Selecting subpopulations for causal inference in regression discontinuity designs

The Brazil Bolsa Família program is a conditional cash transfer program aimed to reduce short-term poverty by direct cash transfers and to fight long-term poverty by increasing human capital among Brazilian households with low income. Eligibility for Bolsa Família benefits depends on a cutoff rule, which classifies it as a regression discontinuity (RD) design. Following Li, Mattei and Mealli (2015) and Branson and Mealli (2019), we formally describe the Bolsa Família RD design as a local regular design (Imbens and Rubin (2015)) within the potential outcome approach. Under this framework, causal effects can be identified and estimated on an unknown but well-defined subpopulation where the following RD assumptions hold: a local overlap assumption, a local SUTVA, and a local ignorability (unconfoundedness) assumption. The potential advantages of this probabilistic framework over local regression methods based on continuity assumptions concern the causal estimands that can be targeted, the design and the analysis as well as the interpretation and generalizability of the results. For the identification of the subpopulation for which we can draw valid causal inference, we propose to use a Bayesian model-based finite mixture approach to clustering to probabilistically classify observations into subpopulations where the RD assumptions hold and do not hold on the basis of the observed data. This approach: (a) allows to account for the uncertainty in the subpopulation membership, which is typically neglected, (b) does not impose any constraint on the shape of the subpopulation, (c) allows to target alternative causal estimands than the average treatment effects (ATEs), and (d) is robust to a certain degree of manipulation/selection of the forcing variable. We apply our proposed approach to assess causal effects of the Bolsa Família program on leprosy incidence in 2009 for Brazilian households who registered in the Brazilian National Registry for Social Programs in 2007–2008 for the first time. We find evidence that being eligible for the program reduces the risk of leprosy.