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Using heteroscedasticity-non-consistent or heteroscedasticity-consistent variances in linear regression

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  • Sin, C.Y. (Chor-yiu)
  • Lee, Cheng-Few

Abstract

The properties of the heteroscedasticity non-consistent variances and heteroscedasticity consistent variances are reviewed. Unlike the related existing results, the following cases are discussed separately: (i) the cases where the explanatory variables are strictly exogenous; and (ii) the cases where the explanatory variables may or may not be strictly exogenous. The latter cases allow weakly dependent explanatory variables such as those generating from an autoregressive process. New results on the original robust variance (denoted by HC0) and its variants (denoted by HC1,HC2,HC3,HC4 and HCj) are derived. In particular, the followings are shown: (i) the ordering of the original robust variance and its variants; (ii) the asymptotic equivalence among different variants of robust variance; and (iii) under quadratic form of heteroscedasticity (with mesokurtic/leptokurtic normalized error) or GARCH(1,1)-error, non-robust variance rejects more often than robust variance. Simulation studies suggest HC4 by and large does not over-rejects or mildly under-rejects.

Suggested Citation

  • Sin, C.Y. (Chor-yiu) & Lee, Cheng-Few, 2021. "Using heteroscedasticity-non-consistent or heteroscedasticity-consistent variances in linear regression," Econometrics and Statistics, Elsevier, vol. 18(C), pages 117-142.
    • Handle: RePEc:eee:ecosta:v:18:y:2021:i:c:p:117-142
    DOI: 10.1016/j.ecosta.2020.10.002
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    More about this item

    Keywords

    Asymptotic properties; Finite-sample properties; non-robust variance; Robust variance; Strictly exogenous; Weakly dependent;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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