DP14721 Quantiles of the Gain Distribution of an Early Child Intervention
We offer a new strategy to identify the distribution of treatment effects using the Infant Health and Development Program (IHDP), a relatively understudied intervention for low birth-weight infants. We introduce a new policy parameter, QCD, denoting 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 show that QCD depends on the marginal distributions of potential outcomes given latent health and achieve identification of these distributions by proxying latent health with neonatal anthropometrics and accounting for measurement error in the proxies. The effects of 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.