Confidence intervals for intentionally biased estimators

David Kaplan and Xin Liu

Econometric Reviews, 2024, vol. 43, issue 2-4, 197-214

Abstract: We propose and study three confidence intervals (CIs) centered at an estimator that is intentionally biased to reduce mean squared error. The first CI simply uses an unbiased estimator’s standard error; compared to centering at the unbiased estimator, this CI has higher coverage probability for confidence levels above 91. 7%, even if the biased and unbiased estimators have equal mean squared error. The second CI trades some of this “excess” coverage for shorter length. The third CI is centered at a convex combination of the two estimators to further reduce length. Practically, these CIs apply broadly and are simple to compute.

Date: 2024
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Related works:
Working Paper: Confidence intervals for intentionally biased estimators (2025)
Working Paper: Confidence Intervals for Intentionally Biased Estimators (2023)
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DOI: 10.1080/07474938.2024.2312288

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