Robust standard errors with heteroscedasticity

Summary

Setup

• The LRM with random sampling

$$y_i=β_1+β_2x_{i,2}+β_3x_{i,3}+…+β_kx_{i,k}+ε_i, i=1,…,n$$

• All explanatory variables are exogenous.
• The error terms are heteroscedastic.
• The OLS estimator is unbiased and consistent but the OLS standard errors are inconsistent.

Robust standard errors

• Robust standard errors or White-adjusted standard errors are consistent even when the error terms are heteroscedastic.
• Inference based on OLS estimates and robust standard errors will therefore be approximately correct if $n$ is large.