If public employees are underpaid, they ought to get raises when they switch to the private sector. But they don’t, and that fact is telling.

Debates over compensation for public employees have raged at all levels of government over the past few years. The Federal Salary Council, an official advisory body, claimed in October that federal employees are paid only 65 cents for each dollar earned by workers in comparable jobs outside the federal government.

Federal workers would seem to be drastically underpaid, based on the council’s numbers. But what does it really mean for public employees to be “underpaid” or “overpaid”?

Here’s one way to think about it: If a worker is overpaid, he’d probably receive lower pay from most other employers. Likewise, an underpaid worker should be able to get a raise by performing similar work for a different employer.

This theoretical framework, as simple as it sounds, is an intuitive “sanity check” on comparisons of public and private pay that often can be quite technical. It also carries the advantage of controlling not only for conventional differences in worker skills, such as education and experience, but also for attributes that are difficult or impossible to measure directly.

Analyzing how salaries for the same workers change as they shift between jobs in the public and private sectors automatically controls for worker traits that aren’t directly measured in most datasets – traits such as intelligence, motivation and creativity. Only the job changes in these comparisons; the worker stays the same.

The Census Bureau tracks tens of thousands of households over several years in its Survey of Income and Program Participation (SIPP). Many workers in these households switch jobs during this time, allowing us to observe how workers’ salaries rise or fall as they change jobs.

So what can applying this job-switching test to the SIPP data tell us about public employee pay? Keep in mind that the Federal Salary Council’s numbers imply that in taking a job outside government, the average federal employee would receive a staggering 54 percent increase in salary. In the real world, though, the data show that most federal workers looking to cash in by leaving will end up disappointed.

According to the SIPP data, the average federal worker shifting to a private job actually accepts a small salary reduction of around 3 percent. Similarly, private sector workers who move to federal jobs don’t take a pay cut. They get a first-year raise averaging 9 percent, well above the raise other workers get when they switch jobs within the private sector.

In short, there’s real-world evidence that federal salaries are at least equal to private-sector salaries for workers with the same skills.

Now consider the state and local levels. If any group of public workers is underpaid, conventional wisdom suggests it would be schoolteachers.

Indeed, a prominent study from the Economic Policy Institute concluded that teachers in public schools are paid 14 percent less on average than private-sector workers said to have similar skills. But if that comparison is sound, we’d expect that teachers moving to the private sector would get a raise, while private-sector workers shifting into teaching would take a hit.

Not so. Nationwide, non-teachers who move into teaching receive an average raise of around 8 percent, according to SIPP data, while teachers who leave the profession take an average salary cut of around 3 percent. Similarly, three recent state-level studies (in Florida, Missouri and Georgia) using administrative records found no average wage increase for ex-teachers.

Of course, it’s possible that the public employees who move to the private sector are among the least-skilled workers, helping to explain why they don’t receive big pay increases. Even if this is the case, however, it implies that the most skilled government workers don’t require a salary increase -- since they don’t leave their jobs in the first place.

And at least in the case of teachers, those who quit aren’t necessarily unrepresentative of their peers. Using value-added ratings of teacher effectiveness, the Florida study mentioned above found that teachers who left the profession didn’t have significantly lower ratings than those who stayed.

Importantly, none of the tracked changes in salary after job switches takes into account the job-to-job changes in fringe benefits. Most public employees have guaranteed pensions and retiree health coverage, both of which are increasingly rare in the private sector.

In a competitive labor market, superior benefits should allow governments to offer lower salaries while continuing to attract and retain employees. But the evidence indicates that government salaries alone are comparable to, and often more generous than, those in the private sector.

Many public employees honestly believe that they could earn much more in the private sector. As it happens, though, few actually do. With federal, state and local governments paying out almost $1.5 trillion in employee compensation in 2012, this isn’t a trivial fact.

When policymakers understand that public employees are far from underpaid, they can take steps to control spending at all levels of government.

Jason Richwine is a senior policy analyst at The Heritage Foundation. Andrew G. Biggs is a resident scholar at American Enterprise Institute.