It’s rare that the political blogosphere burns up with arguments regarding statistical methodology, but the comments of Jim Manzi at National Review on a recent report by the Economic Policy Institute’s Jeffrey Keefe on public sector pay in Wisconsin has generated a running debate with Ezra Klein, plus some interesting comments from Megan McArdle and Kevin Williamson. Over the past year, Jason Richwine of the Heritage Foundation and I have spent a lot of time thinking about public sector pay, including articles in the Wall Street Journal last year, the American Spectator, the Weekly Standard, and a new piece on California public employee pay in today’s Wall Street Journal.
The EPI analyzed Wisconsin salaries using survey data on thousands of individuals, containing information on their earnings and a raft of earnings-related characteristics such as age, education, race, gender, marital status and, most importantly, whether the individual works in government or the private sector. EPI’s Keefe used regression analysis to control for differences in these characteristics to isolate the effects of government employment on wages, finding a pay penalty of 11 percent. (We find a smaller 5 percent penalty for Wisconsin workers, presumably due to different specifications.)
We’ve used identical techniques to study federal employee pay, where we find a government pay premium of 14 percent. (If you’re wondering why EPI and other left-leaning think tanks have never produced a study on federal pay, there’s your answer.)
Over at the Corner, Manzi basically took issue with the whole approach that EPI and we have used.
Keefe is considering almost any full-time employee in Wisconsin with the identical years of education, race, gender, etc., as providing labor of equivalent market value, whether they are theoretical physicists, police officers, retail-store managers, accountants, salespeople, or anything else.
Manzi is basically arguing for “omitted variable bias,” in which the lack of data regarding relevant variables leads to a model to generating faulty or misleading results.
In our Weekly Standard article we acknowledged this potential problem:
Perhaps federal workers have some personality trait—greater motivation, for example—that we cannot measure adequately with our standard control variables. Or maybe our “years of education” variable disguises more prestigious degrees held by federal workers.
To address this, we did a second form of analysis that isn’t subject to Manzi’s objections. Rather than comparing different people at one point in time, this second approach – called a “fixed effects model” – follows the same people over time, specifically as private sector workers found new jobs which could be in the public or private sector. If workers get a bigger raise when they switch from private to federal employment than workers who switch from one private job to another, we can infer that the federal government overpays. As it happens, the fixed effects model shows an 8 percent pay premium in the first year of federal employment. We also know from the cross sectional regressions that the pay premium tends to grow with job tenure, so this result confirms our initial findings while addressing Manzi’s concerns.
The fixed effects model’s results on state/local salaries are at least roughly in line with Keefe’s findings, in that it finds that salaries are around the same in the two sectors. For technical reasons, if there’s measurement error in the data it will push the premium/penalty toward zero; so we know that the federal premium is at least 8 percent for new hires, but the state/local penalty could be larger than the fixed effects model shows.
But that doesn’t mean that EPI’s conclusion that Wisconsin workers are underpaid holds true. I recently raised questions regarding EPI’s treatment of benefits, and our new Journal piece shows – using California workers as an example – that generous benefits and job security can easily make up for a modest public sector salary penalty. (See here for a more technical explanation of our results.) An upcoming op-ed will focus on Wisconsin workers and may show the same results.
I suspect there’s a bit of ideological bias on both sides. When a statistical method shows that state/local workers are underpaid on salaries, the left embraces them and the right is skeptical. But if those very same methods show that federal workers receive a hefty salary premium, the left ignores them – is Ezra Klein now going to conclude that federal employees are overpaid? – and the right, or at least my part of it, buys into them. In the end, though, the methods we’re talking about have been widely used in a variety of areas – the union pay premium, gender and race discrimination, and so on – and we should take their results seriously.
Andrew Biggs is a resident scholar at the American Enterprise Institute. His work on public sector pay is co-authored with Jason Richwine, a senior policy analyst at the Heritage Foundation.