The Study of Discretional Monetary and Fiscal Policies Based on Linear Quadratic Approximation

When monetary authority and fiscal authority make their decisions independently, either tries to maximize the overall welfare level subject to the implementation condition and resource constraint. After extending both the objective function and constraints to 2nd order around the steady states, this nonlinear optimal problem is transformed into a pure linear quadratic one. Under this framework we study the discretional fiscal and monetary policies, where they are so tightly integrated that even the feasible sets for monetary and fiscal instruments are greatly restricted. The findings are the following: (1) when both policies are discretional, there is no dominant strategy for the monetary authority, thus both the Nash equilibrium and the fiscal leader equilibrium do not exist, with the monetary leader equilibrium ruled out by the unbounded path of government debts; (2) the equilibrium with fiscal commitment and monetary discretion is also ruled out by the explosive path of government debts.