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

Area of Science:

• Statistics
• Econometrics
• Causal Inference

Background:

• Randomized controlled trials (RCTs) and observational studies are key empirical methods.
• Estimating average treatment effects requires assumptions like ignorability and positivity.
• Propensity scores play a crucial role in causal inference.

Purpose of the Study:

• To clarify the properties of estimators for bounded potential outcomes under ignorability and positivity.
• To differentiate estimation challenges between randomized experiments and observational studies.
• To highlight the necessity of untestable assumptions in observational causal inference.

Main Methods:

• Theoretical analysis of uniformly root-n consistent and asymptotically normal estimators.
• Examination of finite-sample valid confidence intervals and their width shrinkage rates.
• Investigation of conditions for uniform consistency and honest large-sample confidence intervals.

Main Results:

• In RCTs with known propensity scores, simple estimators are uniformly root-n consistent with valid confidence intervals.
• In observational studies with unknown propensity scores, uniform consistency and honest confidence intervals are unattainable without additional assumptions.
• Untestable assumptions on propensity score or conditional outcome functions are required for observational studies.

Conclusions:

• The presence or absence of a known propensity score fundamentally alters the statistical guarantees of causal effect estimation.
• Randomized experiments offer stronger theoretical properties for estimating average treatment effects.
• Practitioners must be aware of the limitations and required assumptions when using observational data for causal inference.