Lattice conditional independence models for seemingly unrelated regressions

Seemingly unrelated regressions (SUR) models appear frequently in econometrics and in the analyses of repeated measures designs and longitudinal data. It is known that iterative algorithms are generally required to obtain the MLEs of the regression parameters. Under a minimal set of lattice conditional independence (LCI) restrictions imposed on the covariance structure, however, closed-form MLEs can be obtained by standard linear regression techniques (Andersson and Perlman, 1993, 1994, 1998). In this paper, simulation is used to study the efficiency of these LCI model-based estimators. We also propose two possible improvements of the usual two-stage estimators for the regression parameters.