[go: up one dir, main page]
IDEAS home Printed from https://ideas.repec.org/p/iza/izadps/dp13283.html
   My bibliography  Save this paper

Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights

Author

Listed:
  • Sloczynski, Tymon

    (Brandeis University)

Abstract
Applied work often studies the effect of a binary variable ("treatment") using linear models with additive effects. I study the interpretation of the OLS estimands in such models when treatment effects are heterogeneous. I show that the treatment coefficient is a convex combination of two parameters, which under certain conditions can be interpreted as the average treatment effects on the treated and untreated. The weights on these parameters are inversely related to the proportion of observations in each group. Reliance on these implicit weights can have serious consequences for applied work, as I illustrate with two well-known applications. I develop simple diagnostic tools that empirical researchers can use to avoid potential biases. Software for implementing these methods is available in R and Stata. In an important special case, my diagnostics only require the knowledge of the proportion of treated units.

Suggested Citation

  • Sloczynski, Tymon, 2020. "Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights," IZA Discussion Papers 13283, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp13283
    as

    Download full text from publisher

    File URL: https://docs.iza.org/dp13283.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Marianne P. Bitler & Jonah B. Gelbach & Hilary W. Hoynes, 2006. "What Mean Impacts Miss: Distributional Effects of Welfare Reform Experiments," American Economic Review, American Economic Association, vol. 96(4), pages 988-1012, September.
    2. Elder, Todd E. & Goddeeris, John H. & Haider, Steven J., 2010. "Unexplained gaps and Oaxaca-Blinder decompositions," Labour Economics, Elsevier, vol. 17(1), pages 284-290, January.
    3. Alberto Alesina & Paola Giuliano & Nathan Nunn, 2013. "On the Origins of Gender Roles: Women and the Plough," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 128(2), pages 469-530.
    4. Fortin, Nicole & Lemieux, Thomas & Firpo, Sergio, 2011. "Decomposition Methods in Economics," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 4, chapter 1, pages 1-102, Elsevier.
    5. Nico Voigtländer & Hans-Joachim Voth, 2012. "Persecution Perpetuated: The Medieval Origins of Anti-Semitic Violence in Nazi Germany," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(3), pages 1339-1392.
    6. Oaxaca, Ronald, 1973. "Male-Female Wage Differentials in Urban Labor Markets," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 14(3), pages 693-709, October.
    7. Graham, Bryan S. & Pinto, Cristine Campos de Xavier, 2022. "Semiparametrically efficient estimation of the average linear regression function," Journal of Econometrics, Elsevier, vol. 226(1), pages 115-138.
    8. Joshua D. Angrist & Jörn-Steffen Pischke, 2009. "Mostly Harmless Econometrics: An Empiricist's Companion," Economics Books, Princeton University Press, edition 1, number 8769.
    9. David Card & Jochen Kluve & Andrea Weber, 2018. "What Works? A Meta Analysis of Recent Active Labor Market Program Evaluations," Journal of the European Economic Association, European Economic Association, vol. 16(3), pages 894-931.
    10. Alan S. Blinder, 1973. "Wage Discrimination: Reduced Form and Structural Estimates," Journal of Human Resources, University of Wisconsin Press, vol. 8(4), pages 436-455.
    11. James J. Heckman, 2001. "Micro Data, Heterogeneity, and the Evaluation of Public Policy: Nobel Lecture," Journal of Political Economy, University of Chicago Press, vol. 109(4), pages 673-748, August.
    12. Gary Solon & Steven J. Haider & Jeffrey M. Wooldridge, 2015. "What Are We Weighting For?," Journal of Human Resources, University of Wisconsin Press, vol. 50(2), pages 301-316.
    13. Guido W. Imbens, 2015. "Matching Methods in Practice: Three Examples," Journal of Human Resources, University of Wisconsin Press, vol. 50(2), pages 373-419.
    14. A. Smith, Jeffrey & E. Todd, Petra, 2005. "Does matching overcome LaLonde's critique of nonexperimental estimators?," Journal of Econometrics, Elsevier, vol. 125(1-2), pages 305-353.
    15. Akanksha Negi & Jeffrey M. Wooldridge, 2021. "Revisiting regression adjustment in experiments with heterogeneous treatment effects," Econometric Reviews, Taylor & Francis Journals, vol. 40(5), pages 504-534, April.
    16. Joshua D. Angrist, 1998. "Estimating the Labor Market Impact of Voluntary Military Service Using Social Security Data on Military Applicants," Econometrica, Econometric Society, vol. 66(2), pages 249-288, March.
    17. 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.
    18. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, April.
    19. LaLonde, Robert J, 1986. "Evaluating the Econometric Evaluations of Training Programs with Experimental Data," American Economic Review, American Economic Association, vol. 76(4), pages 604-620, September.
    20. Alberto Abadie & Susan Athey & Guido W. Imbens & Jeffrey M. Wooldridge, 2020. "Sampling‐Based versus Design‐Based Uncertainty in Regression Analysis," Econometrica, Econometric Society, vol. 88(1), pages 265-296, January.
    21. Anna Aizer & Shari Eli & Joseph Ferrie & Adriana Lleras-Muney, 2016. "The Long-Run Impact of Cash Transfers to Poor Families," American Economic Review, American Economic Association, vol. 106(4), pages 935-971, April.
    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. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881, September.
    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. Paul Goldsmith-Pinkham & Peter Hull & Michal Kolesár, 2024. "Contamination Bias in Linear Regressions," American Economic Review, American Economic Association, vol. 114(12), pages 4015-4051, December.
    2. Paul Goldsmith-Pinkham & Peter Hull & Michal Kolesár, 2024. "Contamination Bias in Linear Regressions," American Economic Review, American Economic Association, vol. 114(12), pages 4015-4051, December.
    3. 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.
    4. Florian Léon & Laurent Weill, 2024. "Elections hinder firms' access to credit," Economics of Transition and Institutional Change, John Wiley & Sons, vol. 32(1), pages 73-107, January.
    5. Jiang, Lingqing & Zhu, Zhen, 2022. "Information exchange and multiple peer groups: A natural experiment in an online community," Journal of Economic Behavior & Organization, Elsevier, vol. 203(C), pages 543-562.

    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. 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).
    2. Tymon S{l}oczy'nski, 2018. "Interpreting OLS Estimands When Treatment Effects Are Heterogeneous: Smaller Groups Get Larger Weights," Papers 1810.01576, arXiv.org, revised May 2020.
    3. Słoczyński, Tymon, 2012. "New Evidence on Linear Regression and Treatment Effect Heterogeneity," MPRA Paper 39524, University Library of Munich, Germany.
    4. Tymon Słoczyński, 2020. "Average Gaps and Oaxaca–Blinder Decompositions: A Cautionary Tale about Regression Estimates of Racial Differences in Labor Market Outcomes," ILR Review, Cornell University, ILR School, vol. 73(3), pages 705-729, May.
    5. Sloczynski, Tymon, 2018. "Average Gaps and Oaxaca's Blinder Decompositions: A Cautionary Tale about Regression Estimates of Racial Differences in Labor Market Outcomes," IZA Discussion Papers 12041, Institute of Labor Economics (IZA).
    6. Jeffrey Smith & Arthur Sweetman, 2016. "Viewpoint: Estimating the causal effects of policies and programs," Canadian Journal of Economics, Canadian Economics Association, vol. 49(3), pages 871-905, August.
    7. Tymon Słoczyński, 2015. "The Oaxaca–Blinder Unexplained Component as a Treatment Effects Estimator," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(4), pages 588-604, August.
    8. Advani, Arun & Sloczynski, Tymon, 2013. "Mostly Harmless Simulations? On the Internal Validity of Empirical Monte Carlo Studies," IZA Discussion Papers 7874, Institute of Labor Economics (IZA).
    9. Sloczynski, Tymon, 2015. "Average Wage Gaps and Oaxaca–Blinder Decompositions," IZA Discussion Papers 9036, Institute of Labor Economics (IZA).
    10. Hugo Ñopo, 2008. "Matching as a Tool to Decompose Wage Gaps," The Review of Economics and Statistics, MIT Press, vol. 90(2), pages 290-299, May.
    11. Goodman-Bacon, Andrew, 2021. "Difference-in-differences with variation in treatment timing," Journal of Econometrics, Elsevier, vol. 225(2), pages 254-277.
    12. Ferman, Bruno, 2021. "Matching estimators with few treated and many control observations," Journal of Econometrics, Elsevier, vol. 225(2), pages 295-307.
    13. Boris Kaiser, 2016. "Decomposing differences in arithmetic means: a doubly robust estimation approach," Empirical Economics, Springer, vol. 50(3), pages 873-899, May.
    14. Castro, Juan F. & Rolleston, Caine, 2018. "The contribution of early childhood and schools to cognitive gaps: New evidence from Peru," Economics of Education Review, Elsevier, vol. 64(C), pages 144-164.
    15. Dehejia Rajeev, 2015. "Experimental and Non-Experimental Methods in Development Economics: A Porous Dialectic," Journal of Globalization and Development, De Gruyter, vol. 6(1), pages 47-69, June.
    16. Oaxaca, Ronald L. & Choe, Chung, 2016. "Wage Decompositions Using Panel Data Sample Selection Correction," IZA Discussion Papers 10157, Institute of Labor Economics (IZA).
    17. Essama-Nssah, B., 2012. "Identification of sources of variation in poverty outcomes," Policy Research Working Paper Series 5954, The World Bank.
    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. Victor Chernozhukov & Iván Fernández‐Val & Blaise Melly, 2013. "Inference on Counterfactual Distributions," Econometrica, Econometric Society, vol. 81(6), pages 2205-2268, November.
    20. James Cloyne & Òscar Jordà & Alan M. Taylor, 2020. "Decomposing the Fiscal Multiplier," Working Paper Series 2020-12, Federal Reserve Bank of San Francisco.

    More about this item

    Keywords

    linear regression; model diagnostics; model misspecification; ordinary least squares; propensity score; heterogeneity; treatment effects;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect 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

    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:iza:izadps:dp13283. 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: Holger Hinte (email available below). General contact details of provider: https://edirc.repec.org/data/izaaade.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.