# A Bayesian hierarchical framework to evaluate policy effects through quasi-experimental designs

## Introduction

This research programme aims to provide a methodological framework to draw causal inference for longitudinal data, accounting for their hierarchical nature, the existence of time series components and the use of NOCs. In particular through a Bayesian framework:

- We will account for the hierarchical nature of the data (in space, such as for electoral wards and/or across organisational units such as schools/universities), which is a key characteristic in many social and epidemiological applications. The flexibility of the approach will allow to incorporate trends deviating from linearity (for instance polynomial or splines) and, in line with existing literature, we will use variable selection techniques such as spike-and-slabs to build a parsimonious regression model for the outcome.

- We will further develop the idea of NOC when they are on a different scales from the treatment series. This avenue of research has not been fully explored and to our knowledge never in the context of Bayesian models. Given the importance of control series for causal inference post-intervention, this will be a useful advancement in the field.

- Through an extensive simulation study, we will be able to evaluate how the different approaches perform to evaluate the effect of interventions, providing a formal comparison, which has never been attempted~before. Specifically, we will be able to determine how sensitive results are to the amount of data available e.g. to answer questions such as: how little information is needed to say something useful under different initial conditions?