Money=Smarts?

The New York Times published this interesting graph on its business blog today, which seems to indicate there is a strong positive correlation between family income level and SAT scores:


But before we start jumping to conclusions and deciding that we have to handicap the SAT by adding points for kids from lower income households (I say that as a joke, but it wouldn't surprise me too much), maybe there is something else at work here.

Greg Mankiw calls it the "least surprising correlation of all time", and argues that the effect is not causal because there is a pretty significant omitted variable bias at work here. In this case, the omitted variable is the parent's IQ. He argues that smart parents tend to make more money, and they pass those good, smart genes (not to mention an interest in learning, no doubt) on to their kids. He also offers this fantastic tidbit:

"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."

Alex Tabarrok of Marginal Revolution takes the same argument and goes one step further with the statistics. He offers this graph, which charts the income of adopted versus biological children with regard to the income of their parents:

While there is a noticeable positive correlation between biological children's income and that of their parents, the correlation is non-existent for adoptees. So, it appears that genetic material plays a stronger role in children's success than simply growing up in a big, expensive house. Score one for nature over nurture here.

In general, I think it is also worth noting that the effect seems to be overstated a bit. Based on the average of the whole graph, moving up an income level equates to a 12 point rise in SAT scores (which is certainly considerable), but most of that effect is on the lower end of the scale. Once you get above a 6-figure income, the trend flattens out. The jump at the end is due to the fact that the last income category is open-ended and thus contains a much larger range of potential components, so that should be disregarded.

Using "family income level" for something like this is ultimately a flawed premise anyway. There are way too many variables in something like how much money a family makes to ever use that as a standard for measuring anything else. It doesn't have to be all about the parent's IQ either. The parent's level of education, their work ethic, and even something as simple as where they live will all impact income level.

How do we know which of these variables is at work as the reason why kids from richer households get higher SAT scores? It could be all three (plus others, I'm sure), or it could be all because they happen to live in richer areas with better schools. The point is, you can't make either of those conclusions from this kind of information.