IDEAS home Printed from https://ideas.repec.org/a/aea/jecper/v36y2022i4p193-204.html
   My bibliography  Save this article

A Linear Panel Model with Heterogeneous Coefficients and Variation in Exposure

Author

Listed:
  • Liyang Sun
  • Jesse M. Shapiro

Abstract

Linear panel models featuring unit and time fixed effects appear in many areas of empirical economics. An active literature studies the interpretation of the ordinary least squares estimator of the model, commonly called the two-way fixed effects (TWFE) estimator, in the presence of unmodeled coefficient heterogeneity. We illustrate some implications for the case where the research design takes advantage of variation across units (say, US states) in exposure to some treatment (say, a policy change). In this case, the TWFE can fail to estimate the average (or even a weighted average) of the units' coefficients. Under some conditions, there exists no estimator that is guaranteed to estimate even a weighted average. Building on the literature, we note that when there is a unit totally unaffected by treatment, it is possible to estimate an average effect by replacing the TWFE with an average of difference-in-differences estimators.

Suggested Citation

  • 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.
    • Handle: RePEc:aea:jecper:v:36:y:2022:i:4:p:193-204
    DOI: 10.1257/jep.36.4.193
    as

    Download full text from publisher

    File URL: https://www.aeaweb.org/doi/10.1257/jep.36.4.193
    Download Restriction: no
    File URL: https://www.aeaweb.org/doi/10.1257/jep.36.4.193.appx
    Download Restriction: no
    File URL: https://www.aeaweb.org/doi/10.1257/jep.36.4.193.ds
    Download Restriction: no
    File URL: https://libkey.io/10.1257/jep.36.4.193?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. Goodman-Bacon, Andrew, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, Elsevier, vol. 225(2), pages 254-277.
    3. 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.
    4. 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.
    5. James J. Heckman & Vytlacil, Edward J., 2007. "Econometric Evaluation of Social Programs, Part II: Using the Marginal Treatment Effect to Organize Alternative Econometric Estimators to Evaluate Social Programs, and to Forecast their Effects in New," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 71, Elsevier.
    6. 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.
    7. Nathan Nunn & Nancy Qian, 2011. "The Potato's Contribution to Population and Urbanization: Evidence From A Historical Experiment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 126(2), pages 593-650.
    8. 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.
    9. Sant’Anna, Pedro H.C. & Zhao, Jun, 2020. "Doubly robust difference-in-differences estimators," Journal of Econometrics, Elsevier, vol. 219(1), pages 101-122.
    10. J.J. Heckman & E.E. Leamer (ed.), 2007. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 6, number 6a.
    11. J.J. Heckman & E.E. Leamer (ed.), 2007. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 6, number 6b.
    12. 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.
    13. 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.
    14. 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.
    15. de Chaisemartin, Clement & D'Haultfoeuille, Xavier, 2014. "Fuzzy Changes-in Changes," CAGE Online Working Paper Series 184, Competitive Advantage in the Global Economy (CAGE).
    16. Oeindrila Dube & Juan F. Vargas, 2013. "Commodity Price Shocks and Civil Conflict: Evidence from Colombia," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(4), pages 1384-1421.
    17. Amy Finkelstein, 2007. "The Aggregate Effects of Health Insurance: Evidence from the Introduction of Medicare," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(1), pages 1-37.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Millimet, Daniel L. & Bellemare, Marc, 2023. "Fixed Effects and Causal Inference," IZA Discussion Papers 16202, Institute of Labor Economics (IZA).
    2. repec:ags:aaea22:335779 is not listed on IDEAS
    3. Lachhab, Rania & Sears, Molly, 2024. "Silver Bullets: Cloud Seeding and Water Resources in California," 2024 Annual Meeting, July 28-30, New Orleans, LA 343893, Agricultural and Applied Economics Association.
    4. Pourya Valizadeh & Bart L. Fischer & Henry L. Bryant, 2024. "SNAP enrollment cycles: New insights from heterogeneous panel models with cross‐sectional dependence," American Journal of Agricultural Economics, John Wiley & Sons, vol. 106(1), pages 354-381, January.
    5. Elizabeth C. Klee & Adair Morse & Chaehee Shin, 2024. "Auto Finance in the Electric Vehicle Transition," Finance and Economics Discussion Series 2024-065, Board of Governors of the Federal Reserve System (U.S.).
    6. Gregory Faletto, 2023. "Fused Extended Two-Way Fixed Effects for Difference-in-Differences With Staggered Adoptions," Papers 2312.05985, arXiv.org, revised Oct 2024.
    7. Arindrajit Dube & Attila S. Lindner, 2024. "Minimum Wages in the 21st Century," NBER Working Papers 32878, National Bureau of Economic Research, Inc.
    8. Khambai Khamjalas, 2024. "Nexuses between Food, Energy, and Water Consumption on Urban-Rural Income Gap in South-Eastern Asian Countries Using Difference in Difference in Modelling Technique," International Journal of Economics and Financial Issues, Econjournals, vol. 14(2), pages 186-195, March.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. Isabelle Chort & Berk Öktem, 2024. "Agricultural shocks, coping policies and deforestation: Evidence from the coffee leaf rust epidemic in Mexico," American Journal of Agricultural Economics, John Wiley & Sons, vol. 106(3), pages 1020-1057, May.
    6. Marcus Roller, Daniel Steinberg, 2023. "Differences-in-Differences with multiple Treatments under Control," Diskussionsschriften credresearchpaper41, Universitaet Bern, Departement Volkswirtschaft - CRED.
    7. 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).
    8. Dalia Ghanem & Pedro H. C. Sant'Anna & Kaspar Wüthrich, 2022. "Selection and Parallel Trends," CESifo Working Paper Series 9910, CESifo.
    9. 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.
    10. 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.
    11. Jaraitė, Jūratė & Kurtyka, Oliwia & Ollivier, Hélène, 2022. "Take a ride on the (not so) green side: How do CDM projects affect Indian manufacturing firms’ environmental performance?," Journal of Environmental Economics and Management, Elsevier, vol. 114(C).
    12. Xin Nie & Jianxian Wu & Han Wang & Weijuan Li & Chengdao Huang & Lihua Li, 2022. "Contributing to carbon peak: Estimating the causal impact of eco‐industrial parks on low‐carbon development in China," Journal of Industrial Ecology, Yale University, vol. 26(4), pages 1578-1593, August.
    13. 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.
    14. Kayaoglu, Aysegul, 2022. "Do refugees cause crime?," World Development, Elsevier, vol. 154(C).
    15. Jiménez, Bruno & Rendon, Silvio, 2023. "Does employment protection unprotect workers? The labor market effects of job reinstatements in Peru," Labour Economics, Elsevier, vol. 80(C).
    16. 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).
    17. Jean-Victor Alipour & Valentin Lindlacher, 2022. "No Surprises, Please: Voting Costs and Electoral Turnout," CESifo Working Paper Series 9759, CESifo.
    18. Alexander Karaivanov & Dongwoo Kim & Shih En Lu & Hitoshi Shigeoka, 2022. "COVID-19 vaccination mandates and vaccine uptake," Nature Human Behaviour, Nature, vol. 6(12), pages 1615-1624, December.
    19. Robert Reinhardt, 2022. "Shaking up Foreign Finance: FDI in a Post-Disaster World," Working Papers halshs-03908250, HAL.
    20. Dmitry Arkhangelsky & Guido Imbens, 2023. "Causal Models for Longitudinal and Panel Data: A Survey," Papers 2311.15458, arXiv.org, revised Jun 2024.

    More about this item

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • H51 - Public Economics - - National Government Expenditures and Related Policies - - - Government Expenditures and Health
    • I13 - Health, Education, and Welfare - - Health - - - Health Insurance, Public and Private
    • I18 - Health, Education, and Welfare - - Health - - - Government Policy; Regulation; Public Health
    • J14 - Labor and Demographic Economics - - Demographic Economics - - - Economics of the Elderly; Economics of the Handicapped; Non-Labor Market Discrimination

    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:jecper:v:36:y:2022:i:4:p:193-204. 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.