IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1808.05293.html
   My bibliography  Save this paper

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

Author

Listed:
  • Susan Athey
  • Guido 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 is an unbiased estimator of a particular weighted average causal effect. We characterize the proeperties of this estimand, and show that the standard variance estimator is conservative.

Suggested Citation

  • Susan Athey & Guido Imbens, 2018. "Design-based Analysis in Difference-In-Differences Settings with Staggered Adoption," Papers 1808.05293, arXiv.org, revised Sep 2018.
    • Handle: RePEc:arx:papers:1808.05293
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1808.05293
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    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. 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.
    5. 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.
    6. 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.
    7. Peter Hull, 2018. "Estimating Treatment Effects in Mover Designs," Papers 1804.06721, arXiv.org.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Chamberlain, G., 1993. "Feedback in Panel Data Medels," Harvard Institute of Economic Research Working Papers 1656, Harvard - Institute of Economic Research.
    14. Athey, Susan & Imbens, Guido W. & Bayati, Mohsen, 2019. "Optimal Experimental Design for Staggered Rollouts," Research Papers 3837, Stanford University, Graduate School of Business.
    15. 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.
    16. 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.
    17. Marianne Bertrand & Esther Duflo & Sendhil Mullainathan, 2004. "How Much Should We Trust Differences-In-Differences Estimates?," The Quarterly Journal of Economics, Oxford University Press, vol. 119(1), pages 249-275.
    18. 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.
    19. Alberto Abadie, 2005. "Semiparametric Difference-in-Differences Estimators," Review of Economic Studies, Oxford University Press, vol. 72(1), pages 1-19.
    20. Sukjin Han, 2018. "Identification in Nonparametric Models for Dynamic Treatment Effects," Papers 1805.09397, arXiv.org, revised Jan 2019.
    21. 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.
    22. 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.
    23. 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.
    24. 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.
    25. 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.
    26. 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.
    27. 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.
    28. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
    29. 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.
    30. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588.
    31. Liyang Sun & Sarah Abraham, 2018. "Estimating Dynamic Treatment Effects in Event Studies with Heterogeneous Treatment Effects," Papers 1804.05785, arXiv.org, revised Sep 2020.
    32. 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.
    33. Arellano, Manuel, 2003. "Panel Data Econometrics," OUP Catalogue, Oxford University Press, number 9780199245291.
    34. Andrew Goodman-Bacon, 2018. "Difference-in-Differences with Variation in Treatment Timing," NBER Working Papers 25018, National Bureau of Economic Research, Inc.
    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. 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.
    2. 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).
    3. Davide Viviano & Jelena Bradic, 2021. "Dynamic covariate balancing: estimating treatment effects over time," Papers 2103.01280, arXiv.org, revised Jun 2021.
    4. Martin Huber, 2019. "An introduction to flexible methods for policy evaluation," Papers 1910.00641, arXiv.org.
    5. Bruno Ferman, 2020. "Inference in Difference-in-Differences with Few Treated Units and Spatial Correlation," Papers 2006.16997, arXiv.org, revised Sep 2021.
    6. Eli Ben-Michael & Avi Feller & Jesse Rothstein, 2019. "Synthetic Controls with Staggered Adoption," Papers 1912.03290, arXiv.org, revised Jan 2021.
    7. Committee, Nobel Prize, 2021. "Answering causal questions using observational data," Nobel Prize in Economics documents 2021-2, Nobel Prize Committee.
    8. Nikolay Doudchenko & Guido W. Imbens, 2016. "Balancing, Regression, Difference-In-Differences and Synthetic Control Methods: A Synthesis," NBER Working Papers 22791, National Bureau of Economic Research, Inc.
    9. 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.
    10. Juliano Assuncao & Robert McMillan & Joshua Murphy & Eduardo Souza-Rodrigues, 2019. "Optimal Environmental Targeting in the Amazon Rainforest," Working Papers tecipa-631, University of Toronto, Department of Economics.
    11. James G. MacKinnon & Morten Ørregaard Nielsen & Matthew D. Webb, 2021. "Cluster-Robust Inference: A Guide to Empirical Practice," Working Paper 1456, Economics Department, Queen's University.
    12. Erlend E. Bø & Joel Slemrod & Thor O. Thoresen, 2015. "Taxes on the Internet: Deterrence Effects of Public Disclosure," American Economic Journal: Economic Policy, American Economic Association, vol. 7(1), pages 36-62, February.
    13. Dmitry Arkhangelsky & Guido Imbens, 2018. "The Role of the Propensity Score in Fixed Effect Models," Papers 1807.02099, arXiv.org, revised Apr 2019.
    14. Matthew D. Webb & James MacKinnon & Morten Nielsen, 2021. "Cluster–robust inference: A guide to empirical practice," Economics Virtual Symposium 2021 6, Stata Users Group.
    15. Schmidheiny, Kurt & Siegloch, Sebastian, 2020. "On event studies and distributed-lags in two-way fixed effects models: Identification, equivalence, and generalization," ZEW Discussion Papers 20-017, ZEW - Leibniz Centre for European Economic Research.
    16. Bruno Ferman, 2019. "Inference in Differences-in-Differences: How Much Should We Trust in Independent Clusters?," Papers 1909.01782, arXiv.org, revised Sep 2020.
    17. Peter Z. Schochet, 2021. "Statistical Power for Estimating Treatment Effects Using Difference-in-Differences and Comparative Interrupted Time Series Designs with Variation in Treatment Timing," Papers 2102.06770, arXiv.org, revised Oct 2021.
    18. Jianfei Cao & Shirley Lu, 2019. "Synthetic Control Inference for Staggered Adoption: Estimating the Dynamic Effects of Board Gender Diversity Policies," Papers 1912.06320, arXiv.org.
    19. Juliano Assunção & Robert McMillan & Joshua Murphy & Eduardo Souza-Rodrigues, 2019. "Optimal Environmental Targeting in the Amazon Rainforest," NBER Working Papers 25636, National Bureau of Economic Research, Inc.
    20. Tamara Bischof & Boris Kaiser, 2021. "Who cares when you close down? The effects of primary care practice closures on patients," Health Economics, John Wiley & Sons, Ltd., vol. 30(9), pages 2004-2025, September.

    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:arx:papers:1808.05293. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://arxiv.org/ .

    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 hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.