@article{cdc40c24655f450cb0a93f95900307da,
title = "Using heteroscedasticity-non-consistent or heteroscedasticity-consistent variances in linear regression",
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.",
keywords = "Asymptotic properties, Finite-sample properties, non-robust variance, Robust variance, Strictly exogenous, Weakly dependent",
author = "Sin, {C. Y.(Chor yiu)} and Lee, {Cheng Few}",
note = "Funding Information: A preliminary version entitled, “Using heteroscedasticity-consistent variances for possibly weakly dependent data: reviews and some new results,” was presented at FCU-Waseda International Symposium: Time Series, Machine Learning and Causality Analysis (September, 2019), 2019 Annual Meeting of the Taiwan Econometric Society (November, 2019), and 2019 Annual Meeting of Chinese Statistical Association (December, 2019). We thank comments by Chih-Hao Chang, Cathy W.S. Chen, Hsin-Yi Lin, Takayuki Shiohama, Mike K.P. So, Masanobu Taniguchi, Hui Wang, and Shih-Ti Yu. SIN{\textquoteright}s research is partially supported by the Ministry of Science and Technology of Taiwan under grant MOST 109-2410-H-007-048. Funding Information: A preliminary version entitled, ?Using heteroscedasticity-consistent variances for possibly weakly dependent data: reviews and some new results,? was presented at FCU-Waseda International Symposium: Time Series, Machine Learning and Causality Analysis (September, 2019), 2019 Annual Meeting of the Taiwan Econometric Society (November, 2019), and 2019 Annual Meeting of Chinese Statistical Association (December, 2019). We thank comments by Chih-Hao Chang, Cathy W.S. Chen, Hsin-Yi Lin, Takayuki Shiohama, Mike K.P. So, Masanobu Taniguchi, Hui Wang, and Shih-Ti Yu. SIN's research is partially supported by the Ministry of Science and Technology of Taiwan under grant MOST 109-2410-H-007-048. Publisher Copyright: {\textcopyright} 2020 EcoSta Econometrics and Statistics",
year = "2021",
month = apr,
doi = "10.1016/j.ecosta.2020.10.002",
language = "English (US)",
volume = "18",
pages = "117--142",
journal = "Econometrics and Statistics",
issn = "2452-3062",
publisher = "Elsevier BV",
}