Robust OLS (OLS with Robust Standard Errors)
Ordinary Least Squares with Heteroscedasticity-Consistent Standard Errors · Also known as: HC robust regression, White robust OLS, sandwich estimator OLS, OLS with robust standard errors
Robust OLS applies ordinary least squares to estimate coefficients and then replaces the classical standard errors with heteroscedasticity-consistent (HC) standard errors — commonly called White standard errors. This leaves the point estimates unchanged while yielding valid t-statistics and confidence intervals even when the error variance is not constant across observations.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
+3 more
When to use it
Use robust OLS whenever you fit a linear regression and have evidence or suspicion of heteroscedasticity — for example after a Breusch-Pagan or White test rejects constant variance, or when residual plots show a fan shape. It is the standard practice in cross-sectional microeconometrics (wage equations, firm-level data) and in many time-series applications. It is appropriate when the sample is large enough for asymptotic theory (roughly n > 100) and the primary concern is valid inference rather than efficiency. Do not use it as a substitute for modelling the variance structure (e.g., WLS or GARCH) when you want efficient estimates; robust OLS corrects inference but does not improve efficiency. It is also not a remedy for omitted variable bias, endogeneity, or model misspecification.
Strengths & limitations
- Provides asymptotically valid standard errors under heteroscedasticity of any unknown form without requiring a model for the variance.
- Coefficient estimates are identical to standard OLS — only inference is corrected.
- Widely accepted as the default inferential approach in applied microeconometrics and increasingly in macroeconometrics.
- Small-sample HC corrections (HC1, HC2, HC3) improve finite-sample performance.
- Easy to implement: a single option in Stata, R (sandwich package), Python (statsmodels), and most econometric software.
- Standard errors are only asymptotically valid; in small samples (n < 100) they can be unreliable even with HC corrections.
- Robust standard errors are generally larger than misspecified OLS standard errors, reducing apparent statistical significance.
- Does not improve the efficiency of coefficient estimates — if the variance structure is known, WLS or GLS yields tighter estimates.
- Cluster-robust or HAC variants are needed when errors are also correlated across observations or over time; plain White SEs do not cover these cases.
Frequently asked
Does robust OLS change the coefficient estimates?
No. Robust OLS uses exactly the same coefficient formula as standard OLS. Only the standard errors — and therefore t-statistics, p-values, and confidence intervals — change.
Which HC variant should I use?
HC3 is generally recommended for smaller samples (roughly n < 250) because it applies a stronger correction that reduces over-rejection of true null hypotheses. HC1 matches Stata's default robust option. For large samples, HC0 (White's original) is typically adequate.
When should I use cluster-robust instead of White standard errors?
Use cluster-robust standard errors when observations are grouped (students in schools, workers in firms, repeated observations per country) and errors within groups are likely correlated. White standard errors assume errors are independent across all observations.
Is robust OLS the same as robust regression?
No. Robust OLS (this method) corrects standard errors for heteroscedasticity but keeps the OLS estimator. Robust regression (M-estimators, least trimmed squares) replaces the OLS estimator itself to downweight outliers. They solve different problems.
If heteroscedasticity is present, should I use WLS instead?
WLS is more efficient when you know or can model the variance structure, but it requires correctly specifying the weights. Robust OLS is preferable when the variance structure is unknown or hard to model — it sacrifices efficiency for guaranteed valid inference.
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 ↗
- Wooldridge, J. M. (2019). Introductory Econometrics: A Modern Approach (7th ed.). Cengage Learning. ISBN: 978-1337558860
How to cite this page
ScholarGate. (2026, June 3). Ordinary Least Squares with Heteroscedasticity-Consistent Standard Errors. ScholarGate. https://scholargate.app/en/econometrics/robust-ols
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- Generalized Least SquaresStatistics↔ compare
- OLS RegressionEconometrics↔ compare
- Panel Fixed Effects ModelEconometrics↔ compare
- Quantile RegressionEconometrics↔ compare
- Robust GLSEconometrics↔ compare
- Weighted Least SquaresStatistics↔ compare