Welfare implications of national debt in a OLG model with endogenous fertility

In the present work we show that, when one allows for endogenous fertility in Diamond's (1965) OLG model, public debt plays still a clear-cut role on dynamic inefficiency (DI): for correcting DI, national debt must be increased. DI is more likely to occur when the economy capital income share and the preference for children are sufficiently low and the degree of patience is sufficiently high. However, differently from Diamond's case, DI turns out to be a necessary but not a succient condition for welfare improvements to obtain via debt increases, since, in presence of endogenous fertility, the optimal level of debt is typically lower than the one associated to the traditional Golden Rule. Hence, not taking fertility choices into account would lead policymakers to overshoot the target, i.e. to issue too high a level of national debt. 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 for debt tightening policies to be optimal in the long run, it is necessary that the cost of rearing children does not increase (or, if anything, reduces).