A Hierarchical Bayesian Structural Time Series model for inferring causal impact of policy implantation on mental health

The Bayesian Structural Times Series (BSTS) model has been adopted to evaluate the causal effects of policy implementations. The framework integrates the synthetic controls method to forecast the counterfactual time series and employs a spike-and-slab prior for variable selection, which requires users to specify the expected number of variables to include. However, eliciting this number from prior knowledge is usually hard. Moreover, the model can only be applied to a single treated unit. To address these limitations, we propose a hierarchical BSTS. This framework is flexible to account for individual-level variance and is more robust to misspecification of the expected number of variables. We apply this model to evaluate the impact of the Immigration Act established by the UK government in 2014 on the mental wellbeing of ethnic minorities.