Regression systems for unbalanced panel data: a stepwise maximum likelihood procedure

The estimation of systems of regression equations with random individual effects from unbalanced panel data, where the unbalance is due to random attrition or accretion, by generalized least squares (GLS) and maximum likelihood (ML) is considered. In order to utilize the previous results for the balanced case, it is convenient to arrange the individuals in groups according to the number of times they are observed. It is shown that the GLS estimator can be interpreted as a matrix weighted average of the group specific GLS estimators with weights equal to the inverse of their respective covariance matrices. A stepwise algorithm for solving the ML problem, which can be interpreted as a compromise between the solution to the group specific ML problems, is presented.