Generalized adding-up in systems of regression equations

This paper clarifies the invariance issue of deletion choice arising in singular systems of linear regression equations, where the singularity is caused by exact linear restrictions on the endogenous variables, adding-up to a predetermined aggregate. In a quite general context allowing for additional exogenous restrictions, collinearities and generalized adding-up, we propose an estimator which circumvents the need for generalized inverses.