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The Frisch--Waugh--Lovell Theorem for Standard Errors

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  • Peng Ding

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.

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  • Peng Ding, 2020. "The Frisch--Waugh--Lovell Theorem for Standard Errors," Papers 2009.06621, arXiv.org.
  • Handle: RePEc:arx:papers:2009.06621
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    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. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Imbens,Guido W. & Rubin,Donald B., 2015. "Causal Inference for Statistics, Social, and Biomedical Sciences," Cambridge Books, Cambridge University Press, number 9780521885881.
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