these groups are often not included in the documentation of offline hate crimes. @davidson2017automated further discuss challenges in distinguishing between hate speech and other types of offensive speech.

[**Observational methods applied to social data.** ]{} Recent studies show that quasi-causal methods can be applied to social media data to e.g., distill the outcomes of a given situation [@olteanu2017distilling], measure the impact of an intervention [@chandrasekharan2018you], or estimate the effect of online social support [@cunha2017warm]. The application of these methods to social data, including propensity score matching [@de2016discovering], difference-in-differences [@chandrasekharan2018you], and instrumental variables [@zhang2016understanding], was found to reduce confounding biases.

@chandrasekharan2018you’s work is closest to ours, as it employs techniques from the causal inference literature to quantify the impact of an intervention on hateful behavior on Reddit. Yet, the intervention they study is platform-specific–a ban on an existing community on Reddit–whereas we look at the impact of external (non-platform specific) events on both Reddit and Twitter. Our focus is on the overall prevalence of hate speech, rather than on the behavior of given groups of users, and we measure the effect of given interventions (events) on various types of hate speech (§\[sec:characterizing\]).

[**Operationalization of hate speech on social media.** ]{} \[subsec:hate-operationalization\] 