Moment conditions for dynamic panel data models with multiplicative individual effects in the conditional variance

Moment conditions are derived for dynamic linear panel data models with linear individual specific effects in the mean and multiplicative individual effects in the conditional ARCH type variance function. The relation and correlation between the linear and multiplicative effects are unrestrained. Moment conditions are derived for non-autocorrelated error processes, MA(q) processes, and for models that allow for time varying parameters on both the linear mean effects and multiplicative variance effects. The small sample performance of a GMM estimator is investigated in a Monte Carlo simulation study.