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The Least Surprising Correlation of All Time

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mwkruse
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Greg Mankiw's Blog: The Least Surprising Correlation of All Time

Sat scores by income

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.

He has a follow up: And I thought I was being boring

And this follow up: Test Scores and Biological Father's Income

Iq and income

 

Comments

5 responses to “The Least Surprising Correlation of All Time”

  1. Chuck North Avatar
    Chuck North

    The basic point is obviously correct – the correlation is driven by at least one other factor that causes both variables in question. But there is a decent amount of research from James Heckman and others that environment matters for test scores. So, while DNA certainly matters for intelligence, it is not all that matters, which means there may be dimensions of intelligence where well-crafted policy interventions would have measurable benefits over the long run.

    Reply
  2. Michael W. Kruse Avatar
    Michael W. Kruse

    “But there is a decent amount of research from James Heckman and others that environment matters for test scores.”
    The bottom graph seems to support that idea. It generally creates an upward curve.

    Reply
  3. JMorrow Avatar
    JMorrow

    While I think there is plenty of evidence to suggest we aren’t all born blank slates and therefore are subject to genetic advantages, disadvantages and just plain differences, I find it hard to believe IQ is the ONLY ommitted variable bias in play here. There are so many questions to be raised with this kind of graph, that I wonder what the use of correlating this data is.
    What do we make of the social advantages of income on the prospects for education and intelligence? What do we make of the fact that certain professions are rewarded financially and some are not? What do we make of the specificity and context of what an IQ test covers? What do we make of “teaching to the test” vs. teaching with a broad understanding of intelligence and aptitude?
    Ultimately, is any of this data sharp enough to make helpful public policy?

    Reply
  4. neil Avatar
    neil

    Glad to hear it. I thought my kids were in big trouble being raised on a pastor’s salary 🙂

    Reply
  5. Michael W. Kruse Avatar
    Michael W. Kruse

    LOL
    My dad took a half cut in pay when I was nine to move from industry into teaching. There are positions that require considerable education that don’t generate high income. And there are some high income professions that require little education. It would be interesting to see how things correlate for children in those environments.

    Reply

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