We formalize the optimal design of experiments when there is interference between units, that is, an individual’s outcome depends on the outcomes of others in her group. We focus on randomized saturation designs, two-stage experiments that first randomize treatment saturation of a group, then individual treatment assignment. We map the potential outcomes framework with partial interference to a regression model with clustered errors, calculate standard errors of randomized saturation designs, and derive analytical insights about the optimal design. We show that the power to detect average treatment effects declines precisely with the ability to identify novel treatment and spillover effects.

Health and income are strongly correlated both within and across countries, yet the extent to which improvements in income have a causal effect on health status remains controversial. We investigate whether short-term fluctuations in aggregate income affect infant mortality using an unusually large data set of 1.7 million births in 59 developing countries. We show a large, negative association between per capita GDP and infant mortality. Female infant mortality is more sensitive than male infant mortality to negative economic shocks, suggesting that policies that protect the health status of female infants may be especially important during economic downturns.