Rejoinder: Nonparametric identification is not enough, but randomized controlled trials are

We thank the editor for organizing a diverse and wide-ranging discussion, and we thank the commentators for their detailed and thoughtful remarks. Most of the commentators provide broader perspectives on randomized experiments and their role in modern empirical practice. We believe this broader perspective is important, and the comments serve as complements to the somewhat narrow points we made in our paper. However, we believe these narrow points are of great consequence, and we find it useful to briefly recapitulate them here. When a practitioner aims to estimate averages of bounded potential outcomes (e.g., the average treatment effect on a binary outcome) in a setting where both ignorability and positivity are known to hold after adjusting for at least one continuous covariate, the following statements are true: • If the propensity score is known, such as in a randomized controlled trial (RCT), there exist simple estimators that are uniformly root-n consistent and asymptotically normal. Confidence intervals based on these estimators are finite-sample valid and their widths shrink at a root-n rate. • If the propensity score is not known, such as in an observational study, there exist neither uniformly consistent estimators nor uniform (i.e., honest) large-sample confidence intervals whose widths are shrinking with the sample size. To achieve these properties, the practitioner must impose untestable assumptions on either the propensity score function or the conditional expectation function of the outcomes.