Causal inference for observational studies extended to a multilevel setting. The impact of fertility on poverty in Vietnam

This work addresses some statistical issues arising in studies of causal inference with observational hierarchical data with an application on the estimation of the effect of fertility on poverty using Vietnamese data. I first contrast matching and instrumental variables methods stressing the fact that their validity relies on the plausibility of the underlying assumptions; which in turn depend on the available data. In the application, the multilevel dimension introduces statistical complications and stimulates interesting research questions. From a methodological point of view, I identify and discuss some issues that are not tied to the considered application but have a general relevance: the role of clusters in the assignment mechanism and the potential violation of SUTVA. I propos combinations of matching methods and multilevel modelling techniques and a weaker version of the SUTVA assumption. I find a negative and substantial effect of fertility on wellbeing; this effect is stronger in high-level fertility communities