Wednesday, February 13, 2013

More fun with charts

Daniel Kuehn and Joseph previously discussed this post by Megan McArdle entitled "Department of Awful Statistics: Income Inequality Edition." They both make good points, but I'd like to approach this from the angle of appropriate visualization. McArdle supports her thesis that the middle class is neither disappearing nor getting poorer with charts derived from census table H-17 which you can and really should download here (the best way to keep us all honest is to play along at home).

The trouble is they're bad graphs.

To the extent that statistics includes data visualization, this is definitely bad statistics. When trying to depict trends and relationships, you generally want to get as much of the pertinent information as possible into the same graph. You don't want to force the reader to jump around the page trying to estimate slopes and compare magnitudes, nor do you want to take a few snapshots when you can easily picture all the data.

There are lots of acceptable ways of laying out the data table H-17, but I'm going just going to go with the simplest (partly because I like simple and partly because I'm doing this on Openoffice). As with McArdle's graphs, the numbers are inflation-adjusted.

I'm not that comfortable with this data (for reasons I'll get to in a minute), but this does look fairly consistent with the hollowing out of the middle class with 35K-75K (the top two lines) dropping more or less steadily for decades. Also check out the more than fourfold increase of people making more than 150K,

The two main things that make me uncomfortable with the data are the start point (with falls close to at least a couple of inflection points) and, on a related note, the failure to account for the baby boom which was at the bottom of its earning power forty years ago and should be close to the maximum now.

As far as I can tell income distribution is not broken down by age in these tables (though I suspect the data are available on request). We can, however, answer the related question of what median income looks like when we control for age and extended over a longer interval. (Download table P8 from here)

You can see why I was nervous about starting in 1967.

The question of income inequality and what's happening to the middle class is a complicated one and is probably best addressed by people who know what they're talking about, but if you are going to try to argue one side of the case graphically, you should at least take the time to use appropriate graphs.

p.s. I picked 35-44 because it seemed like a good representative mid-career interval and because, since I wasn't comparing different age groups, an uncluttered one-line graph seemed sufficient. If you prefer, here's the multi-range version (though I don't know if it adds much information).


  1. One remaining problem in the original articles that got carried over into this article is the use of the words "middle class".

    35-75K household income is NOT middle class, and it never was. It is high end of blue collar / working class. As you can easily see for yourself, for example, by scanning through sociology textbooks on, middle class is "...likely to include college-educated managers, supervisors, executives, owners of small businesses, and professionals (for example, lawyers, doctors, teachers, and engineers") ("Sociology: Exploring the Architecture of Everyday Life, Brief Edition",
    David M. Newman, p. 146), "with very few exceptions, all middle class people are college graduates" and "the middle class as a whole is about 35 percent of the population" [near the top of the social scale, just below the upper class, which constitutes at most 2-3%] ("Basic Sociology", C. Emory Burton, p. 158 and on.)

    Just going from the fact that "all middle class people are college graduates", since, according to the Census Bureau, average earnings of a full time employed male with a bachelor's degree is $92,800 and for a female it's $62,200, and there is a large percentage of two-income households among middle class households, it is typical for a middle class household to have a six-digit income. (You can try to pry this data directly out of the Census database, but you have to make sure to exclude grad students and retirees from the set, or you'll get a misleadingly low number.)

  2. Good middle-class definition reminder.

    An example might be a dual military couple (both commissioned officers) will make six-figures without factoring in allowances for housing and subsistance. Both have degrees (mandatory) so fit into the definition well.

  3. And military would be towards the low end of middle-class income range (precisely because of stuff like the housing subsidy or the most generous pension plan outside California public employee system).

    Identifying households with 50K annual income as "middle class" is a remarkably common mistake among journalists. I suspect that it is an occurrence of the Lake Wobegon Effect. The journalist may be familiar with the definition that middle class status implies having a college degree; journalist's own household income is pretty average by middle class standards (say, low 100's); but the journalist feels that he/she "made it" and thinks that he/she's successful (who doesn't?) and therefore the majority of the "middle class" must be below his/her own income.

    Besides, an article about the (alleged) suffering of the middle class is bound to be more popular than an article that observes that blue collar working class is getting poorer.