I agree with almost everything that Becker says in his post. For example, I agree that whether or not the government should subsidize day care, it should not provide day care facilities; the subsidy should take the form of vouchers, so that the private sector would provide the facilities. Subsidization and provision should normally be separated, since the government is an inefficient service provider compared to private firms.
I also agree that when the purpose of subsidizing child care and work leave is to increase the birth rate, the emphasis should be on subsidizing the second and third child (to prevent population from declining, there must be an average of 2.1 births per woman), since, as Becker points out, most couples have at least one child.
And I agree that there is no good reason to encourage a higher birth rate in the United States. Not because our fertility rate is higher than that of the other rich (and even many poor) countries (the point emphasized by Becker), though it is, but rather because it is close to the replacement rate, and, more important, because the United States is uniquely attractive to high-quality, easily assimilated immigrants, who are good substitutes for native-born citizens.
One thing that puzzles me is the suggestion that child care and work leave subsidies are intended to encourage women to stay home and take care of their children. I had thought the opposite--that the purpose of child care subsidies, when they take the form of subsidies for day care, and compensated work leaves, was to encourage women who want to have children to work. After all, women who don't work don't need day care or work leave.
From an economic standpoint, women should not be encouraged to enter the labor market unless the social value of their output in that market is greater than the social value of their household production, importantly including their contribution as mothers to their children's human capital (broadly defined). I do not know whether it is. Of course if women want to work and do not receive any child care or work leave benefits, they may decide to have no or fewer children, but as Becker points out, if a higher birth rate is the goal, child care and work leave subsidies are not effective means to it.
I do not agree that if women are better mothers if they stay home with their children, the government should require one parent (who as Becker points out will usually be the mother) to stay home. That would put some women to an unnecessarily hard, and socially suboptimal, choice--women who would be far more productive in the labor market, but who also would be, on balance, superior mothers (maybe just because of a superior genetic endowment!).
I do think fertility has to be a major concern for countries, such as most European countries plus Japan, that have at once a birth rate far below the replacement rate and a difficulty in assimilating immigrants. The ideal solution might be simply for these countries to grow smaller in population terms; the problem is that this would place unbearable strains on social services, and so countries faced with a declining population are under irresistible political pressure to admit immigrants, whether or not they can be assimilated. Europe has a large and growing Muslim immigrant population that is not only poorly assimilated, but, to some extent, a danger to their host countries and the world; and that population is growing rapidly not only through immigration but also because of early marriage and large families. These nations might be well advised to pay women to have a second and third child.
It is doubtful that subsidization, however well designed, will raise the birth rate of the European nations that have birth rates far below the replacement level to that level. Children in such nations are extremely expensive, especially in opportunity costs of parents' time (which is why birth rates are so low), and the tax rates necessary to offset those costs enough to have a significant rate on the birth rate might be infeasible. (Another factor in declining birth rates I believe is reduced gains from marriage, the reduction being related to women's opportunity costs of time but to other factors as well.) However, modest subsidies that reduced the rate of population decline might be worthwhile in moderating the demand for immigrants.
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