IDEAS home Printed from https://ideas.repec.org/p/nbr/nberwo/24963.html
   My bibliography  Save this paper

Design-based Analysis in Difference-In-Differences Settings with Staggered Adoption

Author

Listed:
  • Susan Athey
  • Guido W. Imbens

Abstract

In this paper we study estimation of and inference for average treatment effects in a setting with panel data. We focus on the setting where units, e.g., individuals, firms, or states, adopt the policy or treatment of interest at a particular point in time, and then remain exposed to this treatment at all times afterwards. We take a design perspective where we investigate the properties of estimators and procedures given assumptions on the assignment process. We show that under random assignment of the adoption date the standard Difference-In-Differences estimator is an unbiased estimator of a particular weighted average causal effect. We characterize the properties of this estimand, and show that the standard variance estimator is conservative.

Suggested Citation

  • Susan Athey & Guido W. Imbens, 2018. "Design-based Analysis in Difference-In-Differences Settings with Staggered Adoption," NBER Working Papers 24963, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:24963
    Note: IO LS
    as

    Download full text from publisher

    File URL: http://www.nber.org/papers/w24963.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Simon Freyaldenhoven & Christian Hansen & Jesse M. Shapiro, 2019. "Pre-event Trends in the Panel Event-Study Design," American Economic Review, American Economic Association, vol. 109(9), pages 3307-3338, September.
    2. Card, David & Krueger, Alan B, 1994. "Minimum Wages and Employment: A Case Study of the Fast-Food Industry in New Jersey and Pennsylvania," American Economic Review, American Economic Association, vol. 84(4), pages 772-793, September.
    3. 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.
    4. 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.
    5. Dmitry Arkhangelsky & Susan Athey & David A. Hirshberg & Guido W. Imbens & Stefan Wager, 2021. "Synthetic Difference-in-Differences," American Economic Review, American Economic Association, vol. 111(12), pages 4088-4118, December.
    6. Peter Hull, 2018. "Estimating Treatment Effects in Mover Designs," Papers 1804.06721, arXiv.org.
    7. Stephen G. Donald & Kevin Lang, 2007. "Inference with Difference-in-Differences and Other Panel Data," The Review of Economics and Statistics, MIT Press, vol. 89(2), pages 221-233, May.
    8. Kenneth Y. Chay & Michael Greenstone, 2005. "Does Air Quality Matter? Evidence from the Housing Market," Journal of Political Economy, University of Chicago Press, vol. 113(2), pages 376-424, April.
    9. Athey, Susan & Imbens, Guido W. & Bayati, Mohsen, 2019. "Optimal Experimental Design for Staggered Rollouts," Research Papers 3837, Stanford University, Graduate School of Business.
    10. Abadie, Alberto & Athey, Susan & Imbens, Guido W. & Wooldridge, Jeffrey M., 2017. "Sampling-Based vs. Design-Based Uncertainty in Regression Analysis," Research Papers 3349, Stanford University, Graduate School of Business.
    11. Dmitry Arkhangelsky & Guido Imbens, 2018. "The Role of the Propensity Score in Fixed Effect Models," NBER Working Papers 24814, National Bureau of Economic Research, Inc.
    12. Abbring, Jaap H. & Heckman, James J., 2007. "Econometric Evaluation of Social Programs, Part III: Distributional Treatment Effects, Dynamic Treatment Effects, Dynamic Discrete Choice, and General Equilibrium Policy Evaluation," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 72, Elsevier.
    13. Alberto Abadie, 2005. "Semiparametric Difference-in-Differences Estimators," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(1), pages 1-19.
    14. Brantly Callaway & Pedro H. C. Sant'Anna, 2018. "Difference-in-Differences with Multiple Time Periods and an Application on the Minimum Wage and Employment," DETU Working Papers 1804, Department of Economics, Temple University.
    15. Susan Athey & Guido W. Imbens, 2006. "Identification and Inference in Nonlinear Difference-in-Differences Models," Econometrica, Econometric Society, vol. 74(2), pages 431-497, March.
    16. James H. Stock & Mark W. Watson, 2008. "Heteroskedasticity-Robust Standard Errors for Fixed Effects Panel Data Regression," Econometrica, Econometric Society, vol. 76(1), pages 155-174, January.
    17. 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.
    18. Meyer, Bruce D & Viscusi, W Kip & Durbin, David L, 1995. "Workers' Compensation and Injury Duration: Evidence from a Natural Experiment," American Economic Review, American Economic Association, vol. 85(3), pages 322-340, June.
    19. Chamberlain, Gary, 2022. "Feedback in panel data models," Journal of Econometrics, Elsevier, vol. 226(1), pages 4-20.
    20. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2004. "How Much Should We Trust Differences-In-Differences Estimates?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(1), pages 249-275.
    21. Jaap H. Abbring & Gerard J. van den Berg, 2003. "The Nonparametric Identification of Treatment Effects in Duration Models," Econometrica, Econometric Society, vol. 71(5), pages 1491-1517, September.
    22. Abadie, Alberto & Diamond, Alexis & Hainmueller, Jens, 2010. "Synthetic Control Methods for Comparative Case Studies: Estimating the Effect of California’s Tobacco Control Program," Journal of the American Statistical Association, American Statistical Association, vol. 105(490), pages 493-505.
    23. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, December.
    24. Timothy G. Conley & Christopher R. Taber, 2011. "Inference with "Difference in Differences" with a Small Number of Policy Changes," The Review of Economics and Statistics, MIT Press, vol. 93(1), pages 113-125, February.
    25. Andrew Goodman-Bacon, 2018. "Difference-in-Differences with Variation in Treatment Timing," NBER Working Papers 25018, National Bureau of Economic Research, Inc.
    26. Susan Athey & Scott Stern, 1998. "An Empirical Framework for Testing Theories About Complimentarity in Organizational Design," NBER Working Papers 6600, National Bureau of Economic Research, Inc.
    27. 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.
    28. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291.
    29. Athey, Susan. & Stern, Scott, 1969-, 1998. "An empirical framework for testing theories about complementarity in orgaziational design," Working papers WP 4022-98., Massachusetts Institute of Technology (MIT), Sloan School of Management.
    30. Han, Sukjin, 2021. "Identification in nonparametric models for dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 225(2), pages 132-147.
    31. Arellano, M, 1987. "Computing Robust Standard Errors for Within-Groups Estimators," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 49(4), pages 431-434, November.
    32. Peter M. Aronow & Cyrus Samii, 2016. "Does Regression Produce Representative Estimates of Causal Effects?," American Journal of Political Science, John Wiley & Sons, vol. 60(1), pages 250-267, January.
    33. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
    34. Kosuke Imai & In Song Kim, 2019. "When Should We Use Unit Fixed Effects Regression Models for Causal Inference with Longitudinal Data?," American Journal of Political Science, John Wiley & Sons, vol. 63(2), pages 467-490, April.
    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. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Jun 2024.
    2. 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.
    3. 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.
    4. Mark Kattenberg & Bas Scheer & Jurre Thiel, 2023. "Causal forests with fixed effects for treatment effect heterogeneity in difference-in-differences," CPB Discussion Paper 452, CPB Netherlands Bureau for Economic Policy Analysis.
    5. Dalia Ghanem & Pedro H. C. Sant'Anna & Kaspar Wuthrich, 2022. "Selection and parallel trends," Papers 2203.09001, arXiv.org, revised Mar 2024.
    6. Rösner, Anja & Haucap, Justus & Heimeshoff, Ulrich, 2020. "The impact of consumer protection in the digital age: Evidence from the European Union," International Journal of Industrial Organization, Elsevier, vol. 73(C).
    7. 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.
    8. Davide Viviano & Jelena Bradic, 2021. "Dynamic covariate balancing: estimating treatment effects over time with potential local projections," Papers 2103.01280, arXiv.org, revised Jan 2024.
    9. Eli Ben‐Michael & Avi Feller & Jesse Rothstein, 2022. "Synthetic controls with staggered adoption," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 351-381, April.
    10. Bruno Ferman, 2023. "Inference in difference‐in‐differences: How much should we trust in independent clusters?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(3), pages 358-369, April.
    11. Myungkou Shin, 2022. "Finitely Heterogeneous Treatment Effect in Event-study," Papers 2204.02346, arXiv.org, revised Oct 2024.
    12. Goodman-Bacon, Andrew, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, Elsevier, vol. 225(2), pages 254-277.
    13. Christian Alemán & Christopher Busch & Alexander Ludwig & Raül Santaeulàlia-Llopis, 2022. "A Stage-Based Identification of Policy Effects," Working Papers 1369, Barcelona School of Economics.
    14. van der Klaauw, Bas, 2014. "From micro data to causality: Forty years of empirical labor economics," Labour Economics, Elsevier, vol. 30(C), pages 88-97.
    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. Lechner, Michael, 2011. "The Estimation of Causal Effects by Difference-in-Difference Methods," Foundations and Trends(R) in Econometrics, now publishers, vol. 4(3), pages 165-224, November.
    17. Kirill Borusyak & Xavier Jaravel & Jann Spiess, 2021. "Revisiting Event Study Designs: Robust and Efficient Estimation," Papers 2108.12419, arXiv.org, revised Jan 2024.
    18. 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.
    19. Herrero Prieto, Luis César, 2009. "La investigación en economía de la cultura en España: un estudio bibliométrico/Research in Cultural Economics in Spain: A Bibliometric Study," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 27, pages 35-62, Abril.
    20. Damian Clarke & Kathya Tapia-Schythe, 2021. "Implementing the panel event study," Stata Journal, StataCorp LP, vol. 21(4), pages 853-884, December.

    More about this item

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

    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:nbr:nberwo:24963. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/nberrus.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.