Causal Inference under Temporal and Spatial Interference

Many social events and policies generate spillover effects in both time and space. Their occurrence influences not only the outcomes of interest in the future, but also these outcomes in nearby areas. In this paper, we propose a design-based approach to estimate the direct and indirect/spillover treatment effects of any event or policy under the assumption of sequential ignorability, when both temporal and spatial interference are allowed to present. The proposed estimators are shown to be consistent and asymptotically Normal if the degree of interference dependence does not grow too fast relative to the sample size. The conventional difference-in-differences (DID) or two-way fixed effects model, nevertheless, leads to biased estimates in this scenario. We apply the method to examine the impact of Hong Kong's Umbrella Movement on the result of the ensuing election and how an institutional reform affects real estate assessment in New York State.