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Abstract
The linear regression model is commonly used in applications. One of the assumptions made is that the error variances are constant across all observations. This assumption, known as homoskedasticity, is frequently violated in practice. A commonly used strategy is to estimate the regression parameters by ordinary least squares and to compute standard errors that deliver asymptotically valid inference under both homoskedasticity and heteroskedasticity of an unknown form. Several consistent standard errors have been proposed in the literature, and evaluated in numerical experiments based on their point estimation performance and on the finite sample behaviour of associated hypothesis tests. We build upon the existing literature by constructing heteroskedasticity-consistent interval estimators and numerically evaluating their finite sample performance. Different bootstrap interval estimators are also considered. The numerical results favour the HC4 interval estimator.
Acknowledgements
The first author gratefully acknowledges research grants from CNPq. We also thank an anonymous referee and an associate editor for comments and suggestions.
Notes
Zeileis Citation19 describes a computer implementation of these estimators.
Cribari–Neto et al. Citation20 show that it is possible to obtain improved HC0 point estimators by using an iterative bias reducing scheme; see also Cribari–Neto and Galvão Citation21. Godfrey Citation22 argues that restricted (rather than unrestricted) residuals should be used in the HCCMEs when these are used in test statistics with the purpose of testing restrictions on regression parameters.
For consistent covariance matrix estimation under heteroskedasticity, we shall also assume: ASSUMPTION 6 , where S is a positive definite matrix.
The use of the Rademacher distribution in this context has been suggested by several authors; see, e.g., Flachaire Citation23.