Are children normal goods?

I finished a post last week with the question of whether children are normal goods. Below I want to lay out some economic arguments on this, before putting in an evolutionary twist that raises the question of whether we can rely on any of the economic analysis.

A normal good is a good for which demand increases with income. Cars, holidays and jewellery are examples of normal goods. The opposite is an inferior good, with demand decreasing as income rises. An example of an inferior good might be hamburger mince (as people move to steak) or other low-quality products. This change in demand for a good in response to changing income is known as an income effect.

There has been some debate over the years about whether children are normal goods, particularly given the ubiquitous pattern of fertility declining as a country’s residents get richer. However, determining whether children are a normal good is complicated, as we do not get to witness a simple increase in income without other conflating factors.

First, income is not the major input into children. Rather, time is the scarce resource, with that time balanced (crudely) between work, leisure and children. Gary Becker argued back in 1965 that using time was the right way to frame the problem.

Consider a sudden increase in your wage. This increases the relative price of leisure and children and would result in someone wanting to work more and to demand less children and leisure. This is known as a substitution effect. The income effect means that the worker does not need to work as much for the same income. This increase in income increases the time effectively available, and if children are a normal good, a person will have more of them. However, the substitution and income effects operate in opposite directions, making it difficult to determine whether that person will actually have more children. If we see them reducing the number of children they have, we cannot determine the direction of the income effect and whether children are a normal good.

Accordingly, the decline in fertility with wealth witnessed at a country level suggests that the substitution effect is strong and that the income effect, which would be operating in the opposite direction if children are a normal good, does not outweigh it. However, it also leaves open the possibility that children are an inferior good, with both the substitution and income effects contributing to the decline.

Betsey Stevenson made a similar point concerning the need to consider the income and substitution effects in Cato Unbound last year when discussing a drop in the price of children. Stevenson argued that children might be a Giffen good, a type of inferior good for which the income effect is so strong that not only does it counteract the substitution effect, but actually completely outweighs it. If children were a Giffen good, a decrease in the price of children (through decreasing time requirements to raise them) would lead you to consume less.

As a Giffen good must be an inferior good, and not a normal good, Stevenson’s question turned into a debate on whether children are normal goods. Bryan Caplan ran some regressions on General Social Survey data from the United States, and found that once you control for IQ and education, the number of children increases with income. That pattern holds for both men and women. As the price of children and leisure goes up through an increase in income, there is a substitution effect away from children and leisure and towards working. If children are normal goods, there is an income effect to spend more on children. As income has a positive effect on the number of children in Caplan’s analysis, children must be normal goods.

Justin Wolfers came back with an argument that children were inferior goods, largely based on the observation of cross-country fertility declining with income, but it misses the combination of the income and substitution effects discussed above.

A major difference between Caplan and Wolfer’s analyses is that Caplan controls for education. That complicates matters further, and will be a subject of a separate post. There is also the question of whether children are a Veblen good, which means that as the price of children rises, the preference for children also increases as children become a status signal. If the fundamental nature of the product changes, it is even more difficult to unravel. Another post to come for that too.

Now for the evolutionary spanner in the works. Children are a decision of two people. A man must convince a woman, and vice versa, to have a child. Parental investment theory tells us that the man will be doing more of the convincing, but both sides are not free of constraints.

If a man has more children as his income increases, it may be a result of a change in his demand for children as his income increases. Alternatively, it may be due to a change in the constraint that he faces. In other words, suppose men all want the same number of children regardless of income, but women will only mate with higher income men. As a result, we will see a positive relationship between income and children. This is even though we assumed that children are not a normal good.

As women are less constrained, their changing behaviour may be more representative of their preferences, but they are not completely independent. Woman are constrained in the quality (and income) of men that they can attract, and that may affect their willingness to have children. To the extent that their income is representative of traits desired by men, increasing children with female income (as in Caplan’s regressions) may be evidence of lower constraints rather than a response to their own income.

I should note that there are plenty of studies seeking to assess whether children are normal goods. They use all sorts of external shocks, such as the man losing his job or shocks to male income through a resources boom. The evolutionary problem remains. If a man loses his job, he is more likely to run into the female constraint. Unemployment is a strong predictor of divorce.

Is there an experiment in which you can separate male preferences from the constraint?