You might think that the family would be safe from the cold logic of economists but, as Gary Becker long ago demonstrated with his models of the marriage market and children as durable goods, the economic approach knows no bounds! It can ask an economistic question about anything and get an economistic answer. (Whether that's helpful for anything except the publishing record of that economist is another matter.) I recently came across one such example of economics imperialism in the question: Are children public goods? Or else private goods? My answer: No and no. They're children.
The argument that children are public goods seems from the start more of a metaphor than a rigorous use of the economic concept. Surely no one would seriously consider that children meet (or should meet) the standard definition of being non-rivalrous and non-excludable (like air and national defence). On the contrary most parents go to some lengths to exclude strangers (and society tends to agree). But raising children is very expensive and that cost has to fall on someone. The idea is that having children is in some sense a 'public service', which like a genuine public good would not be provided in the socially needed amount on the basis of private interests. Many feminist economists have also always been keen to emphasise the unpaid family work on which the monetary economy (the bits included in 'GDP') depends, and the injustice of that lack of proper recognition and compensation.
But what exactly are these children providing to society? It seems to be future workers to keep up the pension payments for our increasing elderly demographic structure, not children per se. But if you're going to start talking about children as future economic units, then one can also ask whether raising children is the most efficient (cheapest) way of providing that. After all, 1st world children, like pensioners, spend at least 20 years as expensive non-productive dependents - so one is in the strange position of requiring more children in order (partly) to have enough adults to change baby diapers, etc.
Surely a clear, fair, but ruthless guest worker programme such as Singapore has could achieve the same results of obtaining 1st world economic productivity without 1st world child care costs. Robots also seem a promising alternative investment. Even if they can never become smarter than a dog, they have enormous capacity to displace or complement human labour in the service industries as they already have in manufacturing, including taking over much of the tedious, dirty, and emotionally exhausting caring tasks for our elderly dependants that feminists are so keen to have recognised (that seems to be Japan's plan). 'The economy' does not need to produce children to survive!
But in any case there is a more fundamental problem with the economic case for children: why should our priority be to maintain a pension system that dates from Bismarck's Germany and has come to resemble a giant inter-generational Ponzi scheme? Shouldn't we stop to think about that goal before trying to re-create 19th Century demography? This looks like a case of 19th Century imperialism, not economics imperialism. After all, pensioners, unlike children, can be socially and economically productive, and hence independent, given the opportunities made possible by technological assistance, medical advances, and changes in certain social norms. And this is already occurring.
Perhaps, to drift even further from economic talk, this is really about some amorphous 'cultural good': we all value our cultural continuity, but only by raising future citizens within our culture can that be guaranteed. But this is absurd. For a start it implies that all immigration is bad. But it also depends on a very primitive understanding of the value and nature of cultural continuity. Fact 1) continuity has no logical link with stable population size. e.g. The Netherlands has a strong emotional link to its 'Golden Age' of art, commerce, and, um, empire, but the population then was only 2 million or so (versus 16 million now). Fact 2) change is part of continuity - the values of the Dutch Golden Age would be generally as alien and abhorrent to most modern Dutch as those of the contemporary Taliban. Even the values and way-of-life of your grandparents are quite different from your own. Indeed in a modern commercial society radical if incremental change is inevitable, and in a liberal society that should not (automatically) be resisted. If society is afraid of change, a large number of home-grown children is not going to save it.
Children used to be private goods. They were born to be factors in the socio-economic production unit ('factory') that was the household, and paid for from the surplus value they created (which is not to say they weren't still loved). But in the market society the family no longer makes that kind of economic sense. Parents don't need children, so if they have them now, it's because they want them for their own private reasons (economistically, a change from investment to consumption). In fact, since parents are now prevented by the law (where cultural, economic, and moral reasons are insufficient) from extracting economic value from their children, they really look more like a standard consumption choice. Some people like sailing and buy a yacht, some like children and spend their money on them (and much of their leisure time). The desire to have children seems to be just an expensive taste, not a public service to society. But if so, why should anyone but the parent pay for that taste?
Here we need to make a distinction between the having-of-children and the raising-of-children. The decision to have children is a private decision - a lifestyle choice - by parents that society should in principle leave to them and neither encourage nor restrict. On the other hand, once born the raising of children is a matter of public concern that should be based as far as possible on the interests of the children themselves. Unlike yachts.
Whatever the cost-benefit arguments for or against children in the abstract, once here they present a special moral responsibility to all of us because their innocence, fragility, and potential to become better or worse persons makes them so dependent on those who care for them. Parents may not 'need' children, but children do need parents. And indeed ordinarily most responsibility for care falls directly on the parents, who in the normal case care most strongly and carefully for their children, and who additionally made the decisions that created those responsibilities in the first place. But the wider society should offer sufficient support (e.g. through public institutions, money, and services; but also moral respect, recognition, and social solidarity) to satisfy our general responsibility for the wellbeing and interests of the child as a needing human being, and future adult and citizen. It is in this sense that children are a public concern, and the raising of children has public good aspects in so far as parents' private interests alone are insufficient in resources and motivations to meet its needs.
This shift may seem innocuous - who can deny that parents should look after their children's interests? But making this responsibility explicitly primary actually has significant consequences for how we should understand parents' rights and obligations, since it removes any independent justification of parents' customary rights. Instead parental rights are derived in the first place entirely from an instrumental analysis of what is necessary to meet the independent interests of children, although this must include careful attention to parents' ordinary interests and abilities as a second order concern since one must be realistic about what one can expect from them while retaining their commitment to be carers. In the second place, children are protected from failures of parental practice since parental rights now have the character of privileges rather than sovereign rights, and are retained only insofar as parents use them successfully to fulfil their duties to meet the interests of their children.
What follows from this? Children do remain in some sense the private goods of their parents who enjoy such parental pleasures as hearing their first words, teaching them to ride a bike, and so forth. However, this private good aspect is restricted in that parents have no right to treat their children in any way that significantly undermines their own independent interests (both present and future) for whatever reason. In fact they have a positive duty to promote their children's interests, even when they might prefer not to. Nor should parents have the right to decline expert advice and support: after all, the mere fact of being a parent only demonstrates mastery of the act of reproduction, not parenting ability (and many actual parents would not pass the stringent parenting ability requirements for adoption). The fact that it is best in most cases that parents look after their children, and receive society's assistance to do so, should not be taken as a recognising an exclusive or sovereign parental right over their children, for example to decide what kind of adult life their child may have.
A whole host of whacko - e.g. religious-based - parenting styles thereby become questionable and perhaps illegitimate. Since a child cannot represent herself, society may have to act on her behalf to challenge and judge parental practices in the light of an independent conception of the interests of a child. Want to raise your daughter to think she's only worth a fraction of a man? Civilised society disagrees and may decide to modify, or in extreme cases withdraw, the authority delegated to you to care for your child. Of course, few cases are amenable to direct legal intervention since it is generally more important to retain parents' commitment to caring for their children than to insist on the priority of children's interests at every point (the alternatives - public care institutions - are far from perfect). In many cases this line of analysis therefore suggests a more indirect approach of ameliorating problematic but non-dangerous parental values with stronger state institutions, such as mandatory but attractive public schools.
In addition, numerous subtle changes to public attitudes, norms, and laws may follow from the explicit public recognition that parenting is a responsibility not a right, resulting in changes in the scope and nature of what parents presently take for granted as their right to decide. I envisage for example restrictions on giving your child absurd names (actual examples: "Adolf Hitler"; "Loser"; "Red Light"), or chopping bits off your baby's genitals because God told you to. And as for the right to refuse life-saving vaccinations.....You get the idea.
Identity politics would also be affected, and here it is clear that focussing on children's well-being and interests does not mean simply granting absolute authority to the collective prejudices of society. Want to raise your children, and those of your group, to speak only French while living surrounded by 330 million English speakers (public schooling in English as a first language is banned in Quebec) just because you made that part of your identity? To deliberately cut off valuable future options for your children (or those of anyone else), including their effective ability to choose for French themselves, seems an improper imposition of your interests into your child's future - to treat them in some way as a means to achieving your projects. Once parenthood takes children's interests seriously, such narcissism is clearly illegitimate.