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Adapting to Misspecification

Author

Listed:
  • Timothy B. Armstrong
  • Patrick Kline
  • Liyang Sun

Abstract

Empirical research typically involves a robustness‐efficiency tradeoff. A researcher seeking to estimate a scalar parameter can invoke strong assumptions to motivate a restricted estimator that is precise but may be heavily biased, or they can relax some of these assumptions to motivate a more robust, but variable, unrestricted estimator. When a bound on the bias of the restricted estimator is available, it is optimal to shrink the unrestricted estimator towards the restricted estimator. For settings where a bound on the bias of the restricted estimator is unknown, we propose adaptive estimators that minimize the percentage increase in worst‐case risk relative to an oracle that knows the bound. We show that adaptive estimators solve a weighted convex minimax problem and provide lookup tables facilitating their rapid computation. Revisiting some well‐known empirical studies where questions of model specification arise, we examine the advantages of adapting to—rather than testing for—misspecification.

Suggested Citation

  • Timothy B. Armstrong & Patrick Kline & Liyang Sun, 2025. "Adapting to Misspecification," Econometrica, Econometric Society, vol. 93(6), pages 1981-2005, November.
    • Handle: RePEc:wly:emetrp:v:93:y:2025:i:6:p:1981-2005
    DOI: 10.3982/ECTA21991
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    Cited by:

    1. Aristotelis Epanomeritakis & Davide Viviano, 2025. "Learning What to Learn: Experimental Design when Combining Experimental with Observational Evidence," Papers 2510.23434, arXiv.org, revised Dec 2025.
    2. Andr'es Aradillas Fern'andez & Jos'e Blanchet & Jos'e Luis Montiel Olea & Chen Qiu & Jorg Stoye & Lezhi Tan, 2025. "Epsilon-Minimax Solutions of Statistical Decision Problems," Papers 2509.08107, arXiv.org, revised Jan 2026.
    3. Judite Gonçalves & Roxanne Merenda & João Pereira dos Santos, 2024. "Not so sweet: impacts of a soda tax on producers," International Tax and Public Finance, Springer;International Institute of Public Finance, vol. 31(5), pages 1388-1412, October.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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