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Heteroskedasticity-consistent standard errors

Standard errors of coefficients calculated in previous section here are given as

S.E=Var(b∣X)=e′e(n−K)(X′X)−1.\begin{align*} \bold{S.E}=\sqrt{\mathbb{Var}(\bold{b|X})}&=\sqrt{\frac{\bold{e'e}}{(n-K)}\bold{(X'X)}^{-1}}. \end{align*}

While deriving the above expression, we relied on two key assumptions

  1. Homoscedasticity: E[εi2∣X]=σ2\mathbb{E}[\varepsilon_i^2\bold{|X}]=\sigma^2
  2. Non-autocorrelation: Ei≠j[εiεj∣X]=0\mathbb{E}_{i\neq j}[\varepsilon_i\varepsilon_j\bold{|X}]=0