Selected Methods for Designing Monetary and Fiscal Targeting Rules Within the Policy Mix Framework

In the existing literature, targeting rules are typically determined separately for monetary and fiscal policy. This article proposes a framework for determining targeting rules that account for the policy mix of both monetary and fiscal policy. The aim of this study is to compare selected optimization methods used to derive targeting rules as solutions to a constrained minimization problem. The constraints are defined by a model that incorporates a monetary and fiscal policy mix. The optimization methods applied include the linear-quadratic regulator, Bellman dynamic programming, and Euler's calculus of variations. The resulting targeting rules are solutions to a discrete-time optimization problem with a finite horizon and without discounting. In this article, we define targeting rules that take into account the monetary and fiscal policy mix. The derived rules allow for the calculation of optimal values for the interest rate and the balance-to-GDP ratio, which ensure price stability, a stable debt-to-GDP ratio, and the desired GDP growth dynamics. It can be noted that all the optimization methods used yield the same optimal vector of decision variables, and the specific method applied does not affect the form of the targeting rules.