Abstract. The Brazil Bolsa Familia 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 it as a regression discontinuity (RD) design. Following Li et al. (2015) and Branson and Mealli (2019), we formally describe the Bolsa Familia 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. We first discuss the potential advantages of this probabilistic framework in settings where such assumptions are deemed plausible, over local regression methods based on continuity assumptions. The potential advantages concern the causal estimands that can be targeted, the design and the analysis, as well as the interpretation and generalizability of the results.
A critical issue of the probabilistic approach is how to identify 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 Familia 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.
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