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Emission control technologies installed on power plants are a key feature ofmany air pollution regulations in the US. While such regulations are predicatedon the presumed relationships between emissions, ambient air pollution, andhuman health, many of these relationships have never been empirically verified.The goal of this paper is to develop new statistical methods to quantify theserelationships. We frame this problem as one of mediation analysis to evaluatethe extent to which the effect of a particular control technology on ambientpollution is mediated through causal effects on power plant emissions. Sincepower plants emit various compounds that contribute to ambient pollution, wedevelop new methods for multiple intermediate variables that are measuredcontemporaneously, may interact with one another, and may exhibit jointmediating effects. Specifically, we propose new methods leveraging two relatedframeworks for causal inference in the presence of mediating variables:principal stratification and causal mediation analysis. We define principaleffects based on multiple mediators, and also introduce a new decomposition ofthe total effect of an intervention on ambient pollution into the naturaldirect effect and natural indirect effects for all combinations of mediators.Both approaches are anchored to the same observed-data models, which we specifywith Bayesian nonparametric techniques. We provide assumptions for estimatingprincipal causal effects, then augment these with an additional assumptionrequired for causal mediation analysis. The two analyses, interpreted intandem, provide the first empirical investigation of the presumed causalpathways that motivate important air quality regulatory policies.

Bayesian Methods for Multiple Mediators: Relating Principal Stratification and Causal Mediation in the Analysis of Power Plant Emission Controls