Lies, Damn Lies, and Statistics

Greg Mankiw, an economist at Harvard, is busy proving that people with high salaries and high test results are that way because they are just plain smart, i.e. high IQs. Not because wealth buys better education. Nope. He firmly believes that cream rises to the top, so good test results and big incomes just naturally come to those who are "smart".

In his blog, he presents this graph:


Then he makes the statement:

It would be interesting to see the above graph reproduced for adopted children only. I bet that the curve would be a lot flatter.

David Cesarini, an economics professor at MIT, provides him with the desired graph:


Which Mankiw takes as evidence of his claim.

But if Mankiw were truly honest with himself, he would expect the line for the adopted children to be absolutely flat, i.e. completely uncorrelated with income because adopting is about as close to a fair lottery as you can get.

Instead, where he sees a "lot flatter" curve, I see a curve that looks pretty highly correlated with wealth. Yeah, it is kind of flat for the middle 4 deciles, but the overall curve is very strongly correlated with the level of wealth and has the same shape as the ordinary children.

So where I see evidence that wealth buys you good test results, Mankiw sees confirmatory evidence that the smart are just naturally rich and get good test results. Funny.

They say "beauty is in the eye of the beholder" but I think this proves that economic "truths" are also in the eye of the beholder.

There is more info on at Wikipedia on nature versus nurture. And it gets more complicated because of epigenetics where experience changes gene expression. From my perspective, the best approach is probably "nature through nurture" as in...


In other words, the two factors are inextricably intertwined.

Update 2009sep02: In the comments you will find that I am caught out on too quickly reviewing the graphs and not getting the details straight. So look at the comments to see what went wrong.

The more important point is that the debate goes on. There is a very interesting blog by Alex Tabarrok on the Marginal Revolution site. It has this graph:


That appears to be the graph that Greg Mankiw should have presented because it has the "flat line" for adoptees.

Here's some of Alex's commentary:

The graph shows how parent income at the time of adoption relates to child income for the adopted and "biological" (non-adopted) children. The income of biological children increases strongly with parental income but the income of adoptive children is flat in parent income. What does this mean?

The graph does not say that adopted children necessarily have low income. On the contrary, some have high and some have low income and the same is true of biological children. What the graph says is that higher parental income predicts higher child income but only for biological children and not for adoptees.

Now what about education? Sacerdote looks at that as well. He doesn't have a child SAT-score, parent-income correlation but he does find:

Having a college educated mother increases an adoptee's probability of graduating from college by 7 percentage points, but raises a biological child's probability of graduating from college by 26 percentage points.

The effect for father's years of education is even larger; about a ten times larger effect on biological children than on adoptees. Similarly, parent income has a negligible effect, small and not statistically significant, on an adoptee completing college but an 8 times larger and statistically significant effect on a biological child completing college (Table 4, column 3).

So... is the debate over? No.

• Not if you look carefully at Tabarrok's comments. Note that he doesn't have the SAT or IQ scores that Mankiw really wants. But he does have data about scholastic achievement, and it isn't a flat line. In other words, wealth of the family translates into better academic success. That is not what Greg Mankiw wants the data to say.


• Not if you look at the comments to Alex's posting. A lot of people jump all over him with alternative interpretations of "the" data. That's what makes science so interesting. The facts don't "speak for themselves". You have to interpret them. And your theory is your filter through which you see the facts.

This debate of nature/nurture is very old. It won't go away quickly. But it is an interesting debate that merits time looking at it and understanding your own position/prejudice.

Update 2009sep21: There is a very interesting discussion of the shortcomings of Mankiw's interpretation of the data in a posting by Mike Konczal on his blog Rortybomb. Go read the posting!