Abstract
In the presence of heteroscedasticity, different available flavours of the heteroscedasticity consistent covariance estimator (HCCME) are used. However, the available literature shows that these estimators can be considerably biased in small samples. Cribari–Neto et al. (2000) introduce a bias adjustment mechanism and give the modified White estimator that becomes almost bias-free even in small samples. Extending these results, Cribari-Neto and Galvao (2003) present a similar bias adjustment mechanism that can be applied to a wide class of HCCMEs’. In the present article, we follow the same mechanism as proposed by Cribari-Neto and Galvao to give bias-correction version of HCCME but we use adaptive HCCME rather than the conventional HCCME. The Monte Carlo study is used to evaluate the performance of our proposed estimators.
Highlights
Heteroscedasticity is a common problem when estimating linear regression
Three more improved versions of the heteroscedastic covariance matrix estimator (HCCME) are presented by Mackinnon and White (1985) and Davidson and MacKinnon (1993), which are known as HC1, HC2 and HC3 in the available literature
As discussed earlier that in the presence of heteroscedasticity, different available versions of HCCME are used, they can be considerably biased in small samples; see, e.g., MacKinnon and White (1985), Cribari-Neto and Zarkos (1999, 2001), Long and Ervin (2000), Cribari-Neto et al (2005) etc
Summary
Heteroscedasticity is a common problem when estimating linear regression. It gives inefficient least squares estimates and the inconsistent usual covariance matrix estimate. As discussed earlier that in the presence of heteroscedasticity, different available versions of HCCME are used, they can be considerably biased in small samples; see, e.g., MacKinnon and White (1985), Cribari-Neto and Zarkos (1999, 2001), Long and Ervin (2000), Cribari-Neto et al (2005) etc. MacKinnon and White (1985) raise concerns about the performance of HC0 in small samples They noted that the estimator HC0 (3) takes no account of the well-known fact that OLS residuals tend to be ‘too small’. Long and Ervin (2000) recommend that use of HC standard error estimates and by their Monte Carlo findings they report the superb performance of HC3 for small samples (see MacKinnon, 2011 for more discussion).
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