IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2301.01085.html
   My bibliography  Save this paper

The Chained Difference-in-Differences

Author

Listed:
  • Christophe Bell'ego
  • David Benatia
  • Vincent Dortet-Bernardet

Abstract

This paper studies the identification, estimation, and inference of long-term (binary) treatment effect parameters when balanced panel data is not available, or consists of only a subset of the available data. We develop a new estimator: the chained difference-in-differences, which leverages the overlapping structure of many unbalanced panel data sets. This approach consists in aggregating a collection of short-term treatment effects estimated on multiple incomplete panels. Our estimator accommodates (1) multiple time periods, (2) variation in treatment timing, (3) treatment effect heterogeneity, (4) general missing data patterns, and (5) sample selection on observables. We establish the asymptotic properties of the proposed estimator and discuss identification and efficiency gains in comparison to existing methods. Finally, we illustrate its relevance through (i) numerical simulations, and (ii) an application about the effects of an innovation policy in France.

Suggested Citation

  • Christophe Bell'ego & David Benatia & Vincent Dortet-Bernardet, 2023. "The Chained Difference-in-Differences," Papers 2301.01085, arXiv.org, revised Dec 2023.
    • Handle: RePEc:arx:papers:2301.01085
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2301.01085
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Almas Heshmati, 1998. "Efficiency measurement in rotating panel data," Applied Economics, Taylor & Francis Journals, vol. 30(7), pages 919-930.
    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 H. Autor & Susan N. Houseman, 2010. "Do Temporary-Help Jobs Improve Labor Market Outcomes for Low-Skilled Workers? Evidence from "Work First"," American Economic Journal: Applied Economics, American Economic Association, vol. 2(3), pages 96-128, July.
    5. Gross, Robert & Hanna, Richard & Gambhir, Ajay & Heptonstall, Philip & Speirs, Jamie, 2018. "How long does innovation and commercialisation in the energy sectors take? Historical case studies of the timescale from invention to widespread commercialisation in energy supply and end use technolo," Energy Policy, Elsevier, vol. 123(C), pages 682-699.
    6. Kahn, Lisa B., 2010. "The long-term labor market consequences of graduating from college in a bad economy," Labour Economics, Elsevier, vol. 17(2), pages 303-316, April.
    7. Bakker, Gerben, 2013. "Money for nothing: How firms have financed R&D-projects since the Industrial Revolution," Research Policy, Elsevier, vol. 42(10), pages 1793-1814.
    8. Bhattacharya, Debopam, 2008. "Inference in panel data models under attrition caused by unobservables," Journal of Econometrics, Elsevier, vol. 144(2), pages 430-446, June.
    9. Chaudhuri, Saraswata, 2020. "On Efficiency Gains From Multiple Incomplete Subsamples," Econometric Theory, Cambridge University Press, vol. 36(3), pages 488-525, June.
    10. Keisuke Hirano & Guido W. Imbens & Geert Ridder, 2003. "Efficient Estimation of Average Treatment Effects Using the Estimated Propensity Score," Econometrica, Econometric Society, vol. 71(4), pages 1161-1189, July.
    11. Sant’Anna, Pedro H.C. & Zhao, Jun, 2020. "Doubly robust difference-in-differences estimators," Journal of Econometrics, Elsevier, vol. 219(1), pages 101-122.
    12. Michael Lechner & Ruth Miquel & Conny Wunsch, 2011. "Long‐Run Effects Of Public Sector Sponsored Training In West Germany," Journal of the European Economic Association, European Economic Association, vol. 9(4), pages 742-784, August.
    13. Verbeek, Marno & Nijman, Theo, 1992. "Testing for Selectivity Bias in Panel Data Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(3), pages 681-703, August.
    14. Alberto Abadie, 2005. "Semiparametric Difference-in-Differences Estimators," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(1), pages 1-19.
    15. Badi Baltagi & Seuck Song, 2006. "Unbalanced panel data: A survey," Statistical Papers, Springer, vol. 47(4), pages 493-523, October.
    16. Markus Frölich & Martin Huber, 2014. "Treatment Evaluation With Multiple Outcome Periods Under Endogeneity and Attrition," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1697-1711, December.
    17. Philip Oreopoulos & Till von Wachter & Andrew Heisz, 2012. "The Short- and Long-Term Career Effects of Graduating in a Recession," American Economic Journal: Applied Economics, American Economic Association, vol. 4(1), pages 1-29, January.
    18. Pierre Hoonhout & Geert Ridder, 2019. "Nonignorable Attrition in Multi-Period Panels With Refreshment Samples," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 37(3), pages 377-390, July.
    19. Keisuke Hirano & Guido W. Imbens & Geert Ridder & Donald B. Rubin, 2001. "Combining Panel Data Sets with Attrition and Refreshment Samples," Econometrica, Econometric Society, vol. 69(6), pages 1645-1659, November.
    20. Stevens, Ann Huff, 1997. "Persistent Effects of Job Displacement: The Importance of Multiple Job Losses," Journal of Labor Economics, University of Chicago Press, vol. 15(1), pages 165-188, January.
    21. 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.
    22. Howitt, Peter & Aghion, Philippe, 1998. "Capital Accumulation and Innovation as Complementary Factors in Long-Run Growth," Journal of Economic Growth, Springer, vol. 3(2), pages 111-130, June.
    23. Goodman-Bacon, Andrew, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, Elsevier, vol. 225(2), pages 254-277.
    24. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77, Elsevier.
    25. Joshua Angrist & Eric Bettinger & Michael Kremer, 2006. "Long-Term Educational Consequences of Secondary School Vouchers: Evidence from Administrative Records in Colombia," American Economic Review, American Economic Association, vol. 96(3), pages 847-862, June.
    26. 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.
    27. Richard R. Nelson, 1959. "The Simple Economics of Basic Scientific Research," Journal of Political Economy, University of Chicago Press, vol. 67(3), pages 297-297.
    28. Hausman, Jerry A & Wise, David A, 1979. "Attrition Bias in Experimental and Panel Data: The Gary Income Maintenance Experiment," Econometrica, Econometric Society, vol. 47(2), pages 455-473, March.
    29. Scherer, F M, 1982. "Inter-Industry Technology Flows and Productivity Growth," The Review of Economics and Statistics, MIT Press, vol. 64(4), pages 627-634, November.
    30. Thomas A. Mroz & Timothy H. Savage, 2006. "The Long-Term Effects of Youth Unemployment," Journal of Human Resources, University of Wisconsin Press, vol. 41(2).
    31. Frazier, David T. & Renault, Eric, 2017. "Efficient two-step estimation via targeting," Journal of Econometrics, Elsevier, vol. 201(2), pages 212-227.
    32. repec:adr:anecst:y:1999:i:55-56:p:05 is not listed on IDEAS
    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. Diego Daruich & Sabrina Di Addario & Raffaele Saggio, 2023. "The Effects of Partial Employment Protection Reforms: Evidence from Italy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 90(6), pages 2880-2942.
    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. 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.
    4. Lin, Lihua & Zhang, Zhengyu, 2022. "Interpreting the coefficients in dynamic two-way fixed effects regressions with time-varying covariates," Economics Letters, Elsevier, vol. 216(C).
    5. Baker, Andrew C. & Larcker, David F. & Wang, Charles C.Y., 2022. "How much should we trust staggered difference-in-differences estimates?," Journal of Financial Economics, Elsevier, vol. 144(2), pages 370-395.
    6. Markus Frölich & Martin Huber, 2014. "Treatment Evaluation With Multiple Outcome Periods Under Endogeneity and Attrition," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1697-1711, December.
    7. 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.
    8. Goodman-Bacon, Andrew, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, Elsevier, vol. 225(2), pages 254-277.
    9. Albanese, Andrea & Nieto, Adrián & Tatsiramos, Konstantinos, 2022. "Job Location Decisions and the Effect of Children on the Employment Gender Gap," GLO Discussion Paper Series 1113, Global Labor Organization (GLO).
    10. Michelle Marcus & Pedro H. C. Sant’Anna, 2021. "The Role of Parallel Trends in Event Study Settings: An Application to Environmental Economics," Journal of the Association of Environmental and Resource Economists, University of Chicago Press, vol. 8(2), pages 235-275.
    11. Kyunghoon Ban & D'esir'e K'edagni, 2022. "Robust Difference-in-differences Models," Papers 2211.06710, arXiv.org, revised Aug 2023.
    12. Dalia Ghanem & Pedro H. C. Sant'Anna & Kaspar Wüthrich, 2022. "Selection and Parallel Trends," CESifo Working Paper Series 9910, CESifo.
    13. Liyang Sun & Jesse M. Shapiro, 2022. "A Linear Panel Model with Heterogeneous Coefficients and Variation in Exposure," Journal of Economic Perspectives, American Economic Association, vol. 36(4), pages 193-204, Fall.
    14. Pedro Sant'Anna, 2021. "Estimation of average treatment effects in staggered difference-in-differences designs," 2021 Stata Conference 13, Stata Users Group.
    15. Clément de Chaisemartin & Xavier D’Haultfœuille, 2023. "Two-way fixed effects and differences-in-differences with heterogeneous treatment effects: a survey," The Econometrics Journal, Royal Economic Society, vol. 26(3), pages 1-30.
    16. Courtney Coile & Maya Rossin-Slater & Amanda Su, 2022. "The Impact of Paid Family Leave on Families with Health Shocks," NBER Working Papers 30739, National Bureau of Economic Research, Inc.
    17. Jon Ellingsen & Caroline Espegren, 2022. "Lost in transition? Earnings losses of displaced petroleum workers," Working Papers No 06/2022, Centre for Applied Macro- and Petroleum economics (CAMP), BI Norwegian Business School.
    18. Hampton, Matt & McNamara, Scott, 2022. "The impact of educational rewards on the diagnosis of autism spectrum disorder," Economics & Human Biology, Elsevier, vol. 47(C).
    19. Isabelle Chort & Berk Öktem, 2023. "Agricultural shocks, coping policies and deforestation: evidence from the coffee leaf rust epidemic in mexico," Working Papers hal-03715600, HAL.
    20. Rik Chakraborti & Gavin Roberts, 2023. "How price-gouging regulation undermined COVID-19 mitigation: county-level evidence of unintended consequences," Public Choice, Springer, vol. 196(1), pages 51-83, July.

    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:2301.01085. 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.