Policy evaluation using a hierarchical Bayesian structural time series model

Individual-level time series data, such as longitudinal survey data, are increasingly used for policy evaluation. To infer the impact of a policy given such data, we propose a hierarchical Bayesian structural time series (HBSTS) model that extends the existing Bayesian structural time series model. Hierarchical Bayesian structural time series can accommodate multiple observations per time point by adding an extra layer to capture individual-level variation. It also uses a regularized horseshoe prior with a signal-adaptive variable selection algorithm. These extensions provide a more flexible and realistic framework for policy evaluation, and make inference less sensitive to the prior specification of the expected model size (i.e. the expected number of covariates included in the model that are predictive of outcomes). In simulation studies, HBSTS demonstrated greater robustness to misspecification of the expected model size and was more powerful in detecting putative intervention effects compared with BSTS. We apply our model to the UK Household Longitudinal Study to investigate the impact of a UK immigration policy reform. Our findings indicated that the policy led to psychological distress among individuals from Black Caribbean backgrounds, which was also observed in an earlier Bayesian interrupted time series analysis, though derived by comparing them with people from White backgrounds.