Direct solution to an optimal control problem of econometric systems

A direct solution is proposed to an optimal control problem of linear econometric systems with a quadratic welfare loss function when there are linear equality constraints on the control variables. The direct solution proposed here eliminates the problem of non-uniqueness of the optimal solution, which is present when this optimal control problem is solved using the recursive algorithm proposed by Chow,¹ Pindyck² and Tan.³ If a unique solution to the optimal control problem exists, then the direct solution and the recursive solution coincide.