Catherine Rampbell adds to Justin Wolfer’s argument that children are inferior goods. That is the richer we get the fewer we want.

Only a third of people with annual household incomes over $75,000 say they want families with three or more children. Of all Americans with income levels below $75,000, 44 percent say they want families with at least three children.

In Lake Wobegone all children may be above average, but across America, children appear to be inferior — at least economically speaking.

The basic argument goes like this: if we look across countries, across time and across families within any country at a given time, we see the same thing. Richer people have fewer children than poorer people. Moreover, richer people claim to want fewer children than poorer people.

Now, of course it could be that the causation is running the other way. People are richer because they want fewer children. However, that’s not really compelling to me. And, so I’ll ignore it here.

What makes me skeptical of the notion that children are inferior goods per se is that it runs afoul of what I might call my classic critique. First, it defies introspection and conversational empiricism.  Second, the underlying theoretical model is weak. Third, the data analysis is confounded.

Introspection and Conversational Empiricism

When people talk about there reasons for not having children they emphasize the constraints that they face. They don’t have enough time. They don’t have enough energy. They can’t afford it. They don’t have enough room. The ones they have are a handful, etc.

These sound like lack of income problems. Why it is that the rich face them, we’ll get to in a moment.

Also, think about situations in which you were given more resources. You have a great relationship with your mother in-law who decides to come over every day and help take care of the children in the most ideal way possible? You are given a staff who cooks and cleans and takes care of all the house work? One spouse gets a promotion so good – extra pay for no extra work – that the other can easily quit his or her job and stay at home.

If you were on the fence about having another child would these things make you more or less likely to have one? It seems to me that they would make you more likely.

That is to say, lessoning the resource constraint, which is what economists mean by the income effect, would push you towards having another kid.

Underlying Theory

So when we say that a good is an inferior good what are we saying? How does the math of that actually work out? I’ll get a bit nerdy for a second and then bring this back. There has to be some good that is a strong substitute for the good in question but whose marginal utility per dollar of good starts out much lower than the inferior good but declines much more slowly.

Meat and potatoes are a classic example. When you are very hungry a dollar of potatoes satisfies you much more quickly than a dollar of meat. However, as you become richer and can afford to eat more, the value of eating ever more potatoes quickly declines. However, the value of eating more meat stays strong. The thing is, the more meat you eat the less potatoes you want. So, you actually switch from potatoes to meat as you get richer. Potato consumption goes down.

What’s the good that we imagine being paired against children? It has to be a strong substitute. It has to do little to fulfill you at low levels of income but much more at high.  Presumably our good in question would be some form of high priced leisure but its hard to think of ones that make the really make cut.

Travel might do it, if travel really is worse when you have kids. Nights on the town might make sense but its not quite clear why babysitting doesn’t turn this back into a resource constraint rather than clear substitutes.

The best example I can think of is the ability to maintain large networks of friends. If high incomes allow us to keep our friend network larger and friends and children are substitutes then we could see this effect.  This could work but I am unconvinced that the effect is large enough to match what we see in the data.

Confounding Variables

The biggest problem with all of this, however, is that there is a clear substitution effect answer. It goes this way. Over time and space most people have not gotten richer because wealth has come down to them like manna from heaven. They have gotten richer because the price of labor has risen and the price of educated labor has risen even more.

However, both labor and education take time. Children also take time. So, as people have gotten richer the cost of having children has gone up. You have to sacrifice more valuable labor time and more valuable education time in order to have kids.

This also matches how people talk and behave. That it is career vs kids. Or getting a degree vs. having kids. This isn’t an income effect, however, it’s a substitution effect.

Presumably if you gave people more of the basic resource – time – they would have more kids and more education and more work. Imagine, for example if you took a pill that meant you only had to sleep 15 mins a day to be fully rested. This seems like the sort of thing that would encourage people to have more kids and advance their career. Because, of course, they know have much more time.

However, because time is the core resource and because giving you more of it, makes you want to buy more kids and more consumption (via work), kids count as a normal good.

What does it all mean

Now lets tie all of this back to the underlying debate which was over Bryan Caplan’s thesis that people would have more kids if they knew it was less work.

What Bryan claims to be offering is the equivalent of the magic no-sleep pill. You can have your cake and eat it too. You get more time and more energy by realizing that your kids will turn out just fine even if you don’t put as much effort into raising them.

As long as kids are a still a normal good this basic line of reasoning holds.

I think Bryans thesis has other issues. Dealing with the status dimension. Dealing with a feeling of loss of control if Bryan is correct.

And, of course the point I haven’t seen raised elsewhere that “bad kids” probably contribute negatively to parent’s utility. If you have no means of preventing bad kids this makes having children a riskier endeavor than some parents might believe.

I say utility and not happiness because I think the two are importantly different. We might all want to do things that makes us happy, but we do do things which increase our utility, regardless of whether they make us happy or not.