For over a year now, a debate has been raging over whether public-sector workers are paid too much. In the last few days, spurred by the protests in Wisconsin, Jim Manzi, Kevin Williamson and other conservative newcomers to the debate have been embarrassing themselves and making things uncomfortable for some of their fellow conservatives who have been engaged in the debate longer.

If like Manzi, you are new to this, you'd be excused for thinking that the main issue is whether or not it makes sense to gauge the level of public-sector pay using what economists call "human capital" models. These models are among the oldest and most successful empirical models in all of economics. They argue that workers' wages and benefits generally reflect their level of education and their work experience, both of which are proxies for their underlying skills or productivity on the job. A vast empirical literature supports this view, showing a strong relationship between pay, education and experience, in virtually every country and every period that economists have ever examined. That said, even this strong empirical relationship leaves a lot of the variation in wages across workers unexplained. Even with identical levels of education and experience, women make less than men, blacks less than whites, residents of Wyoming less than residents of Connecticut. And even among, say, white women who live in Connecticut and have the exact same level of education and experience, pay can vary substantially. Typically, "human capital" models are lucky to explain 30 or 40 percent of the total variation in wages.

Manzi criticizes recent research in this vein by Rutgers University economist Jeffrey Keefe, who has analyzed the pay of state and local employees nationally and in several states including Wisconsin, for the Economic Policy Institute. (The National Institute for Retirement Security, the Political Economy Research Institute, and CEPR have done similar research.) For Wisconsin, Keefe's standard human capital model showed that state and local public workers receive about five percent less in total compensation than a worker with similar basic characteristics in the private sector.

Manzi argues that Keefe's approach ignores "an all-but-infinite number of ... relevant potential differences between the weight[ed]-average public-sector worker and the weight[ed] average private-sector worker." Manzi's argument is over-the-top -- there may be an "all-but-infinite number" of potential factors -- but there are actually a fairly small number of factors that Keefe has not included that could be relevant: say, the type of education (an English versus an engineering degree); on-the-job training (more likely in the public sector than in the private sector); different degrees of motivation or ambition; a worker's raw "intelligence" (however that can be measured); and a few others. But, Manzi's argument is also basically correct. We know that human capital models explain well less than half of the variation in pay across workers, so we know that they leave a lot out.

The real question over the last year or so, however, is not whether human capital models are a perfect measure of differences in pay between public and private sector workers. The real question is whether they are a better way to measure differences than using simple raw averages. USA Today, for example, has specialized in comparing the average compensation of all public workers and comparing this with the average compensation of all private-sector workers (see, for example, "Federal workers earning double their private counterparts"). And this has become a standard conservative talking point.

John Boehner: ""It’s gotten to a point where the average federal worker makes twice as much as the average private sector worker." 

Tim Pawlenty: "Federal employees receive an average of $123,049 annually in pay and benefits, twice the average of the private sector. And across the country, at every level of government, the pattern is the same." 

Rand Paul: "The average federal employee makes $120,000 a year. The average private employee makes $60,000 a year."

(Hat tip: RolandC.)

What all of these raw comparisons ignore is that the federal, state, and local work forces are on average much better educated and older than the private-sector workforce. The EPI, NIRS, PERI, and CEPR research is a response to these conservative talking points that ignore systematic differences in the public- and private-sector workforces.

Manzi gets very worked up about Keefe's human capital model:

"[Keefe's] use of the statistical tests that he claims show that the total public–private compensation gap is “statistically significant” are worse than useless; they are misleading. The whole question — as is obvious even to untrained observers — is whether or not there are material systematic differences between the public and private employee that are not captured by the list of coefficients in his regression model.  His statistical tests simply assume that there are not."