Ponzi game in OLG model with endogenous growth and productive government spending

Barro's model is an AK model, and there cannot be dynamic inefficiency since the social yield of the capital is higher than the growth rate. But it may be that the private yield and thus the interest rate are lower than the growth rate. One can thus have a Ponzi game and the government can allow a permanent roll-over of debt and cut taxes. However we show that in this model since the capital is under-accumulated, playing a Ponzi game produces a crowding-out of capital and reduces the growth rate and welfare. The practical message of this article is that even when the interest rate is lower than the growth rate, the public debt is not a Pareto improvement when it generates a crowding-out of capital and reduces endogenous growth.