Heteroscedasticity — what breaks and how do you fix it?

medium

Answer

$\operatorname{Var}({\varepsilon}\; \mid \;X)$
$OLS β̂ stays unbiased and consistent, but SEs and t-tests are wrong \to invalid inference.$
$Fixes: (1) Robust ('sandwich', HC0-HC3) SEs — most common fix in econometrics.$
$1 / \operatorname{Var}({\varepsilon}\; \mid \;X)$
$(3) Cluster-robust SEs for panel / clustered data.$
$(4) Transform the response (log for right-skewed outcomes).$
$(5) Model the variance directly (GAMLSS, HGLM).$
$Detect with Breusch-Pagan / White tests or residual-vs-fitted plots.$

Check yourself — multiple choice

Breaks β̂
β̂ still unbiased/consistent, but SEs invalid → use robust SEs (HC0-3) / WLS / cluster-robust / log transform; detect via Breusch-Pagan or White
Same as multicollinearity
Not fixable

Heteroscedasticity: β̂ OK, SEs wrong → robust (sandwich) SEs / WLS.

#regression#assumptions

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