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More Efficient Tests Robust to Heteroskedasticity of Unknown Form

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  • Emmanuel Flachaire

Abstract

In the presence of heteroskedasticity of unknown form, the Ordinary Least Squares parameter estimator becomes inefficient, and its covariance matrix estimator inconsistent. Eicker (1963) and White (1980) were the first to propose a robust consistent covariance matrix estimator, that permits asymptotically correct inference. This estimator is widely used in practice. Cragg (1983) proposed a more efficient estimator, but concluded that tests basd on it are unreliable. Thus, this last estimator has not been used in practice. This article is concerned with finite sample properties of tests robust to heteroskedasticity of unknown form. Our results suggest that reliable and more efficient tests can be obtained with the Cragg estimators in small samples.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Econometric Reviews.

Volume (Year): 24 (2005)
Issue (Month): 2 ()
Pages: 219-241

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Handle: RePEc:taf:emetrv:v:24:y:2005:i:2:p:219-241

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Related research

Keywords: Heteroskedasticity-robust test; Regression model; Wild bootstrap;

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References

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  1. Hansen, Lars Peter, 1985. "A method for calculating bounds on the asymptotic covariance matrices of generalized method of moments estimators," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 203-238.
  2. Cragg, John G, 1983. "More Efficient Estimation in the Presence of Heteroscedasticity of Unknown Form," Econometrica, Econometric Society, vol. 51(3), pages 751-63, May.
  3. Russell Davidson & James G. MacKinnon, 2001. "Bootstrap Tests: How Many Bootstraps?," Working Papers 1036, Queen's University, Department of Economics.
  4. Gonçalves, Sílvia & KILIAN, Lutz, 2003. "Bootstrapping Autoregressions with Conditional Heteroskedasticity of Unknown Form," Cahiers de recherche 01-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  5. DAVIDSON, Russel & MACKINNON, James G., . "Heteroskedastcity-robust tests in regressions directions," CORE Discussion Papers RP -678, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. repec:hal:cesptp:halshs-00175910 is not listed on IDEAS
  7. Russell Davidson & Emmanuel Flachaire, 2001. "The Wild Bootstrap, Tamed at Last," Working Papers 1000, Queen's University, Department of Economics.
  8. Maurice Obstfeld & Robert E. Cumby & John Huizinga, 1983. "Two-Step Two-Stage Least Squares Estimation in Models with Rational Expectations," NBER Technical Working Papers 0011, National Bureau of Economic Research, Inc.
  9. Chesher, Andrew & Jewitt, Ian, 1987. "The Bias of a Heteroskedasticity Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 55(5), pages 1217-22, September.
  10. James G. MacKinnon & Halbert White, 1983. "Some Heteroskedasticity Consistent Covariance Matrix Estimators with Improved Finite Sample Properties," Working Papers 537, Queen's University, Department of Economics.
  11. James G. MacKinnon, 2002. "Bootstrap inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 35(4), pages 615-645, November.
  12. Emmanuel Flachaire, 1999. "A better way to bootstrap pairs," Post-Print halshs-00175892, HAL.
  13. Godfrey, Leslie G. & Orme, Chris D., 2004. "Controlling the finite sample significance levels of heteroskedasticity-robust tests of several linear restrictions on regression coefficients," Economics Letters, Elsevier, vol. 82(2), pages 281-287, February.
  14. Flachaire, Emmanuel, 2005. "Bootstrapping heteroskedastic regression models: wild bootstrap vs. pairs bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 361-376, April.
  15. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996.
  16. Davidson, R., 2000. "Bootstrap Confidence Intervals Based on Inverting Hypothesis Tests," G.R.E.Q.A.M. 00a09, Universite Aix-Marseille III.
  17. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
  18. repec:hal:cesptp:halshs-00175897 is not listed on IDEAS
  19. repec:fth:louvco:9924 is not listed on IDEAS
  20. van Giersbergen, Noud P. A. & Kiviet, Jan F., 2002. "How to implement the bootstrap in static or stable dynamic regression models: test statistic versus confidence region approach," Journal of Econometrics, Elsevier, vol. 108(1), pages 133-156, May.
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Cited by:
  1. Olivier Armantier, 2003. "Estimates Of Own Lethal Risks And Anchoring Effects," Department of Economics Working Papers 03-04, Stony Brook University, Department of Economics.

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