The projection approach for multi-way error components models with partially balanced panel data

This paper presents a new estimation framework for partially balanced panel data models with multiple error components, which are the main source of the endogeneity problem in such models. When the dimension of error components is high, computational difficulty arises even if the data are partially balanced (i.e. balanced in some, but not all, dimensions). For linear models, our proposed projection approach can control for as many error components as the number of balanced dimensions plus one, and gives consistent estimates. For Poisson models, using correlated random effects obtained from multiple projections can also provide consistent estimates. Using Monte Carlo simulations, we confirm that the proposed estimators are consistent and produce correct inferences, with substantial power and no size bias. The proposed estimators are applied to improve the estimates of trade cost elasticity, through proper treatment of zero observations and unobserved factors. We obtain smaller trade cost elasticity estimates in both linear and Poisson models, compared to previous estimates.