This paper presents a model for the heterogeneity and dynamics of the conditional mean and the conditional variance of standardized individual wages. In particular, a heteroskedastic autoregressive model with multiple individual fixed effects is proposed. The expression for a modified likelihood function is obtained for estimation and inference in a fixed-T context. Using a bias-corrected likelihood approach makes it possible to reduce the estimation bias to a term of order 1/T². The small sample performance of the bias corrected estimator is investigated in a Monte Carlo simulation study. The simulation results show that the bias of the maximum likelihood estimator is substantially corrected for designs that are broadly calibrated to the data used in the empirical analysis, drawn from the 1968-1993 Panel Study of Income Dynamics. The empirical results show that it is important to account for individual unobserved heterogeneity and dynamics in the variance, and that the latter is driven by job mobility. The model also explains the non-normality observed in logwage data.