heteroskedasticityconsistent

Heteroskedasticityconsistent refers to methods for estimating the variability of regression coefficients that are valid when the regression errors do not have constant variance across observations. In ordinary least squares, standard errors rely on homoskedasticity; when this assumption fails, conventional t tests and confidence intervals can be biased, leading to unreliable inference. Heteroskedasticity-consistent approaches aim to provide robust standard errors that remain valid under heteroskedasticity.

The most common framework is the heteroskedasticity-consistent covariance matrix estimators (HCCME). The basic version, often called HC0, uses the squared residuals to form a diagonal weighting matrix in the covariance calculation. Variants refine this approach to improve small-sample performance: HC1 multiplies by n/(n−k), HC2 divides each term by (1−hii), and HC3 uses (1−hii)⁻², where hii are the diagonal elements of the hat matrix. Together, these are typically described as robust or heteroskedasticity-robust standard errors. They are implemented in many statistical software environments under names such as vcovHC, vce(robust), or cov_type='HC0/HC1/HC2/HC3'.

Applications and limitations: Heteroskedasticity-consistent methods allow valid inference without specifying a particular form of heteroskedasticity, provided exogeneity and model specification are reasonable. They do not address other issues such as model misspecification, autocorrelation, or dependent errors, and their finite-sample performance can vary. Nevertheless, they are widely used in econometrics and applied statistics to obtain more reliable standard errors when variance of errors is not constant. See also robust standard errors and sandwich estimators.