Causal Inference Under Temporal and Spatial Interference

Ye Wang (New York University)

Abstract: 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, I propose a semi-parametric approach to estimate the direct and indirect/spillover treatment effect of any event or policy under the sequential ignorability assumption, when both temporal and spatial interference are present. The estimator is constructed by combining the idea of spatial "circle means" proposed by Aronow, Samii and Wang (2019) with the marginal structural models (MSM). It is shown to be unbiased, consistent, and normally distributed if the degree of interference does not grow too fast with the sample size. I rely on Stein’s method to derive both its analytical variance and asymptotic distribution. The estimator becomes doubly robust and more efficient after being augmented with a diffusion model. The conventional difference-in-differences (DID) or two-way fixed effects approach, nevertheless, leads to biased estimates in this scenario. I apply the method to examine the impact of Hong Kong’s Umbrella Movement on election results and how an institutional reform in New York state affects real estate assessment.

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