The Public-Private Pay Gap and Simpson’s Paradox

Posted by Nolan Miller on Jun 21, 2010

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With government budget deficits rising across the country, there has been much ado lately about whether government employees are overpaid.  In many cases, attention has been focused on a few unusual cases – football coaches, university presidents, retiring public employees drawing large pensions, etc.  This is fun, and it fans the fires during a period of growing anti-government sentiment, but it doesn’t do much to clarify the question of whether public sector employees are overpaid.  After all, if you are going to look at the highest-paid public employees, shouldn’t you compare them to the highest-paid private ones?  And, compared to a typical hedge fund manager, the salaries earned by football coaches and university presidents is tiny.

 No, the right question is not whether there are a few public employees that are paid a lot.  There are.  And, arguably, there’s nothing wrong with a person being paid a lot.  What would be wrong is if the person is paid dramatically more in the public sector than he or she would be in the private sector due to inefficiency or corruption in the public system.  And, if it were true that the average public employee’s total compensation were higher that could be received in the private sector, this would suggest there are problems with the entire system.  Despite the occasional highly-paid private employee, there seems to be little evidence that total compensation for public employees, on average, is higher than total compensation for those workers were they employed in the private sector instead.

 Two recent stories have pushed the idea that government workers are overpaid.  The first was a USA Today story from earlier this spring that argued that, focusing on occupations that exist both in government and the private sector, in 2008 the average federal employee earned $67,691 while the average private sector employee earned $60,046.  Benefits for the average federal employee were $40,785 per worker while private sector employees received $9,882 per worker on average.  So, federal employees earned a higher salary and more benefits, and total compensation for a typical federal employee was about $38,500 higher than in the private sector.

A BLS report released last week tells a similar story regarding the gap between state and local worker total compensation and that of the private sector.  The report finds that total compensation for state and local workers averaged about $39.81 per hour (in March 2010), while private worker total compensation averaged about $27.73 per hour.  So, the total cost of an average state/local worker is about $12 more per hour than a typical private worker.

Of course, these comparison cannot possibly be right.  It simply doesn’t pass the smell test.  I’ve known people who left the private sector for government work, and they never did so for higher salary.  Shorter hours, yes.  Better benefits, yes.  More job security, yes.  But better pay?  If the average federal employee got almost $40,000 more in total compensation each year than he or she could earn in the private sector, we should expect to see people clamoring to leave their private sector jobs for federal jobs.  The same is true for state/local workers.  We should see a line of private-sector workers trying to move into lucrative government work.  We don’t really seem to see either of these.

The most likely cause of the suspicious numbers is the fact that government employees, as a group, are different than private sector employees.  If government employees are, on average, more educated and more experienced than private sector employees are, on average, then this could account for the difference.  To take a concrete example, suppose the private sector and public sector each hire 10 employees.   Ignore benefits cost to make things simple.  The private sector pays lawyers $120,000 and clerks $40,000 each and hires 3 lawyers and 7 clerks.  The average cost of a private employee is $64,000.  The public sector, on the other hand, pays lawyers $100,000 and clerks $30,000 and hires 5 lawyers and 5 clerks.  Despite the fact that the government pays lawyers less than the private sector and clerks less than the private sector, the average cost of a government employee is $65,000 per worker in this example.   Even though the government pays both high-skill (lawyers) and low-skill (clerks) workers less than the private sector, the average compensation cost in the public sector is higher due to the fact that it employs a greater proportion of high-skill workers!

The previous paragraph illustrates a phenomenon known as Simpson’s Paradox.  I first learned of Simpson’s paradox in the context of airline delays.  To take a simplified version, compare two airports, Seattle and Phoenix.  (I’m making all these numbers up.)  Suppose that when it rains in Seattle the typical flight is delayed 15 minutes and when it doesn’t rain the typical flight is delayed 0 minutes.  In Phoenix, on the other hand, when it rains the typical flight is delayed 30 minutes and when it doesn’t rain the typical flight is delayed 5 minutes.  Now, suppose I were to tell you that the average flight out of Seattle is delayed longer than the average flight out of Phoenix.  How would you make sense of that?  Your response might be “well, that’s because it rains all the time in Seattle!” and that would be the right answer.  Suppose it never rains in Phoenix.  The average delay is 5 minutes.  If it rains 2/3 of the time, the average delay in Seattle is 10 minutes, and 10 is more than 5.  In fact, as long as it rains more than 1/3 of the time, average delays in Seattle will be longer than average delays in Phoenix, despite the fact that Seattle has shorter delays both on days when it rains and days when it doesn’t rain!

Enough for today.  Next time I’ll write about this report, which does a better job with the data and claims to show that government workers are underpaid.  It isn’t perfect either.