Tax smoothing with seigniorage and stochastic processes of government expenditures

This paper determines the optimal trajectories of the tax rate under tax smoothing taking into account the seigniorage and stochastic processes of government expenditures in a partial equilibrium model. The paper optimizes the discounted value of distortions caused by tax instruments, given intra- and intertemporal budget constraints. The authors propose a more general functional form describing distortions due to income and leniency taxes, taking into account the stochastic processes of government expenditures, as compared to the standard quadratic form for finding the ratio between the planned tax rate and inflation at optimal financing of government expenditures. It is shown that the optimal tax rate is proportional to permanent government expenditures. The planned tax rate under smoothing is inversely proportional to the contribution of seigniorage to inflation. The impact of government expenditure shocks on tax smoothing is investigated. As the persistence of government spending shocks increases, permanent government spending increases and, as a consequence, non-lump-sum taxes also increase. All conclusions of the paper apply to the behavior of representative agents with rational expectations. The results of the paper may be of interest to government agencies and the Central Bank.