Saturday, November 21, 2015

Too rich or too thin?

The Behavioral Risk Factor Surveillance System, despite its ominous-sounding name, is just a survey focusing on health.  It asks people for their height and weight.  As a result of an example I used for a class, I started thinking about the relationship between weight and earnings.  The BRFSS doesn't have a measure of individual earnings, but it has a question on family income, and for people who are single (never married) and employed, it seems safe to assume that income and earnings are usually very close.  Since the BRFSS obtains very big samples, that still leaves over 20,000 cases.  I controlled for gender, height and weight.  For both height and weight, I included the original and its square and allowed both to differ by gender.  The following figures show the predicted values for a range of weights at selected heights.

 For women, being thinner goes with having a higher income.  The relationship seems to flatten out at the lowest weights, but basically if your goal is to be rich (or at least reasonably well paid), you can't be too thin.  For men, the relationship is different--the highest expected earnings are at the middle weights, and the penalty for being below the "ideal" weight is at least as large as the penalty for being above it.  For example, at 6 feet, the highest predicted earnings are at a bit over 200 pounds, and the predicted values for a man who weighs 150 and a man who weighs 295 are about the same.

Although I was primarily interested in weight, I noticed that the influence of height also differs by gender.  Women benefit from being taller through the whole range. but the predicted values for tall men (6'4") and fairly tall men (6') are almost identical.

I wouldn't put too much faith in the exact shape of the curves, since I didn't experiment much with alternative specifications, but the possibility that "underweight" men earn less is intriguing.  I put "underweight" in quotes because men who are in what is officially classified as the "normal or healthy" range earn less than men who are in the "overweight" range and sometimes even the lower reaches of "obese."

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