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Design-based identification with formula instruments: a review

Author

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  • Kirill Borusyak
  • Peter Hull
  • Xavier Jaravel

Abstract

SummaryMany studies in economics use instruments or treatments that combine a set of exogenous shocks with other predetermined variables via a known formula. Examples include shift-share instruments and measures of social or spatial spillovers. We review recent econometric tools for this setting, which leverage the assignment process of the exogenous shocks and the structure of the formula for identification. We compare this design-based approach with conventional estimation strategies based on conditional unconfoundedness, and contrast it with alternative strategies that leverage a model for unobservables.

Suggested Citation

  • Kirill Borusyak & Peter Hull & Xavier Jaravel, 2025. "Design-based identification with formula instruments: a review," The Econometrics Journal, Royal Economic Society, vol. 28(1), pages 83-108.
    • Handle: RePEc:oup:emjrnl:v:28:y:2025:i:1:p:83-108.
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    File URL: http://hdl.handle.net/10.1093/ectj/utae003
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    2. Gørtz, Mette & Sander, Sarah & Sevilla, Almudena, 2025. "Does the child penalty strike twice?," European Economic Review, Elsevier, vol. 172(C).
    3. David Autor & David Dorn & Gordon Hanson & Maggie R. Jones & Bradley Setzler, 2024. "Places versus People: The Ins and Outs of Labor Market Adjustment to Globalization," Working Papers 24-78, Center for Economic Studies, U.S. Census Bureau.
    4. Ablam Estel Apeti & Kwamivi Mawuli Gomado, 2025. "International monetary fund conditionality and structural reforms: Evidence from developing countries," Economics of Transition and Institutional Change, John Wiley & Sons, vol. 33(2), pages 439-486, April.
    5. Yoshifumi Konishi & Akari Ono, 2024. "Do Winners Win More from Transport Megaprojects? Evidence from the Great Seto Bridge in Japan," Keio-IES Discussion Paper Series 2024-018, Institute for Economics Studies, Keio University.
    6. Ulrich B. Morawetz & H. Allen Klaiber, 2025. "Regression analysis with independent variables in shares: a guide and an empirical example," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 52(1), pages 63-98, February.
    7. Jiemiao Dong & Zhuangxiong Yu & Xunpeng Shi & Yang Yang, 2024. "Industrial Policy, Product Switching, and Export Performance," China & World Economy, Institute of World Economics and Politics, Chinese Academy of Social Sciences, vol. 32(1), pages 167-196, January.
    8. Bastien Alvarez & Gianluca Orefice & Farid Toubal, 2025. "Trade Liberalization and Working Conditions," CESifo Working Paper Series 11675, CESifo.
    9. Ablam Estel Apeti & Kwamivi Mawuli Gomado, 2024. "International monetary fund conditionality and structural reforms: Evidence from developing countries," Post-Print hal-04723871, HAL.
    10. Kieran Marray, 2024. "Estimating Spillovers from Sampled Connections," Papers 2410.17154, arXiv.org, revised Sep 2025.

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    Keywords

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    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

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