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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. Gonçalves, Sílvia & Kilian, Lutz, 2002. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Working Paper Series 0196, European Central Bank.
  2. Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996.
  3. Davidson, Russell & Flachaire, Emmanuel, 2008. "The wild bootstrap, tamed at last," Journal of Econometrics, Elsevier, vol. 146(1), pages 162-169, September.
  4. Davidson, R., 2000. "Bootstrap Confidence Intervals Based on Inverting Hypothesis Tests," G.R.E.Q.A.M. 00a09, Universite Aix-Marseille III.
  5. Flachaire, Emmanuel, 1999. "A better way to bootstrap pairs," Economics Letters, Elsevier, vol. 64(3), pages 257-262, September.
  6. repec:fth:louvco:9924 is not listed on IDEAS
  7. 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.
  8. Emmanuel Flachaire, 2002. "Bootstrapping heteroskedasticity consistent covariance matrix estimator," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00175897, HAL.
  9. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
  10. Chesher, Andrew & Jewitt, Ian, 1987. "The Bias of a Heteroskedasticity Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 55(5), pages 1217-22, September.
  11. Russell Davidson & James G. MacKinnon, 1985. "Heteroskedasticity-Robust Tests in Regression Directions," Working Papers 616, Queen's University, Department of Economics.
  12. 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.
  13. 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.
  14. 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.
  15. Emmanuel Flachaire, 2005. "Bootstrapping heteroskedastic regression models: wild bootstrap vs. pairs bootstrap," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00175910, HAL.
  16. 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.
  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. 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.
  19. James G. MacKinnon, 2002. "Bootstrap inference in econometrics," Canadian Journal of Economics, Canadian Economics Association, vol. 35(4), pages 615-645, November.
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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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