IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2503.19178.html
   My bibliography  Save this paper

Automatic Inference for Value-Added Regressions

Author

Listed:
  • Tian Xie

Abstract

It is common to use shrinkage methods such as empirical Bayes to improve estimates of teacher value-added. However, when the goal is to perform inference on coefficients in the regression of long-term outcomes on value-added, it's unclear whether shrinking the value-added estimators can help or hurt. In this paper, we consider a general class of value-added estimators and the properties of their corresponding regression coefficients. Our main finding is that regressing long-term outcomes on shrinkage estimates of value-added performs an automatic bias correction: the associated regression estimator is asymptotically unbiased, asymptotically normal, and efficient in the sense that it is asymptotically equivalent to regressing on the true (latent) value-added. Further, OLS standard errors from regressing on shrinkage estimates are consistent. As such, efficient inference is easy for practitioners to implement: simply regress outcomes on shrinkage estimates of value added.

Suggested Citation

  • Tian Xie, 2025. "Automatic Inference for Value-Added Regressions," Papers 2503.19178, arXiv.org.
    • Handle: RePEc:arx:papers:2503.19178
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2503.19178
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Raj Chetty & Nathaniel Hendren, 2018. "The Impacts of Neighborhoods on Intergenerational Mobility II: County-Level Estimates," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(3), pages 1163-1228.
    2. Atila Abdulkadiroğlu & Parag A. Pathak & Jonathan Schellenberg & Christopher R. Walters, 2020. "Do Parents Value School Effectiveness?," American Economic Review, American Economic Association, vol. 110(5), pages 1502-1539, May.
    3. Gonçalves, Sílvia & Perron, Benoit, 2014. "Bootstrapping factor-augmented regression models," Journal of Econometrics, Elsevier, vol. 182(1), pages 156-173.
    4. Thomas J. Kane & Douglas O. Staiger, 2008. "Estimating Teacher Impacts on Student Achievement: An Experimental Evaluation," NBER Working Papers 14607, National Bureau of Economic Research, Inc.
    5. Joshua D. Angrist & Peter D. Hull & Parag A. Pathak & Christopher R. Walters, 2017. "Leveraging Lotteries for School Value-Added: Testing and Estimation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(2), pages 871-919.
    6. Raj Chetty & Nathaniel Hendren, 2018. "The Impacts of Neighborhoods on Intergenerational Mobility I: Childhood Exposure Effects," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(3), pages 1107-1162.
    7. Scott R. Baker & Nicholas Bloom & Steven J. Davis, 2016. "Measuring Economic Policy Uncertainty," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(4), pages 1593-1636.
    8. Patrick Kline & Evan K Rose & Christopher R Walters, 2022. "Systemic Discrimination Among Large U.S. Employers [“Teachers and Student Achievement in the Chicago Public High Schools,”]," The Quarterly Journal of Economics, Oxford University Press, vol. 137(4), pages 1963-2036.
    9. Brian A. Jacob & Lars Lefgren, 2008. "Can Principals Identify Effective Teachers? Evidence on Subjective Performance Evaluation in Education," Journal of Labor Economics, University of Chicago Press, vol. 26(1), pages 101-136.
    10. Patrick Kline & Raffaele Saggio & Mikkel Sølvsten, 2020. "Leave‐Out Estimation of Variance Components," Econometrica, Econometric Society, vol. 88(5), pages 1859-1898, September.
    11. Liran Einav & Amy Finkelstein & Neale Mahoney, 2022. "Producing Health: Measuring Value Added of Nursing Homes," NBER Working Papers 30228, National Bureau of Economic Research, Inc.
    12. Laura Battaglia & Timothy M. Christensen & Stephen Hansen & Szymon Sacher, 2024. "Inference for regression with variables generated from unstructured data," CeMMAP working papers 10/24, Institute for Fiscal Studies.
    13. Bonhomme, Stéphane & Denis, Angela, 2024. "Estimating heterogeneous effects: Applications to labor economics," Labour Economics, Elsevier, vol. 91(C).
    14. Jiafeng Chen & Jiaying Gu & Soonwoo Kwon, 2025. "Empirical Bayes shrinkage (mostly) does not correct the measurement error in regression," Papers 2503.19095, arXiv.org.
    15. Michael Gilraine & Jiaying Gu & Robert McMillan, 2020. "A New Method for Estimating Teacher Value-Added," NBER Working Papers 27094, National Bureau of Economic Research, Inc.
    16. Andrei Zeleneev & Kirill Evdokimov, 2023. "Simple estimation of semiparametric models with measurement errors," CeMMAP working papers 10/23, Institute for Fiscal Studies.
    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. Walters, Christopher, 2024. "Empirical Bayes methods in labor economics," Handbook of Labor Economics,, Elsevier.
    2. Timothy B. Armstrong & Michal Kolesár & Mikkel Plagborg‐Møller, 2022. "Robust Empirical Bayes Confidence Intervals," Econometrica, Econometric Society, vol. 90(6), pages 2567-2602, November.
    3. Raffaella Giacomini & Sokbae Lee & Silvia Sarpietro, 2023. "Individual Shrinkage for Random Effects," Papers 2308.01596, arXiv.org, revised May 2025.
    4. Christine Mulhern & Isaac M. Opper, 2021. "Measuring and Summarizing the Multiple Dimensions of Teacher Effectiveness," CESifo Working Paper Series 9263, CESifo.
    5. Bar, M.; & Bakx, P.; & Wouterse, B.; & van Doorslaer, Eddy.;, 2022. "Estimating the health value added by nursing homes," Health, Econometrics and Data Group (HEDG) Working Papers 22/12, HEDG, c/o Department of Economics, University of York.
    6. Bonhomme, Stéphane & Denis, Angela, 2024. "Estimating heterogeneous effects: Applications to labor economics," Labour Economics, Elsevier, vol. 91(C).
    7. Bär, Marlies & Bakx, Pieter & Wouterse, Bram & van Doorslaer, Eddy, 2022. "Estimating the health value added by nursing homes," Journal of Economic Behavior & Organization, Elsevier, vol. 203(C), pages 1-23.
    8. Nirav Mehta, 2019. "Measuring quality for use in incentive schemes: The case of “shrinkage” estimators," Quantitative Economics, Econometric Society, vol. 10(4), pages 1537-1577, November.
    9. Valentin Verdier, 2020. "Estimation and Inference for Linear Models with Two-Way Fixed Effects and Sparsely Matched Data," The Review of Economics and Statistics, MIT Press, vol. 102(1), pages 1-16, March.
    10. Raffaella Giacomini & Sokbae Lee & Silvia Sarpietro, 2023. "A Robust Method for Microforecasting and Estimation of Random Effects," Working Paper Series WP 2023-26, Federal Reserve Bank of Chicago.
    11. Laura Battaglia & Timothy Christensen & Stephen Hansen & Szymon Sacher, 2024. "Inference for Regression with Variables Generated by AI or Machine Learning," Papers 2402.15585, arXiv.org, revised Apr 2025.
    12. Mookerjee, Sulagna & Slichter, David, 2023. "Test scores, schools, and the geography of economic opportunity," Journal of Urban Economics, Elsevier, vol. 137(C).
    13. Anatolyev, Stanislav & Sølvsten, Mikkel, 2023. "Testing many restrictions under heteroskedasticity," Journal of Econometrics, Elsevier, vol. 236(1).
    14. Timothy B. Armstrong & Michal Koles'ar & Mikkel Plagborg-M{o}ller, 2020. "Robust Empirical Bayes Confidence Intervals," Papers 2004.03448, arXiv.org, revised May 2022.
    15. Mariana Laverde & Elton Mykerezi & Aaron Sojourner & Aradhya Sood, 2025. "Gains from Alternative Assignment? Evidence from a Two-Sided Teacher Market," Boston College Working Papers in Economics 1085, Boston College Department of Economics.
    16. Kline, Patrick & Walters, Christopher, 2019. "Audits as Evidence: Experiments, Ensembles, and Enforcement," Institute for Research on Labor and Employment, Working Paper Series qt3z72m9kn, Institute of Industrial Relations, UC Berkeley.
    17. David Card & Jesse Rothstein & Moises Yi, 2024. "Industry Wage Differentials: A Firm-Based Approach," Journal of Labor Economics, University of Chicago Press, vol. 42(S1), pages 11-59.
    18. Jack Mountjoy & Brent Hickman, 2020. "The Returns to College(s): Estimating Value-Added and Match Effects in Higher Education," Working Papers 2020-08, Becker Friedman Institute for Research In Economics.
    19. Bruhn, Jesse & Imberman, Scott & Winters, Marcus, 2022. "Regulatory arbitrage in teacher hiring and retention: Evidence from Massachusetts Charter Schools," Journal of Public Economics, Elsevier, vol. 215(C).
    20. Patrick Kline & Raffaele Saggio & Mikkel Sølvsten, 2020. "Leave‐Out Estimation of Variance Components," Econometrica, Econometric Society, vol. 88(5), pages 1859-1898, September.

    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:2503.19178. 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.