The Optimal Level of Debt in an OLG Model with Endogenous Fertility Luca Spataro Universita ` di Pisa and CHILD Luciano Fanti Universita ` di Pisa Abstract. In the present work we extend Diamond’s OLG model by allowing for endogenous fertility and look at the consequences of such an extension on the rules for optimal public debt issuing. In particular, we show that the condition according to which the rate of growth of population should be higher than the interest rate is no longer sufficient for obtaining welfare improvements via debt increases and that the level of optimal debt is, ceteris paribus, lower than the one arising with exogenous fertility. Finally, a sensitivity analysis shows that the optimal level of debt is higher the lower the capital share, the higher individuals’ degree of patience, the bigger the child-rearing cost and the lower the preference for children. On policy grounds we argue that debt-tightening policies may be optimal in the long run provided that the cost of rearing children does not increase (or, if anything, does decrease). JEL classification: D91, E62, H63, J13. Keywords: Overlapping generations; endogenous fertility; debt. 1. INTRODUCTION High public debt is one of the major problems in many European countries (especially Italy, Greece and Belgium). On the other hand, the same European countries are facing the problem of very low (even largely below replacement) fertility rates. Moreover, two stylized facts, occurred in the recent years and exacerbated by the current financial crisis 2008–9, are worth mentioning concerning public debt and fertility. First, the different dynamics of public debt between developing and developed countries is impressive: as regards the developing countries, Brazil and Indonesia lowered their own debt from about 100% of GNP to 45% and 34%, respectively, and the debt/GNP ratio of China, South Korea and Russia is 16%, 18% and 6%, respectively. Conversely, as regards developed economies, in the year of financial turmoil (2008/2009), the increase in such a ratio is about 21 percentage points in Germany passing from 66% to 87%, about 13 in France raising from 67% to 80%, about 7 in Italy passing from 105% to 112%, about 27 in the United States passing from 71% to 98%, about 30 in Japan raising from 197% to 227%. By contrast, the demographic dynamics followed an opposite pattern, very low in developed countries and significantly higher in the developing countries (Russia may be considered as an exception, showing very low public debt as well as demographic dynamics). This stylized facts require more attention from a theoretical point of view, for a better understanding both of underlying economic mechanisms and of future dynamics of such relationship. Although the literature has traditionally studied public debt and fertility in separate classes of models, a more integrated analysis of two themes is lacking. In r 2011 The Authors German Economic Review r 2011 Verein fu ¨r Socialpolitik. Published by Blackwell Published Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK and 350 Main Street, Malden, MA 02148, USA. German Economic Review 12(3): 351–369