IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/123848.html
   My bibliography  Save this paper

Design-based identification with formula instruments: a review

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/123848/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Vasco M Carvalho & Makoto Nirei & Yukiko U Saito & Alireza Tahbaz-Salehi, 2021. "Supply Chain Disruptions: Evidence from the Great East Japan Earthquake," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 136(2), pages 1255-1321.
    2. Berman, Nicolas & Berthou, Antoine & Héricourt, Jérôme, 2015. "Export dynamics and sales at home," Journal of International Economics, Elsevier, vol. 96(2), pages 298-310.
    3. Victor Chernozhukov & Denis Chetverikov & Mert Demirer & Esther Duflo & Christian Hansen & Whitney Newey & James Robins, 2018. "Double/debiased machine learning for treatment and structural parameters," Econometrics Journal, Royal Economic Society, vol. 21(1), pages 1-68, February.
    4. Clément de Chaisemartin & Xavier D'Haultfœuille, 2020. "Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects," American Economic Review, American Economic Association, vol. 110(9), pages 2964-2996, September.
    5. David Card, 1989. "The Impact of the Mariel Boatlift on the Miami Labor Market," Working Papers 633, Princeton University, Department of Economics, Industrial Relations Section..
    6. Philippe Aghion & Céline Antonin & Simon Bunel & Xavier Jaravel, 2022. "Modern manufacturing capital, labor demand, and product market dynamics: Evidence from France," SciencePo Working papers Main hal-03943312, HAL.
    7. Janet Currie & Jonathan Gruber, 1996. "Health Insurance Eligibility, Utilization of Medical Care, and Child Health," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 111(2), pages 431-466.
    8. Kirill Borusyak & Peter Hull & Xavier Jaravel, 2022. "Quasi-Experimental Shift-Share Research Designs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(1), pages 181-213.
    9. Stephen Coussens & Jann Spiess, 2021. "Improving Inference from Simple Instruments through Compliance Estimation," Papers 2108.03726, arXiv.org.
    10. Paul Goldsmith-Pinkham & Guido W. Imbens, 2013. "Social Networks and the Identification of Peer Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 253-264, July.
    11. David Card, 2009. "Immigration and Inequality," American Economic Review, American Economic Association, vol. 99(2), pages 1-21, May.
    12. Albert Saiz, 2010. "The Geographic Determinants of Housing Supply," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 125(3), pages 1253-1296.
    13. Machin, Stephen & Costa, Rui & Dhingra, Swati, 2019. "Trade and Worker Deskilling," CEPR Discussion Papers 13768, C.E.P.R. Discussion Papers.
    14. Clément de Chaisemartin & Luc Behaghel, 2020. "Estimating the Effect of Treatments Allocated by Randomized Waiting Lists," Econometrica, Econometric Society, vol. 88(4), pages 1453-1477, July.
    15. Ezra Oberfield & Devesh Raval, 2021. "Micro Data and Macro Technology," Econometrica, Econometric Society, vol. 89(2), pages 703-732, March.
    16. David Card, 1990. "The Impact of the Mariel Boatlift on the Miami Labor Market," ILR Review, Cornell University, ILR School, vol. 43(2), pages 245-257, January.
    17. Timothy J. Bartik, 1991. "Who Benefits from State and Local Economic Development Policies?," Books from Upjohn Press, W.E. Upjohn Institute for Employment Research, number wbsle.
    18. Michael Greenstone & Alexandre Mas & Hoai -Luu Nguyen, 2014. "Do Credit Market Shocks affect the Real Economy? Quasi-Experimental Evidence from the Great Recession and "Normal" Economic Times," Working Papers 584, Princeton University, Department of Economics, Industrial Relations Section..
    19. David Hummels & Rasmus J?rgensen & Jakob Munch & Chong Xiang, 2014. "The Wage Effects of Offshoring: Evidence from Danish Matched Worker-Firm Data," American Economic Review, American Economic Association, vol. 104(6), pages 1597-1629, June.
    20. Imbens, Guido W & Angrist, Joshua D, 1994. "Identification and Estimation of Local Average Treatment Effects," Econometrica, Econometric Society, vol. 62(2), pages 467-475, March.
    21. Rodrigo Ad~ao & Michal Koles'ar & Eduardo Morales, 2018. "Shift-Share Designs: Theory and Inference," Papers 1806.07928, arXiv.org, revised Aug 2019.
    22. Emi Nakamura & J?n Steinsson, 2014. "Fiscal Stimulus in a Monetary Union: Evidence from US Regions," American Economic Review, American Economic Association, vol. 104(3), pages 753-792, March.
    23. Basso, Gaetano & Peri, Giovanni, 2015. "The Association between Immigration and Labor Market Outcomes in the United States," IZA Discussion Papers 9436, Institute of Labor Economics (IZA).
    24. David H. Autor & David Dorn & Gordon H. Hanson, 2013. "The China Syndrome: Local Labor Market Effects of Import Competition in the United States," American Economic Review, American Economic Association, vol. 103(6), pages 2121-2168, October.
    25. Kirill Borusyak & Xavier Jaravel & Jann Spiess, 2024. "Revisiting Event-Study Designs: Robust and Efficient Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 91(6), pages 3253-3285.
    26. Paul Goldsmith-Pinkham & Peter Hull & Michal Kolesár, 2022. "Contamination Bias in Linear Regressions," Working Papers 2022-15, Princeton University. Economics Department..
    27. Kirill Borusyak & Peter Hull, 2023. "Nonrandom Exposure to Exogenous Shocks," Econometrica, Econometric Society, vol. 91(6), pages 2155-2185, November.
    28. Paul Goldsmith-Pinkham & Peter Hull & Michal Kolesár, 2024. "Contamination Bias in Linear Regressions," American Economic Review, American Economic Association, vol. 114(12), pages 4015-4051, December.
    29. Guido W. Imbens & Paul R. Rosenbaum, 2005. "Robust, accurate confidence intervals with a weak instrument: quarter of birth and education," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 168(1), pages 109-126, January.
    30. Edward Miguel & Michael Kremer, 2004. "Worms: Identifying Impacts on Education and Health in the Presence of Treatment Externalities," Econometrica, Econometric Society, vol. 72(1), pages 159-217, January.
    31. Rodrigo Adão & Michal Kolesár & Eduardo Morales, 2019. "Shift-Share Designs: Theory and Inference," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 134(4), pages 1949-2010.
    32. Giovanni Peri & Kevin Shih & Chad Sparber, 2016. "STEM Workers, H-1B Visas, and Productivity in US Cities," World Scientific Book Chapters, in: The Economics of International Migration, chapter 9, pages 277-307, World Scientific Publishing Co. Pte. Ltd..
    33. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-596, May.
    34. Bhuller, Manudeep & Sigstad, Henrik, 2024. "2SLS with multiple treatments," Journal of Econometrics, Elsevier, vol. 242(1).
    35. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    36. Nathan Nunn & Nancy Qian, 2014. "US Food Aid and Civil Conflict," American Economic Review, American Economic Association, vol. 104(6), pages 1630-1666, June.
    37. Rebecca Diamond, 2016. "The Determinants and Welfare Implications of US Workers' Diverging Location Choices by Skill: 1980-2000," American Economic Review, American Economic Association, vol. 106(3), pages 479-524, March.
    38. Newey, Whitney K, 1990. "Efficient Instrumental Variables Estimation of Nonlinear Models," Econometrica, Econometric Society, vol. 58(4), pages 809-837, July.
    39. Chenzi Xu, 2022. "Reshaping Global Trade: The Immediate and Long-Run Effects of Bank Failures [“Shift-Share Designs: Theory and Inference,”]," The Quarterly Journal of Economics, Oxford University Press, vol. 137(4), pages 2107-2161.
    40. Michael Greenstone & Alexandre Mas & Hoai-Luu Nguyen, 2020. "Do Credit Market Shocks Affect the Real Economy? Quasi-experimental Evidence from the Great Recession and "Normal" Economic Times," American Economic Journal: Economic Policy, American Economic Association, vol. 12(1), pages 200-225, February.
    41. Lee, David S., 2008. "Randomized experiments from non-random selection in U.S. House elections," Journal of Econometrics, Elsevier, vol. 142(2), pages 675-697, February.
    42. Chamberlain, Gary, 1987. "Asymptotic efficiency in estimation with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 34(3), pages 305-334, March.
    43. Jonathan Roth & Pedro H. C. Sant'Anna, 2023. "When Is Parallel Trends Sensitive to Functional Form?," Econometrica, Econometric Society, vol. 91(2), pages 737-747, March.
    44. Leah Boustan & Fernando Ferreira & Hernan Winkler & Eric M. Zolt, 2013. "The Effect of Rising Income Inequality on Taxation and Public Expenditures: Evidence from U.S. Municipalities and School Districts, 1970–2000," The Review of Economics and Statistics, MIT Press, vol. 95(4), pages 1291-1302, October.
    45. Xavier Jaravel, 2019. "The Unequal Gains from Product Innovations: Evidence from the U.S. Retail Sector," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 134(2), pages 715-783.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    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. Gørtz, Mette & Sander, Sarah & Sevilla, Almudena, 2025. "Does the child penalty strike twice?," LSE Research Online Documents on Economics 126874, London School of Economics and Political Science, LSE Library.
    5. Bastien Alvarez & Gianluca Orefice & Farid Toubal, 2025. "Trade Liberalization and Working Conditions," CESifo Working Paper Series 11675, CESifo.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kirill Borusyak & Peter Hull & Xavier Jaravel, 2022. "Quasi-Experimental Shift-Share Research Designs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 89(1), pages 181-213.
    2. Kirill Borusyak & Peter Hull, 2020. "Non-Random Exposure to Exogenous Shocks: Theory and Applications," Working Papers 2020-130, Becker Friedman Institute for Research In Economics.
    3. repec:wbk:wbrwps:10250 is not listed on IDEAS
    4. David McKenzie & Dean Yang, 2024. "Field and natural experiments in migration," Chapters, in: William L. Allen & Carlos Vargas-Silva (ed.), Handbook of Research Methods in Migration, chapter 4, pages 48-82, Edward Elgar Publishing.
    5. Peter Hull & Michal Kolesár & Christopher Walters, 2022. "Labor by design: contributions of David Card, Joshua Angrist, and Guido Imbens," Scandinavian Journal of Economics, Wiley Blackwell, vol. 124(3), pages 603-645, July.
    6. Daniel A. Broxterman & William D. Larson, 2020. "An empirical examination of shift‐share instruments," Journal of Regional Science, Wiley Blackwell, vol. 60(4), pages 677-711, September.
    7. Committee, Nobel Prize, 2021. "Answering causal questions using observational data," Nobel Prize in Economics documents 2021-2, Nobel Prize Committee.
    8. Costa, Rui & Dhingra, Swati & Machin, Stephen, 2024. "New dawn fades: Trade, labour and the Brexit exchange rate depreciation," Journal of International Economics, Elsevier, vol. 152(C).
    9. Emilio Gutierrez & David Jaume & Martín Tobal, 2023. "Do Credit Supply Shocks Affect Employment in Middle-Income Countries?," American Economic Journal: Economic Policy, American Economic Association, vol. 15(4), pages 1-36, November.
    10. Elliott Ash & Massimo Morelli & Matia Vannoni, 2022. "More Laws, More Growth? Evidence from U.S. States," BAFFI CAREFIN Working Papers 22178, BAFFI CAREFIN, Centre for Applied Research on International Markets Banking Finance and Regulation, Universita' Bocconi, Milano, Italy.
    11. Michael Pollmann, 2020. "Causal Inference for Spatial Treatments," Papers 2011.00373, arXiv.org, revised Jan 2023.
    12. Kirill Borusyak & Peter Hull & Xavier Jaravel, 2025. "A Practical Guide to Shift-Share Instruments," Journal of Economic Perspectives, American Economic Association, vol. 39(1), pages 181-204, Winter.
    13. Joan Monras, 2020. "Immigration and Wage Dynamics: Evidence from the Mexican Peso Crisis," Journal of Political Economy, University of Chicago Press, vol. 128(8), pages 3017-3089.
    14. Paul Goldsmith-Pinkham & Isaac Sorkin & Henry Swift, 2020. "Bartik Instruments: What, When, Why, and How," American Economic Review, American Economic Association, vol. 110(8), pages 2586-2624, August.
    15. Singer, Gregor, 2024. "Complementary inputs and industrial development: can lower electricity prices improve energy efficiency?," LSE Research Online Documents on Economics 122365, London School of Economics and Political Science, LSE Library.
    16. Sheida Teimouri & Joachim Zietz, 2025. "Housing prices and import competition," Empirical Economics, Springer, vol. 68(1), pages 253-280, January.
    17. Guido W. Imbens & Jeffrey M. Wooldridge, 2009. "Recent Developments in the Econometrics of Program Evaluation," Journal of Economic Literature, American Economic Association, vol. 47(1), pages 5-86, March.
    18. Ganong, Peter & Shoag, Daniel, 2017. "Why has regional income convergence in the U.S. declined?," Journal of Urban Economics, Elsevier, vol. 102(C), pages 76-90.
    19. Bohnet, Lara & Peralta, Susana & Pereira dos Santos, João, 2022. "Cousins from Overseas: The Labour Market Impact of a Major Forced Return Migration Shock," IZA Discussion Papers 15595, Institute of Labor Economics (IZA).
    20. Brey, Björn, 2024. "The effect of recent technological change on US immigration policy," Journal of Economic Behavior & Organization, Elsevier, vol. 227(C).
    21. Stuhler, Jan & Jaeger, David & Ruist, Joakim, 2018. "Shift-Share Instruments and the Impact of Immigration," CEPR Discussion Papers 12701, C.E.P.R. Discussion Papers.

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ehl:lserod:123848. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.