The Economix at NYT:
A few observations:
- There’s a very strong positive correlation between income and test scores. (For the math geeks out there, the R2 for each test average/income range chart is about 0.95.)
- On every test section, moving up an income category was associated with an average score boost of over 12 points.
- Moving from the second-highest income group and the highest income group seemed to show the biggest score boost. However, keep in mind the top income category is uncapped, so it includes a much broader spectrum of families by wealth.
The NY Times Economix blog offers us the above graph, showing that kids from higher income families get higher average SAT scores.
Of course! But so what? This fact tells us nothing about the causal impact of income on test scores. (Economix does not advance a causal interpretation, but nor does it warn readers against it.)
This graph is a good example of omitted variable bias, a statistical issue discussed in Chapter 2 of my favorite textbook. The key omitted variable here is parents’ IQ. Smart parents make more money and pass those good genes on to their offspring.
Suppose we were to graph average SAT scores by the number of bathrooms a student has in his or her family home. That curve would also likely slope upward. (After all, people with more money buy larger homes with more bathrooms.) But it would be a mistake to conclude that installing an extra toilet raises yours kids’ SAT scores.
It would be interesting to see the above graph reproduced for adopted children only. I bet that the curve would be a lot flatter.
But merely saying that correlation is not always causation and dropping the issue is, I think, profoundly unhelpful–and shows a… lack of work ethic as well.
Off the top of my head…
IIRC, the age-adjusted correlation between log income and IQ is 0.4: take someone with a log income higher by one standard deviation than average–these days someone with a middle-age-adjusted family income of $100,000-$120,000 rather than $60,000-$80,000–and their IQ is likely to be 0.4 standard deviations (6 points) above average. The individual heritability of IQ is about 0.5: take an individual with a IQ 6 points above average and their children will be expected to have an IQ 3 points above average. SAT scores have a mean of 500, a standard deviation of 100, and a high but not a perfect (0.7) correlation with IQ.
So if we compare people whose parents have an income of $100,000-$120,000 to those with an income of $60,000-$80,000 we would expect to see 1 x 0.4 x 0.5 x 0.7 x 100 = 14 points. The actual jump in the graph Mankiw refers to is twice as large.
The rule of thumb, I think, is that half of the income-test score correlation is due to the correlation of your test scores with your parents’ IQ; and half of the income-test score correlation is coing purely from the advantages provided by that component of wealth uncorrelated with your parents’ (genetic and environmental!) IQ.
The curve is less steep, but there is definitely a “what” here to be thought about.
Oh, Kay. Greg Mankiw looks at a graph showing that children of high-income families do better on tests, and suggests that it’s largely about inherited talent: smart people make lots of money, and also have smart kids.
But, you know, there’s lots of evidence that there’s more to it than that. For example: students with low test scores from high-income families are slightly more likely to finish college than students with high test scores from low-income families.
It’s comforting to think that we live in a meritocracy. But we don’t.
John Carney at Clusterstock
What both economists are missing is the notion that a meritocracy isn’t actually all that desirable. And it would be highly inefficient.
In order to establish anything like an equality of opportunity, we’d have to deny everyone the advantage of having well-off parents. In a world of unlimited resources and really good educational professionals, this could be done by making sure every kid gets all the educational and cultural advantages that are associated with wealth. In the real world, however, that’s not possible. Here are several limiting factors.
- We don’t really know what it is that wealthy parents impart on their kids that makes them do better. It’s clearly not just having bigger bank accounts.
- We don’t know how to change the way poorer parents raise their children.
- We’re not willing to accept the cultural implications of changing the way parents raise their children.
- We don’t have the resources to raise every kid’s upbringing to the level of the wealthiest 5%.
That sounds terribly pessimistic. And a lot of economics types probably conclude that it means we’re operating a lower than desirable level of societal efficiency because some would be smart kids from poorer backgrounds wind up not realizing their potential. But it really isn’t all that bad.
What the pro-meritocracy ideology overlooks is something every parent knows: one of the key motivating factors to “realize your potential” is to give your kids an advantage. You want their lives to be slightly easier than your own, if possible. You accumulate wealth to pass on to the youngsters. In a world where this were not possible, either because confiscatory taxes eliminated the wealth effect or subsidies accomplished the same thing, the desire to work hard, earn more and save would be highly diminished. Meritocracy would actually diminish our wealth.
UPDATE: Matthew Yglesias