Should federal workers get a raise? With salaries and benefits paid to the government’s civilian workers totaling $271 billion in 2011, deciding whether to extend the freeze enacted last year on cost-of-living increases has important budgetary consequences. Unfortunately, the government’s methodology for comparing pay is too flawed to offer real guidance.

The Federal Salary Council, an advisory body of academics and leaders of public employee unions, suggested last month that federal workers are underpaid by an average of 35 percent relative to nonfederal employees. The council’s data come from the “President’s Pay Agent,” the bureaucratic entity that conducts the federal government’s annual pay comparison.

Employee unions seized on this figure, using it to push back against salary freezes. But the pay agent’s latest conclusions actually highlight the inadequacy of its methods.

If these figures are to be believed, federal employees are paid only 65 cents for every dollar received by nonfederal employees doing the same work. Put another way, the average federal employee who shifts to a job outside government would increase his salary by 54 percent.

The figures are implausible on their face. How could government pay employees more than one-third less than the going rate, yet keep employee turnover at only a fraction of the private-sector turnover rate? Data from the Bureau of Labor Statistics Job Openings and Labor Turnover survey show that, from 2001 to 2010, federal employees quit their jobs at less than half the rate of workers in large private-sector companies.

Here is the truth behind these numbers:

First, the pay agent doesn’t consider fringe benefits, even though benefits for federal workers are famously generous. In addition to a 401(k)-type pension with a handsome employer match, federal workers receive a traditional defined-benefit pension — for which they contribute less than 1 percent of salary — as well as retiree health coverage. A Congressional Budget Office study published in January found that the federal retirement package was 2.7 times more generous than what is paid by large private-sector firms. Federal workers also receive more paid vacation and sick days. Even if they endured a salary penalty of 35 percent, their benefits would make up much of the difference.

But federal salaries are not 35 percent below private-sector levels. All five outside studies reviewed this year by the Government Accountability Office found that federal pay is equal to or higher than those of comparable private-sector workers. This is consistent with three decades of academic research. According to our analysis of Census Bureau data last year, the typical private-sector worker who shifts to a federal job receives a salary increase, while federal workers who leave for the private sector tend to get a salary cut.

So where does the government calculation go wrong? To begin, it compares pay for federal jobs to nonfederal positions at a similar “grade,” or level. Yet both the CBO and the GAO have documented “overgrading” in the federal workforce, meaning that federal jobs could be assigned higher grades on the General Salary Schedule than the pay agent assumes for their nonfederal equivalents. This can create the appearance of pay differences where none exist.

The pay agent also doesn’t consider the relative qualifications of federal employees. In a 2002 study, economist Melissa Famulari concluded: “Federal workers have significantly fewer years of education and experience than private sector workers in the same level of responsibility in an occupation.” For example, a senior accountant in the federal government may have the qualifications of a junior accountant in the private sector. Such skill differences are important determinants of pay.

Additionally, the problems with the official pay comparison are well known. The authors of the pay agent’s annual report regularly call for a reexamination of the underlying methodology.

While the issues here may seem complex, the solutions are relatively straightforward:

First, federal-to-nonfederal pay comparisons must include the value of fringe benefits such as paid leave, health coverage and pensions.

Second, the pay agent should “grade” both federal and nonfederal jobs using the same criteria.

Third, pay comparisons must consider not only the work required but also the skills characteristics of the workers doing the jobs. This approach is favored by most labor economists working on compensation issues and is reflected in numerous studies by academic journals, think tanks and government agencies, including the CBO.

Federal employees should be compensated at fair market levels, which would allow the government to hire and retain workers without overcharging taxpayers. An essential first step toward that goal is ensuring that the government’s annual pay comparison is objective and comprehensive. Unfortunately, the present system is neither.

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