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?