Estimation of moments for linear panel data models with potential existence of time effects

In econometric analysis of panel data, one always doesn’t have enough information to assure the existence/absence of time effects, which can lead to wrong conclusions in statistical inference such as moment estimation and hypothesis testing. In this paper, estimation of second and fourth order moments of the individual effects and the errors are studied for linear panel data models without information on the existence/absence of time effects. With differences of the residuals over the individual index, the orthogonality-based moment estimators of the random individual effects and the errors are respectively obtained without affecting each other. These moment estimators are robust on the potential existence of time effects. Their asymptotic normalities are obtained under some moment conditions. Monte Carlo simulations are carried out for illustration.