Having caught your eye, I direct you to an article in the April 9, 2015 edition of the Grey Lady. It discusses attempts by various countries to boost domestic birthrates. The same issue had been considered earlier by Noah Smith. There are two questions lurking here. First, what is the optimal population size for a country? If the goal was to shrink the population then a declining birth rate is not a bad thing. Suppose the goal is keep the population fixed, because, say of pension obligations. Then, one wants a replacement birth rate of roughly 2 per couple.
If the birth rate is below the target, what should one do? Interestingly, I cannot recall anyone I have asked or read who does not turn to Government interventions of various kinds. Noah Smith, for example, only discusses Government interventions before concluding one should imitate the French. If the birth rate is below what is optimal for society, why doesn’t the market take care of it? Do we have a missing market? Is this a public goods problem? (If so, then, Mankiw who is often castigated for being a selfish beast, is, in this case, an unstinting provider of public goods, see here.)
Analogies are sometimes helpful (if biology is the study of bios, life; geology is the study of geos, earth, what does that make analogy?). Farmers plant crops and after a period, the fruits of their labor are harvested and sent to market. The Farmer must anticipate what will be demanded in the future to decide what to plant now. What if she plants turnips when what is desired are parsnips? This problem is solved with a futures market for parsnips (or turnips or pork etc). Why not a futures market for babies? Those who want warm bodies in the future to support them in their dotage pay for babies now. Swiftian, I know, but interesting to consider. Once one thinks about how to implement the idea, difficulties emerge. One might, for example, be concerned with moral hazard on the part of parents. However, these same difficulties are present even with various Government subsidies.