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.

I. Introduction

When lump-sum taxes are not available, the fiscal consequences of monetary policy and thus the possible fiscal feedbacks to monetary policy are important. The fiscal authority finances the government budget by levying distortion taxes and issuing bonds, whose real values are subject to the fluctuation of both inflation and output that are affected by the monetary policy. Thus if the monetary authority changes the interest rate, fiscal authority would have to adjust its instruments such as public debts or distortion tax rate immediately so as to satisfy the intertemporal government budget constraint. The variation of these variables will conversely affect the inflation rate and the output. In order to achieve its target level of inflation and output, the central bank should take in account the possible fiscal feedbacks. As shown in this paper, the monetary authority can not affect real variables such as inflation and output without the cooperation of fiscal authority in extreme cases. The same argument holds for fiscal authority either, who must consider how monetary authority will respond to its action. So the monetary policy and fiscal policy are integrated tightly. If monetary authority and fiscal authority make their own policy independently, there are possible strategic interactions between them, which are to be addressed in this paper.