Disentangling The Effects of Air Pollution on Social Mobility: A Bayesian Principal Stratification Approach

Principal stratification provides a robust framework for causal inference, enabling the investigation of the causal link between air pollution exposure and social mobility, mediated by the education level. Studying the causal mechanisms through which air pollution affects social mobility is crucial to highlight the role of education as a mediator, and offering evidence that can inform policies aimed at reducing both environmental and educational inequalities for more equitable social outcomes. In this paper, we introduce a novel Bayesian nonparametric model for principal stratification, leveraging the dependent Dirichlet process to flexibly model the distribution of potential outcomes. By incorporating confounders and potential outcomes for the post-treatment variable in the Bayesian mixture model for the final outcome, our approach improves the accuracy of missing data imputation and allows for the characterization of treatment effects. We assess the performance of our method through a simulation study and demonstrate its application in evaluating the principal causal effects of air pollution on social mobility in the United States.