Estimating multiway error-components models with correlated effects in Stata

I derive new estimators and tests of correlated effects for the (possibly) unbalanced multiway error component model (ECM), extending existing results in various aspects. The results by Kang (1985) on specification tests, who extended Hausman and Taylor (1981) and Mundlak (1978) to the two-way balanced model, emerge as particular cases of the present analysis. Davis (2002), who extends the analysis of Wansbeek and Kaptein (1989) to the multiway unbalanced model does not consider the cases of either correlated effects or specification tests. I also uncover new algebraic properties of the multiway ECM covariance matrix that prove useful for both computational and analytical purposes. Finally, I provide some examples using Stata.