Anova-type consistent estimators of variance components in unbalanced multi-way error components models

This paper introduces three new Anova-type consistent estimators of variance components for use in multi-way unbalanced error components models, with possibly non-normal errors and endogenous regressors. They are easy to compute and are proved to be consistent under mild regularity conditions. For the first time proofs of consistency for Anova estimators are offered under such a general class of models, providing novel insights into the impact of unbalancedness on the large-sample properties of the estimators. A battery of Monte Carlo experiments and an empirical application to US production data show that the estimators perform reasonably well, in comparison to unbiased methods incorporating finite-sample corrections.