Is the Use of Autocovariances in Level the Best in Estimating the Income Processes? A Simulation Study

In this simulation study, I compare the efficiency and finite sample bias of parameter estimators for popular income dynamic models using various forms of autocovariances. The dynamic models have a random walk or a heterogeneous growth permanent component, a persistent autoregressive component and a white noise transitory component. I compare the estimators using autocovariances in level, first differences (FD), and autocovariances between level and future first differences (LD), where the last one is new in the literature of income dynamics. To maintain the same information used as in using level covariances, I also augment the FD and LD covariances with level variances in the estimation. The results show that using level covariances can give rise to larger finite sample biases and larger standard errors than using covariances in FD and LD augmented by level variance. Without augmenting the level variances, LD provides more efficient estimators than FD in estimating the non-permanent components. I also show that LD provides a convenient test between random walk and heterogeneous growth models with good power.