Dynamic inefficiency, public debt and endogenous fertility

In this paper we show that, when endogenous fertility is considered via Cobb-Douglas preferences, public debt plays a clear-cut role on dynamic inefficiency (DI) of an OLG economy: in fact, for correcting the DI problem, debt must be increased (decreased) when the economy is overaccumulating (underaccumulating). The occurrence of overaccumulation, and, thus, the necessity of a positive level of debt, is favoured by a small capital income share, on the technological side, and a sufficiently high degree of patience and a low preference for children on preferences grounds. As for the optimal level of debt, our analysis shows that a high level ofdebt is more likely to be optimal for countries with a relatively low share of capital, with high costs for rearing children, with high individuals' degree of patience; as for individuals' preference for children, as expected, the preference for a numerous family reduces the risk of overaccumulation and, thus, the optimal level of national debt. Moreover, interestingly, although in our model the occurrence of dynamic inefficiency (DI) does not depend on the level of the child rearing cost, such cost magnifies the degree of inefficiency and, therefore, a higher public debt is required for correcting DI. Finally, it is argued that such findings can provide useful criteria for assessing the optimality of public debt-cutting policies undertaken by several Europen countries.