  This paper extends the linear grouped fixed effects (GFE) panel model to
allow for heteroskedasticity from a discrete latent group variable. Key
features of GFE are preserved, such as individuals belonging to one of a finite
number of groups and group membership is unrestricted and estimated. Ignoring
group heteroskedasticity may lead to poor classification, which is detrimental
to finite sample bias and standard errors of estimators. I introduce the
"weighted grouped fixed effects" (WGFE) estimator that minimizes a weighted
average of group sum of squared residuals. I establish $\sqrt{NT}$-consistency
and normality under a concept of group separation based on second moments. A
test of group homoskedasticity is discussed. A fast computation procedure is
provided. Simulations show that WGFE outperforms alternatives that exclude
second moment information. I demonstrate this approach by considering the link
between income and democracy and the effect of unionization on earnings.
