Finite Population Identification and Design-Based Sensitivity Analysis

We develop a new approach for quantifying uncertainty in finite populations, by using design distributions to calibrate sensitivity parameters in finite population identified sets. This yields uncertainty intervals that can be interpreted as identified sets, Bayesian credible sets, or frequentist design-based confidence sets. We focus on quantifying uncertainty about the average treatment effect (ATE) due to missing potential outcomes in a randomized experiment, where our approach (1) yields design-based confidence intervals for ATE which allow for heterogeneous treatment effects but do not rely on asymptotics, (2) provides a new motivation for examining covariate balance, and (3) gives a new formal analysis of the role of randomized treatment assignment. We illustrate our approach in three empirical applications.