IDEAS home Printed from https://ideas.repec.org/a/bla/ecinqu/v61y2023i2p402-412.html
   My bibliography  Save this article

Cautions when normalizing the dependent variable in a regression as a z‐score

Author

Listed:
  • Jeffrey Penney

Abstract

It is common in empirical analysis to facilitate inference by transforming the dependent variable to follow a standard normal distribution. In this paper, I show that using this transformation results in the estimated treatment effects being systematically attenuated toward zero and bounded in magnitude. The level of attenuation can be empirically relevant. I propose an alternative normalization wherein the dependent variable is divided by the square root of its within variation, which corrects these issues. I show that, in a simple linear regression, the method produces an estimated treatment effect that is numerically identical to Cohen's d.

Suggested Citation

  • Jeffrey Penney, 2023. "Cautions when normalizing the dependent variable in a regression as a z‐score," Economic Inquiry, Western Economic Association International, vol. 61(2), pages 402-412, April.
    • Handle: RePEc:bla:ecinqu:v:61:y:2023:i:2:p:402-412
    DOI: 10.1111/ecin.13127
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/ecin.13127
    Download Restriction: no
    File URL: https://libkey.io/10.1111/ecin.13127?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
    ---><---

    References listed on IDEAS

    as
    1. Alan B. Krueger, 1999. "Experimental Estimates of Education Production Functions," The Quarterly Journal of Economics, Oxford University Press, vol. 114(2), pages 497-532.
    2. Weili Ding & Steven F. Lehrer, 2010. "Estimating Treatment Effects from Contaminated Multiperiod Education Experiments: The Dynamic Impacts of Class Size Reductions," The Review of Economics and Statistics, MIT Press, vol. 92(1), pages 31-42, February.
    3. Duflo, Esther & Glennerster, Rachel & Kremer, Michael, 2008. "Using Randomization in Development Economics Research: A Toolkit," Handbook of Development Economics, in: T. Paul Schultz & John A. Strauss (ed.), Handbook of Development Economics, edition 1, volume 4, chapter 61, pages 3895-3962, Elsevier.
    4. Nick Huntington‐Klein & Andreu Arenas & Emily Beam & Marco Bertoni & Jeffrey R. Bloem & Pralhad Burli & Naibin Chen & Paul Grieco & Godwin Ekpe & Todd Pugatch & Martin Saavedra & Yaniv Stopnitzky, 2021. "The influence of hidden researcher decisions in applied microeconomics," Economic Inquiry, Western Economic Association International, vol. 59(3), pages 944-960, July.
    5. Blackburn, McKinley L., 2007. "Estimating wage differentials without logarithms," Labour Economics, Elsevier, vol. 14(1), pages 73-98, January.
    6. Krueger, Alan B & Whitmore, Diane M, 2001. "The Effect of Attending a Small Class in the Early Grades on College-Test Taking and Middle School Test Results: Evidence from Project STAR," Economic Journal, Royal Economic Society, vol. 111(468), pages 1-28, January.
    7. Ben Ost & Anuj Gangopadhyaya & Jeffrey C. Schiman, 2017. "Comparing standard deviation effects across contexts," Education Economics, Taylor & Francis Journals, vol. 25(3), pages 251-265, May.
    8. Mueller, Steffen, 2013. "Teacher experience and the class size effect — Experimental evidence," Journal of Public Economics, Elsevier, vol. 98(C), pages 44-52.
    9. Weili Ding, 2020. "Laboratory experiments can pre-design to address power and selection issues," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 6(2), pages 125-138, December.
    10. Weili Ding & Steven Lehrer, 2011. "Experimental estimates of the impacts of class size on test scores: robustness and heterogeneity," Education Economics, Taylor & Francis Journals, vol. 19(3), pages 229-252.
    11. Manning, Willard G. & Mullahy, John, 2001. "Estimating log models: to transform or not to transform?," Journal of Health Economics, Elsevier, vol. 20(4), pages 461-494, July.
    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. Graham McKee & Katharine Sims & Steven Rivkin, 2015. "Disruption, learning, and the heterogeneous benefits of smaller classes," Empirical Economics, Springer, vol. 48(3), pages 1267-1286, May.
    2. Jeffrey Penney, 2017. "Racial Interaction Effects and Student Achievement," Education Finance and Policy, MIT Press, vol. 12(4), pages 447-467, Fall.
    3. Jeffrey Penney, 2018. "Dynamic Treatment Effects Of Teacher'S Aides In An Experiment With Multiple Randomizations," Economic Inquiry, Western Economic Association International, vol. 56(2), pages 1244-1260, April.
    4. Marie Connolly & Catherine Haeck, 2018. "Le lien entre la taille des classes et les compétences cognitives et non cognitives," CIRANO Project Reports 2018rp-18, CIRANO.
    5. Weili Ding, 2020. "Laboratory experiments can pre-design to address power and selection issues," Journal of the Economic Science Association, Springer;Economic Science Association, vol. 6(2), pages 125-138, December.
    6. Ciani Emanuele & Fisher Paul, 2019. "Dif-in-Dif Estimators of Multiplicative Treatment Effects," Journal of Econometric Methods, De Gruyter, vol. 8(1), pages 1-10, January.
    7. Argaw, Bethlehem A. & Puhani, Patrick A., 2018. "Does class size matter for school tracking outcomes after elementary school? Quasi-experimental evidence using administrative panel data from Germany," Economics of Education Review, Elsevier, vol. 65(C), pages 48-57.
    8. Weili Ding & Steven Lehrer, 2011. "Experimental estimates of the impacts of class size on test scores: robustness and heterogeneity," Education Economics, Taylor & Francis Journals, vol. 19(3), pages 229-252.
    9. Ding, Weili & Lehrer, Steven F., 2014. "Understanding the role of time-varying unobserved ability heterogeneity in education production," Economics of Education Review, Elsevier, vol. 40(C), pages 55-75.
    10. Justman, Moshe, 2018. "Randomized controlled trials informing public policy: Lessons from project STAR and class size reduction," European Journal of Political Economy, Elsevier, vol. 54(C), pages 167-174.
    11. Mueller, Steffen, 2013. "Teacher experience and the class size effect — Experimental evidence," Journal of Public Economics, Elsevier, vol. 98(C), pages 44-52.
    12. Moshe Justman, 2016. "Economic Research and Education Policy: Project STAR and Class Size Reduction," Melbourne Institute Working Paper Series wp2016n37, Melbourne Institute of Applied Economic and Social Research, The University of Melbourne.
    13. Simone Balestra & Uschi Backes-Gellner, 2014. "Heterogeneous effects of pupil-to-teacher ratio policies - A look at class size reduction and teacher aide," Economics of Education Working Paper Series 0102, University of Zurich, Department of Business Administration (IBW), revised Apr 2017.
    14. Wo[ss]mann, Ludger & West, Martin, 2006. "Class-size effects in school systems around the world: Evidence from between-grade variation in TIMSS," European Economic Review, Elsevier, vol. 50(3), pages 695-736, April.
    15. Andersson, Christian, 2007. "Teacher density and student achievement in Swedish compulsory schools," Working Paper Series 2007:4, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    16. Giacomo De Giorgi & Michele Pellizzari & William Gui Woolston, 2012. "Class Size And Class Heterogeneity," Journal of the European Economic Association, European Economic Association, vol. 10(4), pages 795-830, August.
    17. Gilpin, Gregory A., 2012. "Teacher salaries and teacher aptitude: An analysis using quantile regressions," Economics of Education Review, Elsevier, vol. 31(3), pages 15-29.
    18. Stephen Machin & Sandra McNally, 2012. "The Evaluation of English Education Policies," National Institute Economic Review, National Institute of Economic and Social Research, vol. 219(1), pages 15-25, January.
    19. Stephen Machin & Sandra McNally & Martina Viarengo, 2018. "Changing How Literacy Is Taught: Evidence on Synthetic Phonics," American Economic Journal: Economic Policy, American Economic Association, vol. 10(2), pages 217-241, May.
    20. Alex Hollingsworth & Mike Huang & Ivan J. Rudik & Nicholas J. Sanders, 2020. "A Thousand Cuts: Cumulative Lead Exposure Reduces Academic Achievement," NBER Working Papers 28250, National Bureau of Economic Research, Inc.

    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:bla:ecinqu:v:61:y:2023:i:2:p:402-412. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/weaaaea.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.