Nonnegative Approximate Solutions to an Econometric Model with Prescribed Goals

Given a linear economic model y* = ðx + b were y* is a prescribed goal vector, a linear programming problem can be used to determine the existence and uniqueness of a nonnegative instrument vector x that attains the goal and obtain such a vector if it exists. If the system y* = ðx + b does not have a solution, the approximate solution x = ðx(y*- b), where ð is the generalized inverse of ð, determines a vector ŷ = ðx that is as close as possible to y* in terms of the Euclidean distance. In this case, a linear programming problem can also be used to determine the existence and uniqueness of a nonnegative approximate solution and obtain such a solution if it exists.