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Thirty Years Of Heteroskedasticity-robust Inference

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  • James G. MacKinnon

    (Queen's University)

Abstract

White (1980) marked the beginning of a new era for inference in econometrics. It introduced the revolutionary idea of inference that is robust to heteroskedasticity of unknown form, an idea that was very soon extended to other forms of robust inference and also led to many new estimation methods. This paper discusses the development of heteroskedasticity-robust inference since 1980. There have been two principal lines of investigation. One approach has been to modify White`s original estimator to improve its finite-sample properties, and the other has been to use bootstrap methods. The relation between these two approaches, and some ways in which they may be combined, are discussed. Finally, a simulation experiment compares various methods and shows how far heteroskedasticity-robust inference has come in just over thirty years.

Suggested Citation

  • James G. MacKinnon, 2012. "Thirty Years Of Heteroskedasticity-robust Inference," Working Paper 1268, Economics Department, Queen's University.
  • Handle: RePEc:qed:wpaper:1268
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    File URL: https://www.econ.queensu.ca/sites/econ.queensu.ca/files/qed_wp_1268.pdf
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    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. A. Colin Cameron & Jonah B. Gelbach & Douglas L. Miller, 2008. "Bootstrap-Based Improvements for Inference with Clustered Errors," The Review of Economics and Statistics, MIT Press, vol. 90(3), pages 414-427, August.
    3. Cribari-Neto, Francisco, 2004. "Asymptotic inference under heteroskedasticity of unknown form," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 215-233, March.
    4. Whitney K. Newey & Kenneth D. West, 1994. "Automatic Lag Selection in Covariance Matrix Estimation," Review of Economic Studies, Oxford University Press, vol. 61(4), pages 631-653.
    5. Chesher, Andrew & Austin, Gerard, 1991. "The finite-sample distributions of heteroskedasticity robust Wald statistics," Journal of Econometrics, Elsevier, vol. 47(1), pages 153-173, January.
    6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    7. James G. MacKinnon & Jeff Racine, 2004. "Simulation-based Tests That Can Use Any Number Of Simulations," Working Paper 1027, Economics Department, Queen's University.
    8. James G. MacKinnon, 2002. "Bootstrap inference in econometrics," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 35(4), pages 615-645, November.
    9. Tony Lancaster, 2006. "A note on bootstraps and robustness," CeMMAP working papers CWP04/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Russell Davidson & James G. MacKinnon, 2014. "Confidence sets based on inverting Anderson–Rubin tests," Econometrics Journal, Royal Economic Society, vol. 17(2), pages 39-58, June.
    11. John C. Driscoll & Aart C. Kraay, 1998. "Consistent Covariance Matrix Estimation With Spatially Dependent Panel Data," The Review of Economics and Statistics, MIT Press, vol. 80(4), pages 549-560, November.
    12. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(3), pages 361-376, June.
    13. Flachaire, Emmanuel, 1999. "A better way to bootstrap pairs," Economics Letters, Elsevier, vol. 64(3), pages 257-262, September.
    14. Tsung-Wu Ho, 2001. "Finite-sample properties of the bootstrap estimator in a Markov-switching model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(7), pages 835-842.
    15. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
    16. Francisco Cribari-Neto & Maria Lima, 2010. "Sequences of bias-adjusted covariance matrix estimators under heteroskedasticity of unknown form," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(6), pages 1053-1082, December.
    17. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
    18. Flachaire, Emmanuel, 2005. "Bootstrapping heteroskedastic regression models: wild bootstrap vs. pairs bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 361-376, April.
    19. 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.
    20. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    21. Froot, Kenneth A., 1989. "Consistent Covariance Matrix Estimation with Cross-Sectional Dependence and Heteroskedasticity in Financial Data," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 24(3), pages 333-355, September.
    22. Paparoditis, Efstathios & Politis, Dimitris N., 2005. "Bootstrap hypothesis testing in regression models," Statistics & Probability Letters, Elsevier, vol. 74(4), pages 356-365, October.
    23. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    24. Davidson, Russell & MacKinnon, James G., 2006. "The power of bootstrap and asymptotic tests," Journal of Econometrics, Elsevier, vol. 133(2), pages 421-441, August.
    25. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    26. Chesher, Andrew & Jewitt, Ian, 1987. "The Bias of a Heteroskedasticity Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 55(5), pages 1217-1222, September.
    27. Horowitz, Joel L., 2001. "The bootstrap and hypothesis tests in econometrics," Journal of Econometrics, Elsevier, vol. 100(1), pages 37-40, January.
    28. 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.
    29. 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.
    30. Davidson, Russell & MacKinnon, James G., 2010. "Wild Bootstrap Tests for IV Regression," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 128-144.
    31. Horowitz, Joel L., 2001. "The Bootstrap," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 52, pages 3159-3228, Elsevier.
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    Cited by:

    1. MacKinnon, James G., 2020. "Wild cluster bootstrap confidence intervals," L'Actualité Economique, Société Canadienne de Science Economique, vol. 96(4), pages 721-743, Décembre.
    2. Guido W. Imbens & Michal Kolesár, 2016. "Robust Standard Errors in Small Samples: Some Practical Advice," The Review of Economics and Statistics, MIT Press, vol. 98(4), pages 701-712, October.
    3. Anatolyev, Stanislav, 2021. "Mallows criterion for heteroskedastic linear regressions with many regressors," Economics Letters, Elsevier, vol. 203(C).
    4. Romano, Joseph P. & Wolf, Michael, 2017. "Resurrecting weighted least squares," Journal of Econometrics, Elsevier, vol. 197(1), pages 1-19.
    5. Matias Cattaneo & Michael Jansson & Whitney K. Newey, 2015. "Treatment effects with many covariates and heteroskedasticity," CeMMAP working papers 37/15, Institute for Fiscal Studies.
    6. Matias D. Cattaneo & Michael Jansson & Whitney K. Newey, 2018. "Inference in Linear Regression Models with Many Covariates and Heteroscedasticity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 1350-1361, July.
    7. Cavaliere, Giuseppe & Nielsen, Morten Ørregaard & Taylor, A.M. Robert, 2015. "Bootstrap score tests for fractional integration in heteroskedastic ARFIMA models, with an application to price dynamics in commodity spot and futures markets," Journal of Econometrics, Elsevier, vol. 187(2), pages 557-579.
    8. Hansen, Bruce E. & Lee, Seojeong, 2019. "Asymptotic theory for clustered samples," Journal of Econometrics, Elsevier, vol. 210(2), pages 268-290.
    9. James G. MacKinnon & Matthew D. Webb, 2017. "Pitfalls When Estimating Treatment Effects Using Clustered Data," Working Paper 1387, Economics Department, Queen's University.
    10. DiCiccio, Cyrus J. & Romano, Joseph P. & Wolf, Michael, 2019. "Improving weighted least squares inference," Econometrics and Statistics, Elsevier, vol. 10(C), pages 96-119.
    11. Startz, Richard, 2012. "Bayesian Heteroskedasticity-Robust Standard Errors," University of California at Santa Barbara, Economics Working Paper Series qt69c4x8m9, Department of Economics, UC Santa Barbara.
    12. Neil Shephard, 2020. "An estimator for predictive regression: reliable inference for financial economics," Papers 2008.06130, arXiv.org.
    13. Cyrus J. DiCiccio & Joseph P. Romano & Michael Wolf, 2016. "Improving weighted least squares inference," ECON - Working Papers 232, Department of Economics - University of Zurich, revised Nov 2017.

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    More about this item

    Keywords

    wild bootstrap; HCCME; power; finite-sample;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General

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