IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2404.00164.html
   My bibliography  Save this paper

Sequential Synthetic Difference in Differences

Author

Listed:
  • Dmitry Arkhangelsky
  • Aleksei Samkov

Abstract

We study the estimation of treatment effects of a binary policy in environments with a staggered treatment rollout. We propose a new estimator -- Sequential Synthetic Difference in Difference (Sequential SDiD) -- and establish its theoretical properties in a linear model with interactive fixed effects. Our estimator is based on sequentially applying the original SDiD estimator proposed in Arkhangelsky et al. (2021) to appropriately aggregated data. To establish the theoretical properties of our method, we compare it to an infeasible OLS estimator based on the knowledge of the subspaces spanned by the interactive fixed effects. We show that this OLS estimator has a sequential representation and use this result to show that it is asymptotically equivalent to the Sequential SDiD estimator. This result implies the asymptotic normality of our estimator along with corresponding efficiency guarantees. The method developed in this paper presents a natural alternative to the conventional DiD strategies in staggered adoption designs.

Suggested Citation

  • Dmitry Arkhangelsky & Aleksei Samkov, 2024. "Sequential Synthetic Difference in Differences," Papers 2404.00164, arXiv.org.
    • Handle: RePEc:arx:papers:2404.00164
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2404.00164
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Eli Ben-Michael & Avi Feller & Jesse Rothstein, 2021. "The Augmented Synthetic Control Method," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1789-1803, October.
    2. M. Hashem Pesaran, 2006. "Estimation and Inference in Large Heterogeneous Panels with a Multifactor Error Structure," Econometrica, Econometric Society, vol. 74(4), pages 967-1012, July.
    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. de Chaisemartin, Clément & D’Haultfœuille, Xavier, 2023. "Two-way fixed effects and differences-in-differences estimators with several treatments," Journal of Econometrics, Elsevier, vol. 236(2).
    6. 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.
    7. Alberto Abadie, 2005. "Semiparametric Difference-in-Differences Estimators," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(1), pages 1-19.
    8. Susan Athey & Mohsen Bayati & Nikolay Doudchenko & Guido Imbens & Khashayar Khosravi, 2021. "Matrix Completion Methods for Causal Panel Data Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1716-1730, October.
    9. Jiafeng Chen, 2023. "Synthetic Control as Online Linear Regression," Econometrica, Econometric Society, vol. 91(2), pages 465-491, March.
    10. 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.
    11. Joachim Freyberger, 2018. "Non-parametric Panel Data Models with Interactive Fixed Effects," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(3), pages 1824-1851.
    12. Holtz-Eakin, Douglas & Newey, Whitney & Rosen, Harvey S, 1988. "Estimating Vector Autoregressions with Panel Data," Econometrica, Econometric Society, vol. 56(6), pages 1371-1395, November.
    13. Matias D. Cattaneo & Yingjie Feng & Rocio Titiunik, 2021. "Prediction Intervals for Synthetic Control Methods," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 116(536), pages 1865-1880, October.
    14. Alberto Abadie & Javier Gardeazabal, 2003. "The Economic Costs of Conflict: A Case Study of the Basque Country," American Economic Review, American Economic Association, vol. 93(1), pages 113-132, March.
    15. Bruno Ferman & Cristine Pinto, 2021. "Synthetic controls with imperfect pretreatment fit," Quantitative Economics, Econometric Society, vol. 12(4), pages 1197-1221, November.
    16. Janet Currie & Henrik Kleven & Esmée Zwiers, 2020. "Technology and Big Data Are Changing Economics: Mining Text to Track Methods," AEA Papers and Proceedings, American Economic Association, vol. 110, pages 42-48, May.
    17. Martha J. Bailey & Andrew Goodman-Bacon, 2015. "The War on Poverty's Experiment in Public Medicine: Community Health Centers and the Mortality of Older Americans," American Economic Review, American Economic Association, vol. 105(3), pages 1067-1104, March.
    18. Sant’Anna, Pedro H.C. & Zhao, Jun, 2020. "Doubly robust difference-in-differences estimators," Journal of Econometrics, Elsevier, vol. 219(1), pages 101-122.
    19. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    20. 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.
    21. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," NBER Working Papers 31942, National Bureau of Economic Research, Inc.
    22. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
    23. Chamberlain, Gary, 1992. "Efficiency Bounds for Semiparametric Regression," Econometrica, Econometric Society, vol. 60(3), pages 567-596, May.
    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 Mar 2024.
    2. Callaway, Brantly & Karami, Sonia, 2023. "Treatment effects in interactive fixed effects models with a small number of time periods," Journal of Econometrics, Elsevier, vol. 233(1), pages 184-208.
    3. Li, Xingyu & Shen, Yan & Zhou, Qiankun, 2024. "Confidence intervals of treatment effects in panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 240(1).
    4. Dennis Shen & Peng Ding & Jasjeet Sekhon & Bin Yu, 2022. "Same Root Different Leaves: Time Series and Cross-Sectional Methods in Panel Data," Papers 2207.14481, arXiv.org, revised Oct 2022.
    5. 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.
    6. Stefano, Roberta di & Mellace, Giovanni, 2020. "The inclusive synthetic control method," Discussion Papers on Economics 14/2020, University of Southern Denmark, Department of Economics.
    7. David Gilchrist & Thomas Emery & Nuno Garoupa & Rok Spruk, 2023. "Synthetic Control Method: A tool for comparative case studies in economic history," Journal of Economic Surveys, Wiley Blackwell, vol. 37(2), pages 409-445, April.
    8. Dmitry Arkhangelsky & David Hirshberg, 2023. "Large-Sample Properties of the Synthetic Control Method under Selection on Unobservables," Papers 2311.13575, arXiv.org, revised Dec 2023.
    9. Viviano, Davide & Bradic, Jelena, 2023. "Synthetic Learner: Model-free inference on treatments over time," Journal of Econometrics, Elsevier, vol. 234(2), pages 691-713.
    10. Sandro Heiniger, 2024. "Data-driven model selection within the matrix completion method for causal panel data models," Papers 2402.01069, arXiv.org.
    11. 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.
    12. Roy Cerqueti & Raffaella Coppier & Alessandro Girardi & Marco Ventura, 2022. "The sooner the better: lives saved by the lockdown during the COVID-19 outbreak. The case of Italy [Using synthetic controls: Feasibility, data requirements, and methodological aspects]," The Econometrics Journal, Royal Economic Society, vol. 25(1), pages 46-70.
    13. Christian Aleman & Christopher Busch & Alexander Ludwig & Raul Santaeulalia-Llopis, 2022. "A Stage-Based Identification of Policy Effects," PIER Working Paper Archive 22-026, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    14. Luis Costa & Vivek F. Farias & Patricio Foncea & Jingyuan (Donna) Gan & Ayush Garg & Ivo Rosa Montenegro & Kumarjit Pathak & Tianyi Peng & Dusan Popovic, 2023. "Generalized Synthetic Control for TestOps at ABI: Models, Algorithms, and Infrastructure," Interfaces, INFORMS, vol. 53(5), pages 336-349, September.
    15. Dmitry Arkhangelsky & Guido Imbens, 2018. "Fixed Effects and the Generalized Mundlak Estimator," Papers 1807.02099, arXiv.org, revised Aug 2023.
    16. Kim, Youngho, 2023. "Payments for Ecosystem Services Programs and Climate Change Adaptation in Agriculture," 2023 Annual Meeting, July 23-25, Washington D.C. 335971, Agricultural and Applied Economics Association.
    17. Guido W. Imbens & Davide Viviano, 2023. "Identification and Inference for Synthetic Controls with Confounding," Papers 2312.00955, arXiv.org.
    18. Keegan Harris & Anish Agarwal & Chara Podimata & Zhiwei Steven Wu, 2022. "Strategyproof Decision-Making in Panel Data Settings and Beyond," Papers 2211.14236, arXiv.org, revised Dec 2023.
    19. Matias D. Cattaneo & Yingjie Feng & Filippo Palomba & Rocio Titiunik, 2022. "scpi: Uncertainty Quantification for Synthetic Control Methods," Papers 2202.05984, arXiv.org, revised Oct 2022.
    20. Anish Agarwal & Vasilis Syrgkanis, 2022. "Synthetic Blip Effects: Generalizing Synthetic Controls for the Dynamic Treatment Regime," Papers 2210.11003, arXiv.org.

    More about this item

    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:2404.00164. 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.