Targets, instruments and generalized inverses

The purpose of this paper is to demonstrate the usefulness of generalized inverses for problems associated with macro economic policy. Previous research on the selection of targets and instruments has specified the problem so that both the values of the instruments and the values realized for the targets are a joint outcome of the constrained optimization of an arbitrarily defined welfare function. Two theorems are developed which suggest that: (1) if the number of instruments exceeds the number of targets, a welfare function need not be defined. It is possible to discriminate between policies with a minimum norm generalized inverse which is based on the values of the instruments: (2) given the number of targets exceeds that of instruments the generalized inverse approach reduces to a special case of Theil's certainty equivalence method. Klein's six equation model from 'Economic Fluctuations in the United States' is used to illustrate these approaches.