Identification of causal diffusion effects using placebo outcomes under structural stationarity

Social and biomedical scientists have long been interested in the process through which ideas and behaviours diffuse. In this article, we study an urgent social problem, the spatial diffusion of hate crimes against refugees in Germany, which has admitted more than 1 million asylum seekers since the 2015 refugee crisis. Despite its importance, identification of causal diffusion effects, also known as peer and contagion effects, remains challenging because the commonly used assumption of no omitted confounders is often untenable due to contextual confounding and homophily bias. To address this long-standing problem, we examine causal identification using placebo outcomes under a new assumption of structural stationarity, which formalizes the underlying diffusion process with a class of nonparametric structural equation models with recursive structure. We show under structural stationarity that a lagged dependent variable is a general, valid placebo outcome for detecting a wide range of biases, including the 2 types mentioned above. We then propose a difference-in-differences style estimator that can directly correct biases under an additional causal assumption. Analysing fine-grained geo-coded hate crime data from Germany, we show when and how the proposed methods can detect and correct unmeasured confounding in spatial causal diffusion analysis.