When should we use hierarchical model for causal inference? This question has bothered me for years. Thanks to this technical report (http://www.stat.columbia.edu/~gelman/research/published/HierarchicalCausal.pdf) by Avi Feller and Andrew Gelman, this question became less mysterious to me.

According to their explanantion, the hierarchical model can aid causal inference when dealing with the following problems

• Accouting for data collection: we need to account for any individual of group charateristics that are predictive of treatment assignment or group characteristics that are predictive of treatment assignment and inclusion in the dataset.
• Adjusting for unmeasured covariates: In observation studies, it is necessary to adjust for differences between treated and control items.
• Modeling variation in treatment effects: sometimes we are not only interested in the average treatment effect but also in how the effect varies across the population.