To answer my own question: I am dubious.
It is true that a country can get into economic trouble if the number of elderly people, who invariably impose heavy costs on a country’s health care system, becomes very large relative to the number of persons of working age, because then the financial burden on the working population can become extremely heavy. The reverse, however, is also true: too high a ratio of young to old can be destabilizing. The experience of many of the poor nations of the world has been that a large youth population creates severe unemployment problems and can lead to violent unrest, as in a number of Middle Eastern countries in the last few years—the naively heralded “Arab Spring” having quickly become a nightmare of violence, political disorder, and regional instability.
It’s amazing that a poor, largely arid country like Egypt should have a population of 84 million. That cannot be a good thing. Much of Egypt’s current problems stem from inability to grow enough food to feed its population, and insufficient productivity to buy abroad all the food its huge population needs.
A growing population implies a growing number of children—not just persons of working age—and children impose heavy opportunity costs on parents (unless child labor is permitted, which however is likely to prevent children from becoming educated) and are costly to educate. A fast-rising population can not only create heavy youth unemployment but also strain public services (such as public educational institutions). And all this is in addition to the environmental impact of increased population, for example on global warming, species extinctions, and traffic congestion.
If children were a “superior” good in the economist’s sense—that is, a good that is purchased in greater quantity when people’s incomes rise—one would expect the birthrate in wealthy countries to be high and rising, but the opposite in most such countries is true. Maybe children are actually an “inferior” good, valued most by poor people either because the children of the poor work to augment family income or because the family lacks the resources for such child substitutes as expensive cars, clothes, homes, entertainment, and travel. Increasingly in the wealthy countries both spouses work, increasing the opportunity costs to both parents of raising children.
A better and certainly cheaper answer to the problem of declining population in countries like Germany and Japan—wealthy countries (though not all countries with declining populations are wealthy—Russia is not, for example)—is immigration. There are some two and a half billion people in China, India, and South Korea alone. Their average IQ seems similar to (maybe even higher than) that of the inhabitants of the United States and the other wealthy countries, including those wealthy countries whose populations are declining (a category that excludes the United States). This implies a very large number of East Asians with IQs well above 100. (Assuming that IQ is normally distributed, an average IQ of 100 means that 2.5 percent of the population has an IQ of at least 130—and 2.5 percent of 2.5 billion is 62.5 million.) Obviously not all want to emigrate, but many are quite open to the possibility. The problem is that few wealthy countries, other than the United States and the other English-speaking countries, are welcoming to immigrants. They have immigrants—Germany for example has many citizens of Turkish origin; Japan has many Koreans. But these countries tend to be insular, ethnocentric, downright hostile to immigrants, and their immigrant populations—not just the first generation, either—have difficulty assimilating, unlike immigrants to the United States, which still really is a melting pot. If those countries can’t solve the assimilation problem, thereby making themselves more attractive to high-quality immigrants, their populations will continue to decline, because the countries probably can’t afford the subsidies necessary to halt the decline.
There is no necessary connection between population and economic growth. The sharp decline of Europe’s population because of the Black Death is thought to have increased per capita incomes significantly by reducing the ratio of people to arable land, resulting in improved nutrition. A larger population can, as Becker points out, increase the rate of technological progress by increasing the number of geniuses and other very creative people. But so can assortative mating, which has become much more common in the advanced countries as a result of falling discrimination and Internet dating search. At some point there may be diminishing returns to the increasing number of computer engineers.
Paying people to have children sounds odd though it can be defended on economic grounds if the additional children yield a net economic benefit. (So for that matter could paying elderly people to forgo end of life medical expenses likewise be defended on economic grounds, depending on how large the subsidy would have to be and how it would be financed.) I am skeptical that such a defense can be established. Too little is known about the economic effects of continued growth of a world population that has now surpassed seven billion.