Public debt in a basic endogenous growth model

We work out the mechanism that makes public debt affect the allocation of resources in the long-run. To do so we analyze an AK growth model with elastic labor supply and a government sector. The government levies a distortionary income tax and issues bonds to finance lump-sum transfers and non-distortionary public spending. We show that the long-run growth rate is the smaller the higher the debt ratio if the government adjusts public spending to fulfill its inter-temporal budget constraint. If the government adjusts lump-sum transfers the public debt ratio does not affect the balanced growth rate.