  In this paper, we investigate seemingly unrelated regression (SUR) models
that allow the number of equations (N) to be large, and to be comparable to the
number of the observations in each equation (T). It is well known in the
literature that the conventional SUR estimator, for example, the generalized
least squares (GLS) estimator of Zellner (1962) does not perform well. As the
main contribution of the paper, we propose a new feasible GLS estimator called
the feasible graphical lasso (FGLasso) estimator. For a feasible implementation
of the GLS estimator, we use the graphical lasso estimation of the precision
matrix (the inverse of the covariance matrix of the equation system errors)
assuming that the underlying unknown precision matrix is sparse. We derive
asymptotic theories of the new estimator and investigate its finite sample
properties via Monte-Carlo simulations.
