Fixed T Dynamic Panel Data Estimators with Multi-Factor Errors

This paper analyzes a growing group of fixed T dynamic panel data estimators with a multi-factor error structure. We use a unified notational approach to describe these estimators and discuss their properties in terms of deviations from an underlying set of basic assumptions. Furthermore, we consider the extendability of these estimators to practical situations that may frequently arise, such as their ability to accommodate unbalanced panels. Using a large-scale simulation exercise, we consider scenarios that remain largely unexplored in the literature, albeit they are of great empirical relevance. In particular, we examine (i) the effect of the presence of weakly exogenous covariates, (ii) the effect of changing the magnitude of the correlation between the factor loadings of the dependent variable and those of the covariates, (iii) the impact of the number of moment conditions on bias and size for GMM estimators, and finally the effect of sample size. Thus, our study may serve as a useful guide to practitioners who wish to allow for multiplicative sources of unobserved heterogeneity in their model.