Finite Population Identification and Design-Based Sensitivity Analysis

We develop an approach to sensitivity analysis that uses design distributions to calibrate sensitivity parameters in a finite population model. We use this approach to (1) give a new formal analysis of the role of randomization, (2) provide a new motivation for examining covariate balance, and (3) show how to construct design-based confidence intervals for the average treatment effect, which allow for heterogeneous treatment effects but do not rely on asymptotics. This approach to confidence interval construction relies on partial identification analysis rather than hypothesis test inversion. Moreover, these intervals also have a non-frequentist, identification-based interpretation. We illustrate our approach in three empirical applications.