Optimal choice of fiscal policy instruments in a stochastic IS–LM model

•We look for the optimal fiscal rule in a stochastic IS–LM model.•Expenditure is preferable to taxation if the two instruments are independent.•The introduction of a fiscal budget rule can make taxation preferable.

This article derives optimal fiscal rules within a stochastic model of Keynesian type in the context of Poole (1970). By using optimal control theory and applying the Hamilton–Jacobi–Bellman equation, we extend the original Poole results concerning the output stabilization properties of monetary policy to the case of fiscal policy. In particular, we look for the optimal setting of government expenditure and lump-sum taxation in the case that the fiscal authority wishes to keep the product close to a reference value and that the economy is assumed to be affected by stochastic disturbances of real and/or monetary type. According to our findings an expenditure rule is preferable to a taxation rule when the two instruments are independent. The introduction of a fiscal budget rule can make taxation preferable under a certain model parametrization.