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How to Use Economic Theory to Improve Estimators: Shrinking Toward Theoretical Restrictions

Author

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  • Pirmin Fessler

    (Foreign Research Division, Oesterreichische Nationalbank)

  • Maximilian Kasy

    (Harvard University)

Abstract

We propose to use economic theories to construct shrinkage estimators that perform well when the theories' empirical implications are approximately correct but perform no worse than unrestricted estimators when the theories' implications do not hold. We implement this construction in various settings, including labor demand and wage inequality, and estimation of consumer demand. We provide asymptotic and finite sample characterizations of the behavior of the proposed estimators. Our approach is an alternative to the use of theory as something to be tested or to be imposed on estimates. Our approach complements uses of theory for identification and extrapolation.

Suggested Citation

  • Pirmin Fessler & Maximilian Kasy, 2019. "How to Use Economic Theory to Improve Estimators: Shrinking Toward Theoretical Restrictions," The Review of Economics and Statistics, MIT Press, vol. 101(4), pages 681-698, October.
    • Handle: RePEc:tpr:restat:v:101:y:2019:i:4:p:681-698
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    2. Loria, Francesca & Matthes, Christian & Wang, Mu-Chun, 2022. "Economic theories and macroeconomic reality," Journal of Monetary Economics, Elsevier, vol. 126(C), pages 105-117.
    3. Adam N. Smith & Jim E. Griffin, 2023. "Shrinkage priors for high-dimensional demand estimation," Quantitative Marketing and Economics (QME), Springer, vol. 21(1), pages 95-146, March.
    4. Ho, Paul, 2023. "Global robust Bayesian analysis in large models," Journal of Econometrics, Elsevier, vol. 235(2), pages 608-642.
    5. Jiaming Mao & Zhesheng Zheng, 2020. "Structural Regularization," Papers 2004.12601, arXiv.org, revised Jun 2020.
    6. Jiaming Mao & Jingzhi Xu, 2020. "Ensemble Learning with Statistical and Structural Models," Papers 2006.05308, arXiv.org.
    7. Ruoyao Shi, 2021. "An Averaging Estimator for Two Step M Estimation in Semiparametric Models," Working Papers 202105, University of California at Riverside, Department of Economics.
    8. Roy Allen & John Rehbeck, 2020. "Counterfactual and Welfare Analysis with an Approximate Model," Papers 2009.03379, arXiv.org.
    9. Maes, Sebastiaan & Malhotra, Raghav, 2024. "Beyond the Mean : Testing Consumer Rationality through Higher Moments of Demand," CRETA Online Discussion Paper Series 85, Centre for Research in Economic Theory and its Applications CRETA.
    10. Edvard Bakhitov, 2020. "Frequentist Shrinkage under Inequality Constraints," Papers 2001.10586, arXiv.org.

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