Tuesday, September 21, 2004

A Rising Tide Lifts All Boats

This opinion column provides some nice examples of the economic principle referred to in the title of the post: That when the economy as a whole grows, everyone in it benefits.

My personal favorite:
Seventy-six percent of poor households have air conditioning. By contrast, 30 years ago, only 36 percent of the entire U.S. population enjoyed air conditioning.

Of course, in all fairness, I should point out that this paragraph is completely inaccurate:
Overall, the typical American defined as poor by the government has a car, air conditioning, a refrigerator, a stove, a clothes washer and dryer, and a microwave. He has two color televisions, cable or satellite TV reception, a VCR or DVD player, and a stereo. He is able to obtain medical care. His home is in good repair and is not overcrowded. By his own report, his family isn't hungry, and he had sufficient funds in the past year to meet his family's essential needs.

The author appears to have simply taken a bunch of items that individually appear in more than 50% of poor households, and stuck them all together as if they were items that all appear together in more than 50% of poor households. In reality, the "typical American defined as poor" probably has one or two of the things in that list, but I would be surprised if more than a very small percentage of them had all of these things, as it is presented here.

As a rough estimate, make the simplifying assumption that these items are independently and randomly distributed among poor households (they wouldn't be, but I don't have any other data to go on). You can them multiply out the percentages of each of the things listed in that paragraph for which percentages are given: Car, air conditioning, microwave, two color televisions, cable or satellite TV reception, a VCR or DVD player, and a stereo (for those given as only "more than half", I assumed 55%). What you end up with is that, assuming a purely random distribution, only about 6% of poor households would actually contain all of these things together.

Unfortunately, the author of this column has buried the valid point ("Most of America's "poor" live in material conditions that would be judged as comfortable or well-off just a few generations ago.") in favor of attempting to make a point that is much less supported by the evidence he cites ("While this individual's life is not opulent, it is equally far from the popular images of dire poverty...")

1 comment:

Kwik2Jujj said...

You're absolutely right! In fact, it seems like this statistical fallacy should have a name. I nominate "Fallacy of the Perfectly Average Army," i.e. the notion that independent majoritarian group characteristics are all true of a majority of individuals.