heteroskedasticityrobust

Heteroskedasticity‑robust refers to statistical methods that remain valid when the assumption of constant variance (homoskedasticity) of the error terms in a regression model is violated. Classical ordinary least squares (OLS) estimates of coefficients are unbiased even under heteroskedasticity, but the usual variance estimates and t‑statistic calculations become inconsistent. This leads to unreliable hypothesis tests and confidence intervals. Heteroskedasticity‑robust techniques adjust the estimated covariance matrix of the parameter vector to account for non‑constant variance, allowing correct inference while retaining the OLS coefficient estimates.

The most common implementation is the “sandwich” estimator introduced by White. It weights the contribution of each observation by its squared residual, producing a consistent estimate of the asymptotic covariance matrix. In linear regression, this yields the robust standard errors often reported as the “White” or “HC0” errors. Variants such as HC1, HC2, HC3, and HC4 apply small‑sample corrections to improve performance when the sample size is modest or the design matrix is poorly conditioned. In many statistical software packages robust errors are available via built‑in commands or flags, for example in R (sandwich, lmrob), Stata (robust), and Python (statsmodels).

Beyond linear regression, heteroskedasticity‑robust methods extend to generalized linear models, time‑series models, and panel data. In GARCH or autoregressive conditional heteroskedasticity models, the heteroskedasticity is modeled explicitly, but robust inference can still be applied to parameters not captured by the volatility specification. In panel data, cluster‑robust standard errors accommodate heteroskedasticity within clusters while allowing for arbitrary within‑cluster correlation.

Researchers routinely report robust standard errors when heteroskedasticity is suspected or detected via diagnostic tests such as Breusch‑Pagan, White’s test, or the Goldfeld‑Quandt test. While robust errors mitigate certain inference problems, they do not correct for omitted variables or endogeneity. Therefore, robust inference is often accompanied by other methodological safeguards, such as instrument variables or fixed‑effects controls, to address broader econometric concerns.