IDEAS home Printed from https://ideas.repec.org/a/aea/aecrev/v110y2020i9p2964-96.html
   My bibliography  Save this article

Two-Way Fixed Effects Estimators with Heterogeneous Treatment Effects

Author

Listed:
  • Clément de Chaisemartin
  • Xavier D'Haultfœuille

Abstract

Linear regressions with period and group fixed effects are widely used to estimate treatment effects. We show that they estimate weighted sums of the average treatment effects (ATE) in each group and period, with weights that may be negative. Due to the negative weights, the linear regression coefficient may for instance be negative while all the ATEs are positive. We propose another estimator that solves this issue. In the two applications we revisit, it is significantly different from the linear regression estimator.

Suggested Citation

  • 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.
    • Handle: RePEc:aea:aecrev:v:110:y:2020:i:9:p:2964-96
    DOI: 10.1257/aer.20181169
    as

    Download full text from publisher

    File URL: https://www.aeaweb.org/doi/10.1257/aer.20181169
    Download Restriction: no
    File URL: https://doi.org/10.3886/E118363V2
    Download Restriction: no
    File URL: https://www.aeaweb.org/doi/10.1257/aer.20181169.appx
    Download Restriction: no
    File URL: https://www.aeaweb.org/doi/10.1257/aer.20181169.ds
    Download Restriction: Access to full text is restricted to AEA members and institutional subscribers.
    File URL: https://libkey.io/10.1257/aer.20181169?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. C de Chaisemartin & X D’HaultfŒuille, 2018. "Fuzzy Differences-in-Differences," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 85(2), pages 999-1028.
    2. Mirko Draca & Stephen Machin & Robert Witt, 2011. "Panic on the Streets of London: Police, Crime, and the July 2005 Terror Attacks," American Economic Review, American Economic Association, vol. 101(5), pages 2157-2181, August.
    3. Richard Hornbeck, 2012. "The Enduring Impact of the American Dust Bowl: Short- and Long-Run Adjustments to Environmental Catastrophe," American Economic Review, American Economic Association, vol. 102(4), pages 1477-1507, June.
    4. Nicholas Bloom & Raffaella Sadun & John Van Reenen, 2012. "Americans Do IT Better: US Multinationals and the Productivity Miracle," American Economic Review, American Economic Association, vol. 102(1), pages 167-201, February.
    5. Gordon B. Dahl & Lance Lochner, 2012. "The Impact of Family Income on Child Achievement: Evidence from the Earned Income Tax Credit," American Economic Review, American Economic Association, vol. 102(5), pages 1927-1956, August.
    6. Soren T. Anderson & James M. Sallee, 2011. "Using Loopholes to Reveal the Marginal Cost of Regulation: The Case of Fuel-Economy Standards," American Economic Review, American Economic Association, vol. 101(4), pages 1375-1409, June.
    7. Mark Duggan & Fiona Scott Morton, 2010. "The Effect of Medicare Part D on Pharmaceutical Prices and Utilization," American Economic Review, American Economic Association, vol. 100(1), pages 590-607, March.
    8. Andrew Ellul & Marco Pagano & Fausto Panunzi, 2010. "Inheritance Law and Investment in Family Firms," American Economic Review, American Economic Association, vol. 100(5), pages 2414-2450, December.
    9. Thomas Chaney & David Sraer & David Thesmar, 2012. "The Collateral Channel: How Real Estate Shocks Affect Corporate Investment," American Economic Review, American Economic Association, vol. 102(6), pages 2381-2409, October.
    10. 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.
    11. Timothy Simcoe, 2012. "Standard Setting Committees: Consensus Governance for Shared Technology Platforms," American Economic Review, American Economic Association, vol. 102(1), pages 305-336, February.
    12. 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.
    13. Yann Algan & Pierre Cahuc, 2010. "Inherited Trust and Growth," American Economic Review, American Economic Association, vol. 100(5), pages 2060-2092, December.
    14. Taryn Dinkelman, 2011. "The Effects of Rural Electrification on Employment: New Evidence from South Africa," American Economic Review, American Economic Association, vol. 101(7), pages 3078-3108, December.
    15. Kyle Bagwell & Robert W. Staiger, 2011. "What Do Trade Negotiators Negotiate About? Empirical Evidence from the World Trade Organization," American Economic Review, American Economic Association, vol. 101(4), pages 1238-1273, June.
    16. Nathaniel Baum-Snow & Byron F. Lutz, 2011. "School Desegregation, School Choice, and Changes in Residential Location Patterns by Race," American Economic Review, American Economic Association, vol. 101(7), pages 3019-3046, December.
    17. V. Joseph Hotz & Mo Xiao, 2011. "The Impact of Regulations on the Supply and Quality of Care in Child Care Markets," American Economic Review, American Economic Association, vol. 101(5), pages 1775-1805, August.
    18. 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.
    19. Timothy Besley & Hannes Mueller, 2012. "Estimating the Peace Dividend: The Impact of Violence on House Prices in Northern Ireland," American Economic Review, American Economic Association, vol. 102(2), pages 810-833, April.
    20. Leemore Dafny & Mark Duggan & Subramaniam Ramanarayanan, 2012. "Paying a Premium on Your Premium? Consolidation in the US Health Insurance Industry," American Economic Review, American Economic Association, vol. 102(2), pages 1161-1185, April.
    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. Shing-Yi Wang, 2011. "State Misallocation and Housing Prices: Theory and Evidence from China," American Economic Review, American Economic Association, vol. 101(5), pages 2081-2107, August.
    23. Gilles Duranton & Matthew A. Turner, 2011. "The Fundamental Law of Road Congestion: Evidence from US Cities," American Economic Review, American Economic Association, vol. 101(6), pages 2616-2652, October.
    24. Petra Moser & Alessandra Voena, 2012. "Compulsory Licensing: Evidence from the Trading with the Enemy Act," American Economic Review, American Economic Association, vol. 102(1), pages 396-427, February.
    25. Atif Mian & Amir Sufi, 2011. "House Prices, Home Equity-Based Borrowing, and the US Household Leverage Crisis," American Economic Review, American Economic Association, vol. 101(5), pages 2132-2156, August.
    26. repec:hal:spmain:info:hdl:2441/75koqefued8i7pihbrl9u84p4u is not listed on IDEAS
    27. Paula Bustos, 2011. "Trade Liberalization, Exports, and Technology Upgrading: Evidence on the Impact of MERCOSUR on Argentinian Firms," American Economic Review, American Economic Association, vol. 101(1), pages 304-340, February.
    28. 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.
    29. Andrew Goodman-Bacon, 2018. "Difference-in-Differences with Variation in Treatment Timing," NBER Working Papers 25018, National Bureau of Economic Research, Inc.
    30. Hanming Fang & Alessandro Gavazza, 2011. "Dynamic Inefficiencies in an Employment-Based Health Insurance System: Theory and Evidence," American Economic Review, American Economic Association, vol. 101(7), pages 3047-3077, December.
    31. Joshua D. Angrist & Kathryn Graddy & Guido W. Imbens, 2000. "The Interpretation of Instrumental Variables Estimators in Simultaneous Equations Models with an Application to the Demand for Fish," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 67(3), pages 499-527.
    32. Patrick Bajari & Jane Cooley Fruehwirth & Kyoo il Kim & Christopher Timmins, 2012. "A Rational Expectations Approach to Hedonic Price Regressions with Time-Varying Unobserved Product Attributes: The Price of Pollution," American Economic Review, American Economic Association, vol. 102(5), pages 1898-1926, August.
    33. 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.
    34. Amitabh Chandra & Jonathan Gruber & Robin McKnight, 2010. "Patient Cost-Sharing and Hospitalization Offsets in the Elderly," American Economic Review, American Economic Association, vol. 100(1), pages 193-213, March.
    35. Scott A. Imberman & Adriana D. Kugler & Bruce I. Sacerdote, 2012. "Katrina's Children: Evidence on the Structure of Peer Effects from Hurricane Evacuees," American Economic Review, American Economic Association, vol. 102(5), pages 2048-2082, August.
    36. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
    37. Xiaoquan (Michael) Zhang & Feng Zhu, 2011. "Group Size and Incentives to Contribute: A Natural Experiment at Chinese Wikipedia," American Economic Review, American Economic Association, vol. 101(4), pages 1601-1615, June.
    38. Anna Aizer, 2010. "The Gender Wage Gap and Domestic Violence," American Economic Review, American Economic Association, vol. 100(4), pages 1847-1859, September.
    39. repec:hal:spmain:info:hdl:2441/432sbils8u9t7qa99cii5psht1 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. Damian Clarke & Kathya Tapia-Schythe, 2021. "Implementing the panel event study," Stata Journal, StataCorp LP, vol. 21(4), pages 853-884, December.
    2. 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.
    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. Luis Alvarez & Bruno Ferman, 2020. "Inference in Difference-in-Differences with Few Treated Units and Spatial Correlation," Papers 2006.16997, arXiv.org, revised Apr 2023.
    5. Ashesh Rambachan & Jonathan Roth, 2020. "Design-Based Uncertainty for Quasi-Experiments," Papers 2008.00602, arXiv.org, revised Feb 2024.
    6. Kurt Schmidheiny & Sebastian Siegloch, 2023. "On event studies and distributed‐lags in two‐way fixed effects models: Identification, equivalence, and generalization," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(5), pages 695-713, August.
    7. 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).
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Tal Gross & Raymond Kluender & Feng Liu & Matthew J. Notowidigdo & Jialan Wang, 2019. "The Economic Consequences of Bankruptcy Reform," NBER Working Papers 26254, National Bureau of Economic Research, Inc.
    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. Baum-Snow, Nathaniel & Ferreira, Fernando, 2015. "Causal Inference in Urban and Regional Economics," Handbook of Regional and Urban Economics, in: Gilles Duranton & J. V. Henderson & William C. Strange (ed.), Handbook of Regional and Urban Economics, edition 1, volume 5, chapter 0, pages 3-68, Elsevier.
    15. Han, Sukjin, 2021. "Identification in nonparametric models for dynamic treatment effects," Journal of Econometrics, Elsevier, vol. 225(2), pages 132-147.
    16. Cl'ement de Chaisemartin & Xavier D'Haultfoeuille, 2020. "Difference-in-Differences Estimators of Intertemporal Treatment Effects," Papers 2007.04267, arXiv.org, revised Nov 2023.
    17. Sloczynski, Tymon, 2018. "A General Weighted Average Representation of the Ordinary and Two-Stage Least Squares Estimands," IZA Discussion Papers 11866, Institute of Labor Economics (IZA).
    18. Kirill Borusyak & Xavier Jaravel & Jann Spiess, 2021. "Revisiting Event Study Designs: Robust and Efficient Estimation," Papers 2108.12419, arXiv.org, revised Jan 2024.
    19. Bhattacharjee, Arnab & Aravena, Claudia & Castillo, Natalia & Ehrlich, Marco & Taou, Nadia & Wagner, Thomas, 2022. "Agroforestry Programs in the Colombian Amazon: Selection, Treatment and Exposure Effects on Deforestation," National Institute of Economic and Social Research (NIESR) Discussion Papers 537, National Institute of Economic and Social Research.
    20. Don Fullerton & Chi L. Ta, 2022. "What Determines Effectiveness of Renewable Energy Standards? General Equilibrium Analytical Model and Empirical Analysis," CESifo Working Paper Series 9565, CESifo.

    More about this item

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • D72 - Microeconomics - - Analysis of Collective Decision-Making - - - Political Processes: Rent-seeking, Lobbying, Elections, Legislatures, and Voting Behavior
    • J31 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Wage Level and Structure; Wage Differentials
    • J51 - Labor and Demographic Economics - - Labor-Management Relations, Trade Unions, and Collective Bargaining - - - Trade Unions: Objectives, Structure, and Effects
    • L82 - Industrial Organization - - Industry Studies: Services - - - Entertainment; Media

    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:aea:aecrev:v:110:y:2020:i:9:p:2964-96. 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: Michael P. Albert (email available below). General contact details of provider: https://edirc.repec.org/data/aeaaaea.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.