We directly compare two institutions, a family compact—a parent makes a
transfer to her parent in anticipation of a possible future gift from her children—with
a pay-as-you-go, public pension system, in a life cycle model with endogenous fertility
wherein children are valued both as consumption and investment goods. Absent
intragenerational heterogeneity, we show that a benevolent government has no welfare
justification for introducing public pensions alongside thriving family compacts
since the former is associated with inefficiently low fertility. This result hinges critically
on a fiscal externality—the inability of middle age agents to internalize the
impact of their fertility decisions on old-age transfers under a public pension system.
With homogeneous agents, a strong-enough negative aggregate shock to middle-age
incomes destroys all family compacts, and in such a setting, an optimal public pension
system cannot enter. This suggests the raison d’etre ˆ for social security must lie
outside of its function as a pension system—specifically its redistributive function
which emerges with heterogeneous agents. In a simple modification of our benchmark
model—one that allows for idiosyncratic frictions to compact formation such as

• Private versus public old-age security