The Variance of Fat

I was under the impression that the whole distribution of body weight was shifting to the right.

That is, the average person weighs more but there is an approximately constant distribution around the mean. This is wrong.

Check the following figure from a discussion of obesity trends by the Center for Disease Control:

Obesity has almost tripled since the early 1960s (13% to 35%). Extreme obesity has risen by more than a factor of 6 (0.9% to 6.2%). Yet mere overweight status, a BMI between 25 and 30, has remained stable at about 32% of the population. The action is in the tails!

For a more complete view of the distributions for 1976-80 and 2005-6, look at the density figure on page 2 of this data brief.

To me it looks like BMI is distributed log-normally and the sigma parameter has increased. I don't see how this would be predicted by either the biological or economic explanations discussed in my last post. Two ideas occur to me: First there is heterogeneity in the response parameter. As fat becomes cheaper, many are unaffected but some respond a great deal. Second, there are multiple equilibria. Given the opportunity to get fat people take it only when their neighbors do.

Why are people so fat and what should be done about it?

Elizabeth Kolbert has a very nice article in the The New Yorker about the rise in obesity (July 20, 2009). She summarizes some of the competing--and possibly complementary--hypotheses. I have come across some other thought-provoking articles in the Becker-Posner blog. (August 2nd, 2009)

The biological argument, summarized by Kolbert, says we humans were designed by evolution to put on fat whenever possible. Famine situations were much more likely than abundance so it was costless in evolutionary terms to give us insatiable desires for fatty foods.

The economic argument, summarized by Kolbert, Becker, and Posner is that it's now cheaper to get fatty foods than it used to be and opportunity cost of exercise has risen. Becker adds that medical treatments for health consequences of obsesity have also improved. Economic agents naturally do more of things that have become cheaper and less of things that have become more costly.

These explanations don't really conflict with each other in terms of predictions but they have different implications for the optimality of the rise in obesity. The economic story is consistent with the idea that getting fat is a utility-maximizing response to the falling cost of fat.

Posner thinks there are externalities so the rise in obesity may not be socially optimal.

The biological and economic explanations don't address the issue of why we have not ALL become fat. Presumably there is heterogeneity in the desire for fatty foods. Another idea that Posner alludes to is heterogeneity in self-control. He supports this by pointing out that higher educated people tend to be slimmer, and this difference does not seem to be just an income effect. Both education and low-fat diets involve decisions to make costly efforts now for future benefits. Presumably people with more develop pre-frontal cortexes are better able to make both decisions.

I like the idea that I have a better PFC than other people. But actually I think I'm slimmer mainly because of lower appetite.

Outliers I: Far from Obvious

In the next few posts I plan to write about Malcolm Gladwell's book, Outliers. I am about halfway through listening to the Audible.com version that is read by Gladwell. While the book keeps my attention as well as a good novel, the writing and reporting are engaging, the ideas fascinating, I frequently find myself complaining, "No way!" out loud in the car or on the walking path. So I decided yesterday to see what critiques the book has already received. I started with the Wikipedia article of course. And there I found a link to a review in The Independent. The harshest criticism is contained in the following passage:

Not for the first time, you wonder why Gladwell does not yet hold a tenured professorship at the University of the Bleedin' Obvious. Yes, he's right, but too often in a trivial, short-winded and centrifugal style.

The review in The Guardian finds the same fault in the book.

the conclusions he arrives at here are so obviously self-evident as to be banal.

Did we read the same book? While there are some claims that Gladwell makes that may seem obvious, I don't think that is a key problem. Rather I think it is the opposite. There are numerous claims that are not only far from obvious, they just look downright dubious. I don't have a hard copy of the book so I will paraphrase.

1. Every great contributor in a field had to spend 10,000 hours of practice to learn the techniques of the field. It is not totally clear to me whether Gladwell intends this as a necesssary condition or a sufficient condition or both. I think it is a necessary condition because it also seems to matter that the outlier have some particular form of practice, which only a limited number of candidates would have access to (e.g. Bill Gate's computer access and Beatle's Hamburg shows)
2. Intelligence only helps up to a threshold: After about 130, a higher IQ does not contribute to success.
3. Jews dominate the best New York law firms because they had been excluded by the blue-blood firms in the past, when hostile take-overs were shunned, and because their parents and grandparents worked in the garment industry.
4. Cohort is critical. To be a leader in your field, you should have been born in the right window, e.g. 1952-1956 for the modern computer/software industry, and the early 1930s for New York lawyers.
5. "Practical intelligence" is orthogonal to analytic intelligence (what IQ tests measure) and more important in determining success. Also practical intelligence is entirely a learned ability (no genetic component).

I don't believe the threshold effects at 10,000 for hours of practice or an IQ of 130. I have never seen non-linearities like that in the data and I can't think of any plausible mechanism whereby practice less than 10,000 hours would not increase probability of succes and intelligence over 130, would not continue to be of use, other things equal. I will have to look into the evidence underlying these claims, but at this point I would categorize #1 or #2 as totally implausible.

As for #3, it feels like a stretch. The theory (story) is constructed after looking at the data. It is so particular that I don't see this as a provable or easily falsified claim. I find #4 to be plausible but I would like to see rigorous statistical evidence. I have found a paper, "Dissecting practical intelligence theory: Its claims and evidence" (LS Gottfredson - Intelligence, 2003 - Elsevier) that criticises the evidence alleged to support Practical Intelligence. The author argues that practical intelligence is not clearly defined, that the tests used to measure it are not always orthogonal to IQ. Moreover, the tests were administered on groups such that were already selected for high IQ, restricting the range of IQ in the tested subjects and thereby lowering the observed correlations. Furthermore, Gottfredson says that IQ is asserted to have a 0.2 correlation with success whereas the literature finds results in the .2-.5 range.

These are key claims in the book. Gladwell spends large amounts of time explaining them, referring to academic studies alleged to support them, and providing anecdotal support through his own reporting. Not one of them is "bleedin obvious." Tenure denied.