Working Paper: NBER ID: w25456
Authors: Isaiah Andrews; Toru Kitagawa; Adam McCloskey
Abstract: Many empirical questions concern target parameters selected through optimization. For example, researchers may be interested in the effectiveness of the best policy found in a randomized trial, or the best-performing investment strategy based on historical data. Such settings give rise to a winner’s curse, where conventional estimates are biased and conventional confidence intervals are unreliable. This paper develops optimal confidence intervals and median-unbiased estimators that are valid conditional on the target selected and so overcome this winner’s curse. If one requires validity only on average over targets that might have been selected, we develop hybrid procedures that combine conditional and projection confidence intervals to offer further performance gains relative to existing alternatives.
Keywords: winners curse; confidence intervals; median unbiased estimators
JEL Codes: C12; C13
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| Corrections (K14) | Reduce bias and improve coverage (C83) |
| Conventional estimates for the average effect of the best-performing treatment (C51) | Bias upwards due to the winners curse (D44) |
| Conventional methods (C60) | Understate uncertainty in confidence intervals (C46) |
| Optimal median-unbiased estimators and confidence intervals (C51) | Eliminate bias (C90) |
| Hybrid procedures (C60) | Offer shorter confidence intervals while maintaining valid coverage (C46) |