This paper considers estimation of panel data models with (multiplicative) individual fixed effects in the variance, e.g., σ_{i,t}² = σ_{i}² or σ_{i,t}² = σ_{i}² τ_{t}². The cross-section dimension of the panel (N) is assumed to be large but the time dimension (T) can be small or large. The paper shows that under certain conditions, which depend on whether T is fixed or large, the common parameters in static (or stationary) and non-stationary dynamic linear panel data models can be consistently estimated by a Weighted First Difference Maximum Likelihood (FDML) estimator and a Weighted Random Effects or Fixed Effects ML (REML or FEML) estimator, respectively, and derives their asymptotic distributions. These estimators weight the data with estimates of the σ_{i}² and are shown to be asymptotically efficient under joint N,T asymptotics and suitable conditions. We also discuss two-step weighted Quasi ML estimators and Hybrid Quasi ML estimators that are generally still consistent for the common parameters in non-stationary dynamic linear panel data models with arbitrary heteroskedasticity, i.e., when σ_{i,t}² ≠ σ_{i}² τ_{t}². The paper then introduces Individually Weighted GMM (IWGMM) estimators that generalize the Minimum Distance estimator of Chamberlain (1982). Under normality and when T is fixed, the optimally weighted IWGMM estimators are more efficient than the corresponding Weighted ML estimators, whereas their unweighted ML and GMM counterparts are both efficient under (cross-sectional) homoskedasticity. Finally, Monte Carlo results show that the weighted estimators are more efficient than their unweighted counterparts when T is not too small and there is a significant degree of heteroskedasticity in the cross-section dimension of the panel.

PLEASE NOTE that σ_{i}² τ_{t}² stands for (sigma subscript i)²  times (tau subscript i)².