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Design-based identification with formula instruments: a review

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  • Borusyak, Kirill
  • Hull, Peter
  • Jaravel, Xavier

Abstract

Many 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

  • Borusyak, Kirill & Hull, Peter & Jaravel, Xavier, 2024. "Design-based identification with formula instruments: a review," LSE Research Online Documents on Economics 123848, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:123848
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    2. David H. Autor & David Dorn & Gordon Hanson & Maggie R. Jones & Bradley Setzler, 2025. "Places versus People: The Ins and Outs of Labor Market Adjustment to Globalization," Opportunity and Inclusive Growth Institute Working Papers 112, Federal Reserve Bank of Minneapolis.
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    5. 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.
    6. Ablam Estel Apeti & Kwamivi Mawuli Gomado, 2024. "International monetary fund conditionality and structural reforms: Evidence from developing countries," Post-Print hal-04723871, HAL.
    7. 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.
    8. Kieran Marray, 2024. "Estimating Spillovers from Sampled Connections," Papers 2410.17154, arXiv.org.

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    More about this item

    Keywords

    formula instruments; shift-share instruments; network spillovers; design-based identification;
    All these keywords.

    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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