Selecting Subpopulations for Causal Inference in Regression Discontinuity Designs

The Brazil Bolsa Familia (BF) 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 poor Brazilian people. Eligibility for Bolsa Familia benefits depends on a cutoff rule, which classifies the BF study as a regression discontinuity (RD) design. Extracting causal information from RD studies is challenging. Following Li et al (2015) and Branson and Mealli (2019), we formally describe the BF RD design as a local randomized experiment within the potential outcome approach. Under this framework, causal effects can be identified and estimated on a subpopulation where a local overlap assumption, a local SUTVA and a local ignorability assumption hold. Potential advantages of this framework over local regression methods based on continuity assumptions concern the causal estimands, the analysis, and the interpretation of the results. A critical issue of this local randomization approach is how to choose subpopulations for which we can draw valid causal inference. We propose a Bayesian model-based finite mixture approach to clustering to classify observations into subpopulations where the RD assumptions hold and do not hold. This approach has important advantages: a) it allows to account for the uncertainty in the subpopulation membership, which is typically neglected; b) it does not impose any constraint on the shape of the subpopulation; c) it is scalable to high-dimensional settings; e) it allows to target alternative causal estimands than average effects; and f) it is robust to a certain degree of manipulation/selection of the running variable. We apply our proposed approach to assess causal effects of the BF 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