IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v168y2021ics0167715220302480.html
   My bibliography  Save this article

The Frisch–Waugh–Lovell theorem for standard errors

Author

Listed:
  • Ding, Peng

Abstract

The Frisch–Waugh–Lovell Theorem states the equivalence of the coefficients from the full and partial regressions. I further show the equivalence between various standard errors. Applying the new result to stratified experiments reveals the discrepancy between model-based and design-based standard errors.

Suggested Citation

  • Ding, Peng, 2021. "The Frisch–Waugh–Lovell theorem for standard errors," Statistics & Probability Letters, Elsevier, vol. 168(C).
    • Handle: RePEc:eee:stapro:v:168:y:2021:i:c:s0167715220302480
    DOI: 10.1016/j.spl.2020.108945
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715220302480
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2020.108945?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. T. Lumley & P. Heagerty, 1999. "Weighted empirical adaptive variance estimators for correlated data regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 459-477, April.
    3. Michael C. Lovell, 1963. "Seasonal Adjustment of Economic Time Series and Multiple Regression," Cowles Foundation Discussion Papers 151, Cowles Foundation for Research in Economics, Yale University.
    4. 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.
    5. Joshua Angrist & Philip Oreopoulos & Tyler Williams, 2014. "When Opportunity Knocks, Who Answers?: New Evidence on College Achievement Awards," Journal of Human Resources, University of Wisconsin Press, vol. 49(3), pages 572-610.
    6. A. Colin Cameron & Douglas L. Miller, 2015. "A Practitioner’s Guide to Cluster-Robust Inference," Journal of Human Resources, University of Wisconsin Press, vol. 50(2), pages 317-372.
    7. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(4), pages 631-653.
    8. Zeileis, Achim, 2004. "Econometric Computing with HC and HAC Covariance Matrix Estimators," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i10).
    9. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    10. 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.
    11. Luke W. Miratrix & Jasjeet S. Sekhon & Bin Yu, 2013. "Adjusting treatment effect estimates by post-stratification in randomized experiments," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(2), pages 369-396, March.
    12. 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.
    13. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    14. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    15. MacKinnon, James G. & White, Halbert, 1985. "Some heteroskedasticity-consistent covariance matrix estimators with improved finite sample properties," Journal of Econometrics, Elsevier, vol. 29(3), pages 305-325, September.
    16. 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.
    17. 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. Deepankar Basu, 2023. "The Yule-Frisch-Waugh-Lovell Theorem," Papers 2307.00369, arXiv.org.
    2. Deepankar Basu, 2023. "The Yule-Frisch-Waugh-Lovell Theorem for Linear Instrumental Variables Estimation," Papers 2307.12731, arXiv.org, revised Aug 2023.
    3. Peng Ding, 2022. "Peng Ding’s contribution to the Discussion of ‘Assumption‐lean inference for generalised linear model parameters’ by Vansteelandt and Dukes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(3), pages 691-693, July.
    4. Zhao, Anqi & Ding, Peng, 2024. "No star is good news: A unified look at rerandomization based on p-values from covariate balance tests," Journal of Econometrics, Elsevier, vol. 241(1).
    5. Ding Peng, 2021. "Two seemingly paradoxical results in linear models: the variance inflation factor and the analysis of covariance," Journal of Causal Inference, De Gruyter, vol. 9(1), pages 1-8, January.

    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. Peng Ding, 2020. "The Frisch--Waugh--Lovell Theorem for Standard Errors," Papers 2009.06621, arXiv.org.
    2. Hartigan, Luke, 2018. "Alternative HAC covariance matrix estimators with improved finite sample properties," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 55-73.
    3. James G. MacKinnon, 2012. "Thirty Years Of Heteroskedasticity-robust Inference," Working Paper 1268, Economics Department, Queen's University.
    4. repec:jss:jstsof:11:i10 is not listed on IDEAS
    5. Härdle, Wolfgang & Horowitz, Joel L. & Kreiss, Jens-Peter, 2001. "Bootstrap methods for time series," SFB 373 Discussion Papers 2001,59, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    6. Helene Hamisultane, 2010. "Utility-based pricing of weather derivatives," The European Journal of Finance, Taylor & Francis Journals, vol. 16(6), pages 503-525.
    7. Jushan Bai & Sung Hoon Choi & Yuan Liao, 2021. "Feasible generalized least squares for panel data with cross-sectional and serial correlations," Empirical Economics, Springer, vol. 60(1), pages 309-326, January.
    8. Hirukawa, Masayuki, 2023. "Robust Covariance Matrix Estimation in Time Series: A Review," Econometrics and Statistics, Elsevier, vol. 27(C), pages 36-61.
    9. Clark, Todd & McCracken, Michael, 2013. "Advances in Forecast Evaluation," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 1107-1201, Elsevier.
    10. Issler, João Victor & Soares, Ana Flávia, 2019. "Central Bank credibility and inflation expectations: a microfounded forecasting approach," FGV EPGE Economics Working Papers (Ensaios Economicos da EPGE) 812, EPGE Brazilian School of Economics and Finance - FGV EPGE (Brazil).
    11. Politis, D N, 2009. "Higher-Order Accurate, Positive Semi-definite Estimation of Large-Sample Covariance and Spectral Density Matrices," University of California at San Diego, Economics Working Paper Series qt66w826hz, Department of Economics, UC San Diego.
    12. Alastair R. Hall, 2015. "Econometricians Have Their Moments: GMM at 32," The Economic Record, The Economic Society of Australia, vol. 91(S1), pages 1-24, June.
    13. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(6), pages 1130-1164, December.
    14. repec:jss:jstsof:16:i09 is not listed on IDEAS
    15. Politis, Dimitris, 2005. "Higher-order accurate, positive semi-definite estimation of large-sample covariance and spectral density matrices," University of California at San Diego, Economics Working Paper Series qt7qg2m9rz, Department of Economics, UC San Diego.
    16. Inoue, Atsushi & Shintani, Mototsugu, 2006. "Bootstrapping GMM estimators for time series," Journal of Econometrics, Elsevier, vol. 133(2), pages 531-555, August.
    17. Chistiano, Lawrence J & den Haan, Wouter J, 1996. "Small-Sample Properties of GMM for Business-Cycle Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(3), pages 309-327, July.
    18. Scott Gilbert & Petr Zemčík, 2005. "Testing for Latent Factors in Models with Autocorrelation and Heteroskedasticity of Unknown Form," Southern Economic Journal, John Wiley & Sons, vol. 72(1), pages 236-252, July.
    19. Fitzenberger, Bernd, 1998. "The moving blocks bootstrap and robust inference for linear least squares and quantile regressions," Journal of Econometrics, Elsevier, vol. 82(2), pages 235-287, February.
    20. Preinerstorfer, David, 2014. "Finite Sample Properties of Tests Based on Prewhitened Nonparametric Covariance Estimators," MPRA Paper 58333, University Library of Munich, Germany.
    21. repec:jss:jstsof:34:i11 is not listed on IDEAS
    22. Giacomini, Raffaella & Komunjer, Ivana, 2005. "Evaluation and Combination of Conditional Quantile Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 416-431, October.
    23. Zeileis, Achim, 2004. "Econometric Computing with HC and HAC Covariance Matrix Estimators," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 11(i10).

    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:eee:stapro:v:168:y:2021:i:c:s0167715220302480. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.