Efficiency with endogenous population growth. Do children have too many rights?

Fertility rates are declining in many countries. But are fertility rates inefficiently low? This paper addresses this question by exploring the efficiency properties of equilibria in an overlapping generations setting with endogenous fertility and dynastic parental altruism, using a particular formulation of the notion of P-efficiency proposed by Golosov, Jones, and Tertilt (2007). In this formulation, new lives increase social welfare only if the agents living those lives are not worse off than those agents of the same generation living in any allocation. In contrast with Schoonbroodt and Tertilt (2014), who show that any equilibrium for which non-negativity constraints on intergenerational transfers are binding is A-inefficient (and, under the assumption that new lives always increase social welfare, also P-inefficient), I characterize symmetric, P-efficient allocations as the equilibria arising from different distribution of rights among the agents, and show that many equilibria exhibiting binding constraints on transfers are P-efficient. To be more precise, except for dynamically inefficient equilibria, there is no need to alter children's rights in order to achieve efficiency.