Fallacies of Composition

Just because you combine things and make a chart out of the results doesn’t necessarily mean it makes any sense to do so. That was my reaction to this post at Econbrowser. Scan down to the two bar charts comparing public and private wages and compensation.

Skipping over that under the “All employees” classification (which, interestingly, shows that public and private compensation is about equal which sounds odd to me), the graphs illustrate that employees with bachelors only make slightly more in the private sector than in the public sector. However, I believe there’ are problems with this: it presumes that all bachelors degrees are worth about the same or, at least, that the particular bachelors degrees in the private sector have about the same worth as those in the public sector and it doesn’t account for differences in workloads.

Teachers with bachelors in education-only who attended state schools with relatively low academic standards and have, putting it kindly, lightweight programs who work a 10 month schedule (which accounts for the preponderance of primary education teachers) are being bundled with, for example, MIT grads with bachelors in electrical engineering. Should we be surprised or outraged that the latter earns more than the former? I don’t think so but the differences between those don’t show up in that bar graph.

Let’s take one, single occupation that’s employed in numbers in both the private and public sectors: lawyers. According to the BLS about a fifth of all lawyers are employed by local, state, and federal governments (I would contend that such a high proportion of government employees means that you can’t reasonably think of a market in legal services but that’s a topic for a different post). The median income for a lawyer is $113,240 and the income for lawyers who work fulltime for the government is significantly lower than for those fulltime in the private sector. Does this demonstrate that lawyers who work for the government are underpaid relative to their private sector counterparts?

The answer is a resounding “No”. Earnings in the practice of a law are in a bi-modal distribution. On the low end of that barbell are lawyers who make a median income of $35,000. On the high end of that barbell are lawyers who make a median income of $135,000. And then there are a rarified few who make significantly higher incomes than that, trailing off on the right hand side of the chart.

The point in all this is that the absence of a normal distribution means that it’s hooey to talk of means and medians in discussing earnings in the practice of law. I would further suggest that the “U” in that distribution represents lawyers who work for the government and that it’s as reasonable to suggest that they’re enormously overpaid as it is to suggest that they’re underpaid. I also guess that the right hand side of the distribution represents legal graduates who’ve graduated at the tops of their classes or who’ve graduated from a very, very small number of institutions.

Drawing a graph with a big bar on it that shows “Professionals” is very pretty and all but it doesn’t mean a damned thing. You’re comparing apples and oranges. It’s a fallacy of composition.

To produce something meaningful on this subject you’d need to go job by job, credential by credential and do a comparison of total compensation in the public and private sectors between things that were really comparable. The closest thing that I know to that is a recent study by the GAO of military compensation. It found that those in the military were significantly more highly compensated than their private sector counterparts, e.g. a truck driver in the military was more highly paid than a civilian truck driver.

3 comments… add one
  • Drew

    I’m feeling like a gentleman today, so let’s just say I have alot of time for James Hamilton, but for Menzie, as they say, – not so much. Menzie I find Krugmanesque……..

    Oh, what the hell. That post at Econbrowser was flat damned dishonest, constructed by someone smart enough to know how to throw dust in most people’s eyes, and by someone smart enough to know better. That leaves only one unfortunate conclusion.

  • PD Shaw

    I think that CATO or some other think tank did a decent study on this, with like-comparisons-to-like.

    I’ll say this with substantial confidence in my job market. Ninety-nine percent of private employers cannot compete with the salary and benefits provided by state government for a person engaged in secretarial/data entry/clerk type positions.

  • I’m pretty sure there was something about this on Outside The Beltway, actually. Though even then, Joyner pointed out that the comparisons were not apples-to-apples because of how government work can differ from non-government work (pilots being in the armed services, for example, and cafeterias vs restaurants).

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