Abstract
The performance of heteroscedasticity consistent covariance matrix estimators (HCCMEs), namely, HC0, HC1, HC2, HC3 and HC4 have been evaluated by numerous researchers for the heteroscedastic linear regression models. This study focuses on examining the performance of these covariance estimators in case of groupwise heteroscedasticity. With the help of the Monte Carlo simulations, we evaluate the performance of these covariance estimators and the associated quasi-t tests. We consider the cases when data are divided into 10, 20 and 30 groups of different sizes and the regression is run on the mean values of the dependent variable and the regressor of these groups. The numerical results show that HCCMEs perform appealingly well in case of groupwise heteroscedasticity.
Highlights
The linear regression models for cross-sectional data often exhibit the problem of heteroscedasticity i.e. the error variances are not constant for all observations
Using the Monte Carlo simulations, we evaluated the performance of heteroscedasticity consistent covariance matrix estimators (HCCMEs) for groupwise heteroscedasticity
Following Cribari-Neto and Lima (2009), we evaluated the performance of the ordinary least square (OLS) and HCCMEs, under groupwise heteroscedasticity, for interval estimation
Summary
The linear regression models for cross-sectional data often exhibit the problem of heteroscedasticity i.e. the error variances are not constant for all observations In this situation, the ordinary least square (OLS) estimators of the parameters remain unbiased and consistent but become inefficient. Since the OLS standard errors are based directly on these variances, so the inferences drawn on the basis of these estimators become misleading and erroneous It becomes necessary to build and use alternative covariance matrix estimators that are consistent under both homoscedasticity and heteroscedasticity of unknown form. The numerical results in Cribari-Neto (2004) showed that the asymptotic inferences in linear regression models were much affected by the presence of high leverage points in the design matrix. By the Monte Carlo simulations, Cribari-Neto (2004) showed that the quasi-t tests, based on the HC4 estimator, were reliable even in the presence of influential observations in the design matrix
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