Aggregating Distributional Treatment Effects: A Bayesian Hierarchical Analysis of the Microcredit Literature

This paper develops methods to aggregate evidence on distributional treatment effects from multiple studies conducted in different settings, and applies them to the microcredit literature. Several randomized trials of expanding access to microcredit found substantial effects on the tails of household outcome distributions, but the extent to which these findings generalize to future settings was not known. Aggregating the evidence on sets of quantile effects poses additional challenges relative to average effects because distributional effects must imply monotonic quantiles and pass information across quantiles. Using a Bayesian hierarchical framework, I develop new models to aggregate distributional effects and assess their generalizability. For continuous outcome variables, the methodological challenges are addressed by applying transforms to the unknown parameters. For partially discrete variables such as business profits, I use contextual economic knowledge to build tailored parametric aggregation models. I find generalizable evidence that microcredit has negligible impact on the distribution of various household outcomes below the 75th percentile, but above this point there is no generalizable prediction.