In child discipline, as in pretty much everything else, the rich have more options than the poor. If you're rich (or even modestly middle-class), you can take away the Game Boy, confiscate the car keys, or turn off the Instant Messenger. But for families with no Game Boys, no cars, and no Internet access, that whole range of punishments is unavailable.
If you're rich or middle-class, you can cut your kid's allowance; if you're poor, your kid might need the allowance to live on. When a middle-class kid loses his allowance, he makes do with fewer CDs or video games. When a poor kid loses his allowance, he makes do with fewer school lunches. Depriving a kid of luxuries can be an effective punishment; depriving a kid of necessities can be a form of child abuse.
Spanking, by contrast, is an equal-opportunity punishment; it works equally well whether you're rich or poor. So simple economics suggests that the very poor, with fewer alternatives available, should spank their kids more—and they do. Professor Bruce Weinberg of Ohio State University has studied this. He found that if you're a kid in a $6,000-a-year household, you probably get spanked every six weeks or so. If your parents' annual income goes up to $17,000, you'll get spanked about once every four months. As income rises above about $17,000, spanking falls off more slowly; $40,000 and $120,000 households are not much different from $17,000 households. That makes sense; in today's America, you don't have to be very wealthy before your kid has a Game Boy, so even a $20,000 household has good non-spanking alternatives.
For allowance withdrawal, the numbers go exactly the opposite way, Weinberg found. If you're a kid in a typical $6,000-a-year family, you'll almost never lose your allowance, but in a family that makes $17,000 or more, you'll lose your allowance four or five times a year.
It might seem like a stretch to explain spanking with economics, but what else could account for these patterns? Well, there's always culture. The very poor are disproportionately black, and blacks physically discipline their children more than whites do. But according to Weinberg, the effect of income persists even after you've controlled for race and other cultural variables.
Anyway, black parents punish their children more than white parents in all ways. If you're black and you misbehave, you're both more likely to get spanked and more likely to lose your allowance than your white neighbor, who in turn is both more likely to get spanked and more likely to lose his allowance than the Hispanic kid down the street. So on average, poor people spank more and withdraw allowances less, whereas black people spank more and withdraw allowances more. The income pattern fails to match the racial pattern, so the income pattern can't be fully explained by race.
It is true, though, that racial differences are more pronounced for spanking than for allowance denial: In both cases blacks punish the most, then whites, then Hispanics, but the gaps between racial groups are much bigger for corporal than for financial punishment.
There are other cultural factors: Boys are punished more than girls, with substantially more spankings and a bit more in the way of allowance withdrawals. Single mothers spank a little less, and withdraw allowances quite a bit less, than other parents. Older and better-educated parents are a bit less likely to spank and a bit more likely to withdraw allowances. Bigger families spank less and withdraw allowances more. But Weinberg's study finds that the poor spank more even after you've accounted for all of these effects. The question is why.
Here's one good alternative to the economic explanation: University of New Hampshire sociologist Murray Straus has published multiple studies concluding that children who are spanked are less successful as adults. If the link is causal—that is, if being spanked actually lowers your earnings potential—and if spanking runs in families, then we have an alternative explanation for Weinberg's numbers: Low-income parents are more likely to spank their children because low-income parents are more likely to have been spanked themselves. Or maybe it's as simple as this: Poverty breeds frustration, and frustrated parents lash out at their kids. Does any reader have a better story?