"Scapegoating,” claimed the American Federation of Government Employees. “Punishment,” said the Federal Managers Association. “Transparently cynical,” declared Paul Krugman. President Obama’s late November announcement of a two-year pay freeze for federal workers has been poorly received by unions and left-wing activists, who see it as the end result of a year-long campaign to reduce federal salaries. Taxpayers should hope it is just the beginning. Fundamental reform of federal pay would save tens of billions of dollars annually, and it would be a strong indication that lawmakers are serious about reducing long-term deficits in all parts of the budget.

Unfortunately, the debate over federal pay has been fraught with extreme claims. Some politicians have accused federal workers of making double what they deserve, while government unions maintain they are underpaid by around 25 percent. The rhetorical back and forth has largely hidden a substantial academic literature, dating back to the 1970s, that compares the pay of federal and private workers. Economists have addressed the issue with a variety of techniques and from a number of different angles. Over the past year, we have worked to update their results with the most recent data, and our conclusions have been the same as theirs: Federal employees do receive a substantial wage premium by comparison with similar private workers. 

The standard approach to comparing the salaries of different groups is to employ the “human capital model,” which assumes that workers are paid according to their skills and personal characteristics. If any group differences in wages remain after controlling for age, education, experience, race, gender, marital status, immigration status, state of residence, and so on, then one group is said to enjoy a wage premium over the others. Economists using this approach find that federal workers generally earn wages 10 percent to 20 percent higher than comparable private sector workers. When we ran a similar analysis with 2009 wage data from the Current Population Survey (CPS), the result was a 12 percent premium. James Sherk of the Heritage Foundation found that the federal premium today could be as much as 22 percent, depending on the specific control variables employed. In general, the federal pay premium is very large for lower and middle-skilled employees and shrinks for the best-qualified federal workers.

Because we have datasets like the CPS—large, representative samples of American workers providing abundant demographic details—the human capital method is the best and most widely accepted method of comparing pay across groups. But the method does have some limitations, which defenders of federal pay use to cast doubt on these results. The press often has obliged by portraying the pay debate as a he-said, she-said question that can never really be answered.

It’s useful then to approach the federal pay question from more than one angle. For instance, we might ask whether economists’ human capital model can really account for all of the relevant differences among workers. 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. Neither of these hypotheses seems particularly likely, but we can’t falsify them with the standard human capital model. It’s not feasible to measure directly every single human capital trait.

To address this concern, we can change the approach. Rather than comparing different people at one point in time, we can follow the same people through time. Workers frequently change jobs, and sometimes they switch between federal and private sector jobs. Their change in wages when they make this switch can tell us a lot about federal pay. If workers get a much 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.

Following individuals over time builds into the analysis an ideally rich set of control variables. When people change jobs, they bring with them not just their observable skills like work experience and education, but also their intelligence, their motivation, their specific training, and whatever else affects their productivity. We need not directly measure these variables. All are naturally controlled for when we compare the change in wages people experience when switching between the federal and private sectors.

The specific econometric procedure is called “fixed effects,” because it focuses on wage changes for individual workers, who have many characteristics that are fixed from year to year. One of the first economists to apply fixed effects analysis to the federal pay issue was Princeton’s Alan Krueger in 1988. Using a dataset called the Displaced Workers Survey, Krueger found that workers who lost jobs in the private sector and then joined the federal government earned about 12 percent more than displaced workers who found another private sector job. (Somewhat ironically, Krueger would go on to become President Obama’s chief economist at the Treasury Department.) 

A forthcoming Heritage Foundation report updates Krueger’s analysis using a much larger and more representative dataset known as the Survey of Income and Program Participation (SIPP). The SIPP follows tens of thousands of people over several years, carefully documenting their wages and labor force status on a monthly basis. Combining the SIPP waves that began in 2004 and 2008, the fixed effects analysis indicates a federal wage premium of at least 8 percent.

A similar approach confined to postal workers reached a similar conclusion. In the late 1990s, the Postal Service surveyed all new hires, asking them how much they were paid in their previous job. Overall, new postal hires received salaries over 28 percent higher than what they had been paid in the private sector, which University of Pennsylvania law professor Michael Wachter and his co-authors called “enormous wage increases over their previous wages in full-time private sector jobs.” 

If fixed effects analysis works so well, why use the human capital method at all? Because fixed effects analy-sis has its own limitations. For one thing, the smaller samples make measurement error more of a problem. If some private workers are incorrectly identified as federal workers or vice versa, then the federal wage premium will appear smaller than it really is. Furthermore, the SIPP covers a relatively small part of a worker’s life cycle. We know from the human capital studies that the federal premium tends to get larger as experience grows. Since the SIPP data capture pay in only the first year a worker switches to federal employment, the observed 8 percent pay premium probably underestimates the overall pay gap. 

Human capital and fixed effects models tell us a lot about wages in the federal versus the private sector, but they tell us nothing about nonwage compensation. To supplement the findings on wages, analysts commonly estimate the value of pension and health benefits offered by each sector and then add them to the wage results from the human capital model. But even this is incomplete, because benefits come in many forms that can be hard to quantify. Even a low-salary job without a 401(k) or a health plan could be relatively attractive if it offered other forms of compensation, such as generous sick leave, lengthy vacation time, reliable job security, and flexible scheduling. Federal employment offers all of these, but how do we incorporate every perk into the federal-private comparison?

One method is to use quit rates. Federal workers quit their jobs at less than one-third the rate of private workers, which suggests federal employees don’t feel they can get a better combination of salary, benefits, and job perks in the private sector. Just as fixed effects naturally accounts for many hard-to-measure skill differences, quit rate analysis automatically encompasses the full range of compensation in each sector. 

For years, defenders of federal pay have attributed low quit rates to the fact that federal employees receive traditional defined benefit pensions, which reward long job tenure and discourage midcareer employees from leaving. Richard Ippolito, the author of a 1987 study that made this claim, suggested what he called a “litmus test” for his theory: Switch federal employees from traditional defined benefit to 401(k)-type defined contribution plans, then see if quit rates change. “If federal workers are paid too much relative to their quality level,” Ippolito wrote, “the quit rate will not change much; if their pay is too low, the quit rate will increase markedly.”

As it happens, history has provided this test: While federal employees hired before 1984 have only defined benefit pensions, those hired after 1984 have a smaller defined benefit pension coupled with a defined contribution plan. If the pension job lock theory were correct, quit rates today should be much higher than in 1984. In fact, precisely the opposite is the case: Quit rates among federal workers hired after 1984 are actually around 30 percent lower than for similar workers in 1984. This casts serious doubt on the claim that the structure of federal pensions, not generous overall compensation, explains the small number of federal employees who leave their jobs.

Just as few federal employees quit their jobs, many private sector workers seek federal employment, seeing it as both well compensated and secure in a time when many private sector jobs are not. While data on the number of applicants per federal or private sector job are scant, research in the late 1980s indicated that federal jobs on average received 25 percent to 38 percent more applicants than private sector positions. A 1985 study by economist Steven Venti concluded that from 18 percent to 29 percent of workers would accept federal employment if offered. Roughly three times as many men would be willing to accept federal employment as are actually offered federal jobs; for women, the ratio is six times, implying that federal jobs provide a significantly more attractive overall package than private sector options. 

These results, Venti concluded, suggest “the government could continue to attract a workforce of current size with substantially lower wages.” Moreover, even significantly lower wages would only slightly reduce the quality of federal job applicants. We will have the opportunity to test this view as the administration’s pay freeze takes effect. Will federal quit rates rise as pay is frozen? We doubt it.

The left often portrays any criticism of public sector employees as an attack on government, unions, or working Americans. In addition, they say, even if claims of overpayment are true, the numbers are small relative to looming deficits from entitlement programs such as Social Security, Medicare, and Medicaid. 

But this misses an important point: If ordinary Americans are to accept significant sacrifices in programs that are dear to them, they need to know that there isn’t a protected class receiving better treatment. 

A number of studies of fiscal consolidations in OECD countries over the past several decades have shown that reductions in the government wage bill—that is, the size and pay of the public sector work force—are an important part of larger efforts to balance the budget. A recent study published by the American Enterprise Institute showed that countries that succeeded in reducing their fiscal gaps placed a lot of weight on reducing public sector pay. 

One reason is that reducing the public workforce shifts resources to the private sector, where they are almost certainly better utilized and so benefit the economy. A second, and probably more important, reason is basic credibility: When a government is willing to take on entrenched interests, it demonstrates to both citizens and financial markets that it is serious about reform. Individuals are more willing to invest when they feel confident their taxes will not rise in the future, and lenders are more willing to purchase government debt when they know it can be paid back. 

A 1996 International Monetary Fund study concluded: “Fiscal consolidation that concentrates on the expenditure side, and especially on transfers and government wages, is more likely to succeed in reducing the public debt ratio than tax-based consolidation.” Given the size of the fiscal gap the federal government must close, it seems foolish to leave the government wage bill out of the equation.

The devil is in the details. Cutting or freezing federal pay across the board would be an improvement over the status quo, but more fundamental reform is needed. Without a change in the basic system of setting pay, salaries could easily creep upward again with little fanfare. In addition, we do not want to cut the wages and benefits of certain federal workers—research scientists, engineers, and senior lawyers, for example—who are not currently overpaid.

We could offer some specific proposals—cutting down on excessive vacation pay and phasing out the defined benefit pension come to mind—but more important for now are the principles a new system should follow. Rather than a rigid pay schedule, the federal government should attempt to at least approximate the effects of supply and demand that private labor markets exhibit. While academic studies can attempt to account for differing salaries, benefits, job security, and work conditions, the ultimate test is the market itself, where job seekers compare the overall package offered in federal employment with the offer from private employers. Probably the best way to capture market effects is to track the number of applications submitted for a given federal job. When large numbers apply for a position, that is a signal that the compensation package may be overly attractive; likewise, when a federal position attracts few applicants—and many high level positions do—then better pay may be warranted. But to act as if a small number of salary-setting bureaucrats can accurately set pay and compensation for thousands of jobs of different types is folly, which hurts taxpayers and reduces the effectiveness of the federal workforce. 

The question of whether federal workers are overpaid is often portrayed in the media as unanswerable, with each side of the debate citing its own numbers. In fact, the academic evidence is much more one-sided: Generally speaking, federal workers do receive higher salaries than similar private employees; individuals changing jobs receive bigger pay increases when their new job is with the federal government; federal employees quit less than private workers; and private workers line up to get federal jobs.

Fundamental reform of federal compensation—not merely temporary pay freezes or furloughs—could offer significant benefits to taxpayers. At the same time, we must acknowledge that there is no perfect solution. No amount of “good government” reforms can ensure that federal workers are paid exactly the same way as their private sector counterparts, because the federal government can never be subject to market forces the way the private sector is. 

Taxpayers should recognize that bureaucratic inefficiencies like excessive pay are part and parcel of large government. Reform of the pay system is important and necessary, but ultimately the best means of reducing excessive federal paychecks is to reduce the size of the federal government.

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