Quantiles of the Gain Distribution of an Early Childhood Intervention

We offer a new strategy to identify the distribution of treatment effects using data from the Infant Health and Development Program (IHDP), a relatively understudied early-childhood intervention for low birth-weight infants. We introduce a new policy parameter, QCD, which denotes quantiles of the effect distribution conditional on latent neonatal health. The dependence between potential outcomes originates from a new class of factor models where latent health can affect the location and shape of distributions. We first show that QCD depends on quantiles of marginal outcome distributions given latent health. We then achieve identification of these marginal distributions and QCD by proxying latent health with neonatal anthropometrics and accounting for measurement error in these proxies. The effects of enrolling in IHDP are widely distributed across children and depend on neonatal health. Moreover, the large average effects documented in past work for close to normal birth weight children from low-income families are driven by a minority of children in this group.