Monday, June 13, 2011

Children: Normal or Inferior?

Justin Wolfers has an interesting data-intensive post on the debate about whether children are a normal or an inferior good. Here's the quote that he uses to end the post:

In a related paper, Alice Schoonbroodt and Michele Tertilt say that, “There is overwhelming empirical evidence that fertility is negatively related to income in most countries at most times.” They are right. Whether you cut the data across countries, through time, or across people at a point in time, the same fact arises: The richer you get, the fewer kids you have.

Yep, kids aren’t normal.

Although the graphics are impressive, I was rather frustrated upon reading this post. It misses on on a subtle point about what it means for a good to be normal. A good is normal if greater income leads the individual (or household) to consume more of the product, holding constant prices of the good and other related goods.

In other words, children are a normal good if more income leads to more children ... at the same prices. If you like to see it in graphical form, here's what a normal good looks like:
Here's what children as an inferior good looks like:

None of the Wolfers' graphs hold constant the opportunity cost of raising children. These graphs are just comparisons of rich individuals with poor individuals or rich countries with poor countries. If being rich implies that you have to give up more to have children (not a foregone conclusion, but the opportunity cost seems higher), there is a price effect as well as an income effect. Either of which could explain why rich people have fewer children.

For example, consider the graph where children are a normal good (i.e., more income implies that the household selects B instead of A; more children), but the higher price implies fewer children. In the graph, the higher price more than offsets the positive income effect.

In the raw data on rich-poor fertility, we observe points A and C and we might be tempted to conclude (as Wolfers did) that children are an inferior good. But, effects go in opposite directions and the data in the plots are uninformative on this point. In fact, my graph depicts a normal good and would still generate graphs like the ones Wolfers presents.

The theoretical possibility of a price effect doesn't invalidate Wolfers' claim that children are an inferior good, but it does make it an empirical question. Bryan Caplan has an interesting post (incidentally, it is the one Wolfers is responding to) where he highlights that controlling for education may hold constant some of these omitted factors. After running some regressions, he concludes:

Controlling for education, higher income predicts higher fertility. (Adding age as a control variable slightly reduces the magnitude, but not too much). The simplest story is that the elite values typical of the well-educated depress fertility - but regardless of your values, the higher your income, the more kids you want.

If you believe that controlling for education is an effective way to hold prices (read: opportunity cost) constant, this regression analysis suggests that children may be a normal good. The way I think about the problem, this seems much more sensible than connecting points A and C to conclude that children are an inferior good.

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