IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2405.12083.html
   My bibliography  Save this paper

Instrumented Difference-in-Differences with Heterogeneous Treatment Effects

Author

Listed:
  • Sho Miyaji

Abstract

Many studies exploit variation in policy adoption timing across units as an instrument for treatment. This paper formalizes the underlying identification strategy as an instrumented difference-in-differences (DID-IV). In this design, a Wald-DID estimand, which scales the DID estimand of the outcome by the DID estimand of the treatment, captures the local average treatment effect on the treated (LATET). We extend the canonical DID-IV design to multiple period settings with the staggered adoption of the instrument across units. Moreover, we propose a credible estimation method in this design that is robust to treatment effect heterogeneity. We illustrate the empirical relevance of our findings, estimating returns to schooling in the United Kingdom. In this application, the two-way fixed effects instrumental variable regression, the conventional approach to implement DID-IV designs, yields a negative estimate. By contrast, our estimation method indicates a substantial gain from schooling.

Suggested Citation

  • Sho Miyaji, 2024. "Instrumented Difference-in-Differences with Heterogeneous Treatment Effects," Papers 2405.12083, arXiv.org, revised Jan 2025.
  • Handle: RePEc:arx:papers:2405.12083
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2405.12083
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Andreas Olden & Jarle Møen, 2022. "The triple difference estimator [Semiparametric difference-in-differences estimators]," The Econometrics Journal, Royal Economic Society, vol. 25(3), pages 531-553.
    2. 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.
    3. Philip Oreopoulos, 2006. "Estimating Average and Local Average Treatment Effects of Education when Compulsory Schooling Laws Really Matter," American Economic Review, American Economic Association, vol. 96(1), pages 152-175, March.
    4. Esther Duflo, 2001. "Schooling and Labor Market Consequences of School Construction in Indonesia: Evidence from an Unusual Policy Experiment," American Economic Review, American Economic Association, vol. 91(4), pages 795-813, September.
    5. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, May.
    6. Costas Meghir & Mårten Palme & Emilia Simeonova, 2018. "Education and Mortality: Evidence from a Social Experiment," American Economic Journal: Applied Economics, American Economic Association, vol. 10(2), pages 234-256, April.
    7. Manudeep Bhuller & Tarjei Havnes & Edwin Leuven & Magne Mogstad, 2013. "Broadband Internet: An Information Superhighway to Sex Crime?," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(4), pages 1237-1266.
    8. Imai, Kosuke & Kim, In Song, 2021. "On the Use of Two-Way Fixed Effects Regression Models for Causal Inference with Panel Data," Political Analysis, Cambridge University Press, vol. 29(3), pages 405-415, July.
    9. Rucker C. Johnson & C. Kirabo Jackson, 2019. "Reducing Inequality through Dynamic Complementarity: Evidence from Head Start and Public School Spending," American Economic Journal: Economic Policy, American Economic Association, vol. 11(4), pages 310-349, November.
    10. Olivier Deschênes & Michael Greenstone & Joseph S. Shapiro, 2017. "Defensive Investments and the Demand for Air Quality: Evidence from the NOx Budget Program," American Economic Review, American Economic Association, vol. 107(10), pages 2958-2989, October.
    11. Sandra E. Black & Paul J. Devereux & Kjell G. Salvanes, 2005. "Why the Apple Doesn't Fall Far: Understanding Intergenerational Transmission of Human Capital," American Economic Review, American Economic Association, vol. 95(1), pages 437-449, March.
    12. Athey, Susan & Imbens, Guido W., 2022. "Design-based analysis in Difference-In-Differences settings with staggered adoption," Journal of Econometrics, Elsevier, vol. 226(1), pages 62-79.
    13. Michal Kolesár & Christoph Rothe, 2018. "Inference in Regression Discontinuity Designs with a Discrete Running Variable," American Economic Review, American Economic Association, vol. 108(8), pages 2277-2304, August.
    14. Sun, Liyang & Abraham, Sarah, 2021. "Estimating dynamic treatment effects in event studies with heterogeneous treatment effects," Journal of Econometrics, Elsevier, vol. 225(2), pages 175-199.
    15. Callaway, Brantly & Sant’Anna, Pedro H.C., 2021. "Difference-in-Differences with multiple time periods," Journal of Econometrics, Elsevier, vol. 225(2), pages 200-230.
    16. Edward Vytlacil & James J. Heckman, 2001. "Policy-Relevant Treatment Effects," American Economic Review, American Economic Association, vol. 91(2), pages 107-111, May.
    17. 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.
    18. Abadie, Alberto, 2003. "Semiparametric instrumental variable estimation of treatment response models," Journal of Econometrics, Elsevier, vol. 113(2), pages 231-263, April.
    19. Erica Field, 2007. "Entitled to Work: Urban Property Rights and Labor Supply in Peru," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(4), pages 1561-1602.
    20. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, vol. 70(1), pages 331-341, January.
    21. Petter Lundborg & Anton Nilsson & Dan-Olof Rooth, 2014. "Parental Education and Offspring Outcomes: Evidence from the Swedish Compulsory School Reform," American Economic Journal: Applied Economics, American Economic Association, vol. 6(1), pages 253-278, January.
    Full references (including those not matched with items on IDEAS)

    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. Sho Miyaji, 2024. "Instrumented Difference-in-Differences with Heterogeneous Treatment Effects," Discussion Paper Series DP2024-22, Research Institute for Economics & Business Administration, Kobe University.
    2. Sho Miyaji, 2024. "Two-way fixed effects instrumental variable regressions in staggered DID-IV designs," Papers 2405.16467, arXiv.org.
    3. Huber, Martin, 2019. "An introduction to flexible methods for policy evaluation," FSES Working Papers 504, Faculty of Economics and Social Sciences, University of Freiburg/Fribourg Switzerland.
    4. Zhang, Hongliang & Assaad, Ragui, 2024. "Women’s access to school, educational attainment, and fertility: Evidence from Jordan," Journal of Development Economics, Elsevier, vol. 170(C).
    5. Bhuller, Manudeep & Sigstad, Henrik, 2024. "2SLS with multiple treatments," Journal of Econometrics, Elsevier, vol. 242(1).
    6. 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.
    7. Goodman-Bacon, Andrew, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, Elsevier, vol. 225(2), pages 254-277.
    8. Arne Henningsen & Guy Low & David Wuepper & Tobias Dalhaus & Hugo Storm & Dagim Belay & Stefan Hirsch, 2024. "Estimating Causal Effects with Observational Data: Guidelines for Agricultural and Applied Economists," IFRO Working Paper 2024/03, University of Copenhagen, Department of Food and Resource Economics.
    9. 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.
    10. Pedro Carneiro & Michael Lokshin & Nithin Umapathi, 2017. "Average and Marginal Returns to Upper Secondary Schooling in Indonesia," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(1), pages 16-36, January.
    11. Pereda-Fernández, Santiago, 2023. "Identification and estimation of triangular models with a binary treatment," Journal of Econometrics, Elsevier, vol. 234(2), pages 585-623.
    12. Cl'ement de Chaisemartin & Xavier D'Haultf{oe}uille, 2021. "Two-Way Fixed Effects and Differences-in-Differences with Heterogeneous Treatment Effects: A Survey," Papers 2112.04565, arXiv.org, revised Jun 2022.
    13. Jorge Rodríguez & Fernando Saltiel & Sergio Urzúa, 2022. "Dynamic treatment effects of job training," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(2), pages 242-269, March.
    14. OKUDAIRA Hiroko & TAKIZAWA Miho & YAMANOUCHI Kenta, 2022. "Does Employee Downsizing Work? Evidence from Product Innovation at Manufacturing Plants," Discussion papers 22015, Research Institute of Economy, Trade and Industry (RIETI).
    15. Roth, Jonathan & Sant’Anna, Pedro H.C. & Bilinski, Alyssa & Poe, John, 2023. "What’s trending in difference-in-differences? A synthesis of the recent econometrics literature," Journal of Econometrics, Elsevier, vol. 235(2), pages 2218-2244.
    16. Timo Schenk, 2023. "Time-Weighted Difference-in-Differences: Accounting for Common Factors in Short T Panels," Tinbergen Institute Discussion Papers 23-004/III, Tinbergen Institute.
    17. Pinotti, Paolo & Bhalotra, Sonia & Britto, Diogo & Sampaio, Breno, 2021. "Job Displacement, Unemployment Benefits and Domestic Violence," CEPR Discussion Papers 16350, C.E.P.R. Discussion Papers.
    18. Li, Ping & Zhang, ZhongXiang, 2023. "The effects of new energy vehicle subsidies on air quality: Evidence from China," Energy Economics, Elsevier, vol. 120(C).
    19. Yingying DONG & Ying-Ying LEE & Michael GOU, 2019. "Regression Discontinuity Designs with a Continuous Treatment," Discussion papers 19058, Research Institute of Economy, Trade and Industry (RIETI).
    20. Silvia Moler‐Zapata & Richard Grieve & Anirban Basu & Stephen O’Neill, 2023. "How does a local instrumental variable method perform across settings with instruments of differing strengths? A simulation study and an evaluation of emergency surgery," Health Economics, John Wiley & Sons, Ltd., vol. 32(9), pages 2113-2126, September.

    More about this item

    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:arx:papers:2405.12083. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.