Debt and growth: Is there a non-monotonic relation?

In this note we theoretically investigate the question of whether the relationship between public debt and economic growth is characterized by an inverse U-shaped functional form. Starting point of our analysis is the paper by Checherita-Westphal et al. (2012) who present an endogenous growth model with public capital and public debt that displays a hump-shaped relation between debt and economic growth. We highlight the mechanism that generates this outcome and we generalize their model by allowing for a more general debt policy. We demonstrate that this non-monotonic relation only holds if public deficits are exogenously fixed and exactly equal to public investment at each point in time. With a more general debt policy, one realizes that smaller public deficits and lower public debt always lead to a higher balanced growth rate. Thus, starting from a situation where the public deficit equals public investment, governments can raise the long-run growth rate by reducing their deficits.