Causal Inference Under Temporal and Spatial Interference

• In Event: Causal Inference

Abstract

This paper aims at providing a systematic investigation on what causal conclusions could be reached in TSCS data under general interference and common assumptions in the literature. I start from defining causal estimands when both temporal (within-unit) and spatial (between-unit) interference are present. I argue that researchers can construct theory-driven “spillover mapping” to aggregate each unit’s influence on the others into meaningful quantities. Essentially, these quantities describe the expected difference brought forth by the change of treatment assignment history at a representative unit on itself or its neighbors within a particular time period.

I then show that these estimands can be non-parametrically identified and unbiasedly estimated via a group of IPTW estimators under the assumption of sequential ignorability, which requires that the propensity score of each observation can be fully predicted by the history. Estimation proceeds by first predicting the propensity scores via statistical models or covariate balancing techniques (Imai and Ratkovic, 2015; Kallus and Santacatterina, 2018), and then plugging the predicted values into a Horvitz-Thompson/Hajek estimator with the spillover mapping’s value as the outcome. The estimator can be augmented by employing a diffusion model that predicts the outcome values with a higher accuracy.

I exploit Stein’s method to prove that the proposed estimators are consistent and asymptotically normal when the maximal degree of interference dependence in the sample does not increase too fast with the sample size (Stein et al., 1972; Ogburn et al. 2020). Valid confidence intervals could be obtained either analytically or via Fisher’s randomization test (FRT). The analytic variance estimate is shown to be asymptotically equivalent to the spatial HAC variance (Conley, 1999).

If unobservable attributes, or “fixed effects” exist, however, the introduced estimands are identifiable only under very strong (and often implausible) assumptions on the homogeneity of treatment effects. In addition, classic approaches such difference-in-differences or fixed effects models are inconsistent in this scenario. They converge to a weighted average of individualistic causal quantities which has no substantive meaning. But when the fixed effects vary continuously over the geography of interest, researchers may eliminate their influence by combining the IPTW estimators with a propensity score model that includes a smooth function of the geographic coordinates of the units.

The proposed method works well in both simulation and real-world examples. I apply it to re-analyze two empirical studies. The first one is Wang and Wong (2019), in which the authors investigate the impact of Hong Kong’s 2014 Umbrella Movement on the opposition’s vote share in the ensuing election. Under weaker assumptions, the result confirms the authors’ original conclusion that the protest reduced the opposition’s vote share in constituencies that were close to the protest sites. The second study is Sances (2016), an examination of how the change of selection mechanism reshapes the incentives of real estate assessors in New York State. The estimates of effects caused by temporal interference are consistent with the original findings, but I am able to show that the estimates are unlikely to be contaminated by spatial interference.

In summary, the paper extends the idea in Aronow, Samii and Wang (2020) to TSCS data and considers causal identification under both the assumption of sequential ignorability (Robins, Hernan and Brumback, 2000; Blackwell, 2013; Papadogeorgou et al., 2020) and the assumption of strict exogeneity (Xu, 2017; Imai and Kim, 2018; Strezhnev, 2018; Liu, Wang and Xu, 2020). It builds up a bridge between the two different fields in political methodology and offers instructions to practitioners when interference is serious concern in TSCS data analysis.

Author

• Ye Wang, New York University