions could have had on COVID-19 related deaths across nations. Synthetic control (SC) has emerged as a standard tool in such scenarios to produce counterfactual estimates if a particular interventionhad not occurred, using just observational data.However, it remains an important open problem of how to extend SC to obtain counterfactual estimates if a particular intervention had occurred - this is exactly the question of the impact of mobility restrictions stated above. As our main contribution, we introduce\le  synthetic interventions (SI), which helps resolve this open problem by allowing one to produce counterfactual estimates if there are multiple interventions of interest .
After revision: Consider a panel data setting with observations of N units over T time steps. Each of the N units undergoes exactly one of D interventions at time step T_0, with 1\le synthetic interventions (SI), which helps resolve this open problem by allowing one to produce counterfactual estimates if there are multiple interventions of interest .