Bryan Caplan  

Wolfers on Kids and Income

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Over at Freakonomics, Justin Wolfers has a data-intensive critique of my claim that kids are, appearances withstanding, normal goods.  This naturally makes me nervous.  Wolfers has a disconcerting habit of publicly correcting others.  If I had an unlimited budget, I'd hire Wolfers to preview everything I write to spare me potential embarrassment.  Nevertheless, after reviewing his evidence, I conclude that he's criticizing a position I explicitly disavowed - and not addressing my actual argument.

Wolfers expertly presents an array of evidence showing that the bivariate relationship between income and family size is clearly negative.  I freely admit this.  Indeed, my first regression showed this negative relationship, though it was on the weak side.  The issue I address is whether this relationship is causal.  That's what being a normal good means: If increasing your income causes you to buy more X, X is a normal good.

The cleanest test for causality is a bona fide experiment.  But the next best thing is a multiple regression where you check whether controlling for potential confounding variables weakens or reverses the relationship you see on the surface.  That's why I added various control variables to my original regressions, and found that the coefficient on income did indeed reverse sign.  I have no idea why Wolfers would call this "tying myself in regression knots, rather than getting at the issue."  Regressions at least consider the possibility that something other than income - say education, or secularization - has been driving declining fertility.  Wolfers' many graphs, in contrast, don't get at this issue.  If he'd just done a horserace between income, education, and a trend, we'd have a lot more to talk about.

When I discussed my original post with Tyler Cowen, he remarked that "sometimes you should look at the unadjusted coefficient, not the adjusted coefficient."  The key, of course, is "sometimes."  If you simply want to predict fertility in a country that's modernizing - experiencing simultaneous increases in income, education, secularization, etc. -  Wolfers' evidence is quite relevant.  But if you want to predict families' fertility in response to an exogenous income shock - like a sudden inheritance or lottery win - my admittedly simple regressions are more informative. 

This brings us back to my original disagreement with Betsey Stevenson.  My claim: When people discard needlessly laborious and painful forms of parenting, they enjoy an exogenous income shock.  Consider a parent who adopts the Ferber method, gaining years of extra sleep.  In a sense, he's suddenly richer.  But who on earth would see this sharp reduction of sleep deprivation as a reason to have fewer kids? 


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COMMENTS (13 to date)
Phil writes:

>"Wolfers has a disconcerting habit of publicly correcting others."

Umm, don't the writers on this blog do that too? Or does Wolfers do it in a different way?

HispanicPundit writes:

It's posts like this that remind me why I consider you my favorite economists of all. Seriously! And I say this as someone who reads alot of economists blogs. I may even become a pacifist because of you - and seriously, that would really suck! I've already developed a reputation as a hardcore rightwinger who also supported all previous wars. Made fun of people who didn't as simplistic, idealistic, etc and if I had to backtrack, it wouldn't be easy.

Anyway, your ability to explain and defend your positions is great. Love this post. Love your idea of betting on views. Love your radical free market views. Love your blunt and I would argue generally true talk on statistical discrimination. Love your honesty, courage, and incisiveness and ability to understand areas that far surpasses what I have seen from other bloggers, academics or regular pundits.

Robin Hanson writes:

Odd that Wolfers doesn't even mention the possibility of controlling for other things, such as education. That was the whole point of your previous post!

Petter Patton writes:

Gotta say, as a kid who had an allowance at ahe 3, had never heard my parents say 'kirfew', ever even when arresed for shoplefting at age 9, my Dad abused policed once for being 'to stupid to appreciate irony (mine).

So Bryan, haven't read you interbiew with Amy Chua, I was Chua 1000%

PrometheeFeu writes:

I remember chatting with my Econometrics professor in college and asking him why we don't take all those series out there and assign a supercomputer to try every permutation possible and spit out all the significant correlations to see what would happen. His answer: "There are people who do that and they are despicable." What he meant was that if you take correlations and then try to make theories out of them instead of using regressions to test theories, you will be engaged in post-hoc reasoning which is not very rigorous and ultimately can be used to "confirm" any theory you cherish.

I think this is what Wolfers is doing here. What he should have done is looked at your theory, formulated an alternative, agreed with you (even if through cranking through your own reasoning himself) about where the two theories might provide different predictions and then gone out to test it. I have generally found that Freakonomics does a lot of post-hoc reasoning and very little rigorous testing.

AMW writes:

I didn't see your original post on the Ferber method. But I will say that I'm a father of four and with each we ignored their bed-time crying starting somewhere around the 6 month mark. For the first three they were sleeping like logs with no fussing within a week. For the fourth it took longer to get good sleep, but that's largely because a long-distance move and attendant obligations messed up his sleep schedule during the day.

I highly recommend that all parents lower the costs of parenthood by sleep training their children at a young age.

Mark writes:

I may be missing something, but as my income increases, I don't necessarily by two and three more homes, I buy a bigger home. Consequently, as my income increases, my expenditures on housing also increases because housing is typically a normal good.

As incomes have increased around the world, we spend more money on them. In fact, we spend a whole lot more money on fewer children. Isn't a more relevant comparison the total expenditures on children through time as our incomes increase rather than just the number of children we have?

Glen writes:

I haven't read the whole debate, but it seems like the question isn't whether kids are an inferior good, but whether they're a Giffen good. Bryan's argument is that serenity parenting reduces the price of raising children. A lower price yields a substitution effect and an income effect. If kids are an inferior good, the income effect says to have fewer kids. But so what? The substitution effect says to have more kids. And the substitution effect dominates the income effect for almost every good, potatoes in 1840s Ireland notwithstanding. Giffen goods are extremely rare. (And if kids are not inferior, then the income and substitution effects reinforce each other in the have-more-kids direction.)

As an aside, I dislike the economics terminology that makes inferior and normal opposites. I prefer the terminology, used in some econ texts but not the majority, which says a normal good is the opposite of a Giffen good, while the opposite of inferior is superior. But this doesn't affect my argument above.

astonerii writes:

If the number of children a society has is really to be based on economic metrics, then I propose that the closest relationship is capital investment.
It does not matter if you are rich or poor, you have certain needs. Being rich means you can satisfy those needs in various ways, but staying rich requires you to do so efficiently. What other differences are there between rich and poor nations as well as past and present generations. I contend that slavery, effective slavery (imported servants) and modern automation are probably the more likely economic variables that determines individual society production of children. Children are simply capital investments. The production of which can increase your productivity, but as other forms of productivity become prevalent in a society, whether it is slavery, servant service industry, automated machinery or some other productivity increasing product I am unable to think of at the moment, people replace children with those forms of productivity which are more efficient, or seem to be more efficient.

Coupon_Clipper writes:

Glen wrote:

it seems like the question isn't whether kids are an inferior good, but whether they're a Giffen good.

Yup. What Glen said. Of course, maybe I missed something too, but this whole debate seems focused on the wrong question.

dullgeek writes:

Ok. I recognize that I'm not very good at this stuff, but I don't understand how these two fit together:

1) "Wolfers expertly presents an array of evidence showing that the bivariate relationship between income and family size is clearly negative. I freely admit this."

2) "The issue I address is whether this relationship is causal. That's what being a normal good means: If increasing your income causes you to buy more X, X is a normal good."

I don't understand how Caplan can agree with Wolfers' data, and then say that increased income causes *greater* family size. Wolfers' data shows *decreased* family size correlated with greater income.

If +A and -B are correlated, I understand that +A could be a cuase of -B, or the other way round, or there's some 3rd thing that is causing both. But I've never heard of +A & -B being correlated AND +A causes +B.

I'm sure that it's just my ignorance. Anyone willing to take a shot at explaining this to me?

Dave Hedengren writes:

When I run the simple bi-variate regression on 2009 ACS data I get a positive relationship between number of children and household income. I assume this is partly due to age (older people have higher incomes and have had more time to have more children) but the relationship still holds when controlling for age. Surely marriage will have an effect as well (more possible incomes in the household). But I think we should note that at least some cross sectional data suggest children are normal goods.

Of course, I also agree with Glen even if the sign is most often negative.

dullgeek writes:

Nevermind. I'm reading the comments and it's apparent that this is *WAAAY* over my head. I'm content with that.

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