The maximum debt-GDP ratio and endogenous growth in the Diamond overlapping generations model: Three overlapping generations are better than two

While the public debt has an interior maximum in the Diamond OLG model, due to an inherent nonlinearity [Rankin and Roffia (2003)], this feature also extends to a linear, AK model when it is conjoined with a backward-looking adjustment process for public debt [Braeuninger (2005)]. We show that if the debt dynamics are forward-looking, the maximum will instead be at a degeneracy – another possibility considered by Rankin and Roffia. However, the main point of the present paper is to show that any debt maximum in a finite-horizon model will be of an implausibly low order of magnitude, unless households save over at least two periods. This is because it is the debt flow that crowds-out investment flows, while this is synonymous with the debt stock in a model with only two, non-altruistic, overlapping generations, thus leading to a low maximum stock by default. Removing this restriction produces plausible results, and causes a low rate of economic growth to be a cause as well as a consequence of a high public debt.