Heteroscedasticity-Robust (HC) Standard Errors
Heteroscedasticity-Consistent (HC) Standard Errors · Also known as: robust standard errors, White standard errors, Huber-Eicker-White standard errors, sandwich standard errors, HC0, HC1, HC2, HC3, HC4, Heterokedastisiteye Robust Standart Hatalar (HC)
Heteroscedasticity-robust standard errors are a correction to the covariance matrix of an OLS regression that yields valid inference when the error variance is not constant. Introduced by Halbert White in 1980 and refined into the finite-sample variants HC1-HC4 by MacKinnon and White in 1985, they leave the coefficient estimates unchanged but rebuild the standard errors so that t and F tests remain trustworthy under heteroscedasticity.
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When to use it
Use HC standard errors after fitting an OLS regression on a continuous outcome whenever you suspect or detect non-constant error variance — typically confirmed with a Breusch-Pagan test. They require an already-estimated OLS model and a reasonable sample size (about 30 or more observations). They are the standard remedy for heteroscedasticity in cross-sectional and longitudinal data, but they do not address correlated errors within clusters (use cluster-robust errors) and become unreliable in very small samples or with strong leverage points, where HC3, HC4, or a wild bootstrap are safer.
Strengths & limitations
- Gives valid standard errors and trustworthy t and F tests under heteroscedasticity without specifying the form of the variance.
- Leaves the OLS point estimates unchanged, so interpretation of the coefficients is identical to ordinary OLS.
- Simple to apply and available as a one-line covariance option in standard software; the HC1-HC4 variants offer better finite-sample behaviour.
- In small samples (n < 30) the HC standard errors can be unreliable; HC3 or a wild bootstrap is preferred.
- High-leverage points distort HC0 and HC1, so HC3 or HC4 should be used when influential observations are present.
- They correct only for heteroscedasticity, not for autocorrelation or within-cluster dependence, which need other robust estimators.
Frequently asked
Do robust standard errors change my coefficients?
No. The point estimates β̂ are exactly the ordinary least-squares values. Only the covariance matrix — and therefore the standard errors, t statistics, and p values — is recomputed to be valid under heteroscedasticity.
Which HC variant should I use?
HC0 is White's original estimator. HC1 applies a degrees-of-freedom correction, HC2 and HC3 adjust for leverage, and HC4 is tuned for high-leverage points. HC3 is a widely recommended default, especially in smaller samples; switch to HC4 or a wild bootstrap when influential observations dominate.
How do I know I need robust standard errors?
Fit OLS and run a Breusch-Pagan (or White) test on the residuals. If it indicates non-constant error variance, the classical standard errors are no longer valid and HC standard errors are the standard remedy.
Can robust standard errors handle clustered data?
Not on their own. HC standard errors correct for heteroscedasticity but assume observations are otherwise independent. When errors are correlated within groups (schools, firms, regions), use cluster-robust standard errors instead.
Sources
- White, H. (1980). A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity. Econometrica, 48(4), 817-838. DOI: 10.2307/1912934 ↗
- MacKinnon, J. G. & White, H. (1985). Some Heteroskedasticity-Consistent Covariance Matrix Estimators with Improved Finite Sample Properties. Journal of Econometrics, 29(3), 305-325. DOI: 10.1016/0304-4076(85)90158-7 ↗
How to cite this page
ScholarGate. (2026, June 1). Heteroscedasticity-Consistent (HC) Standard Errors. ScholarGate. https://scholargate.app/en/statistics/heteroscedasticity-robust-se
Which method?
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