President Obama’s puzzling claim that “the private sector is doing fine” has been met with much skepticism, and even ridicule. To many observers, it is self-evidently wrong. While many in the media are content to label the incident a “gaffe” and move on, some of the president’s supporters insist that he actually voiced a fundamental truth, albeit inelegantly. Are they right?

In the eyes of his defenders, Obama simply was pointing out that the private sector has been adding jobs in recent months while the public sector has been losing them. “Doing fine” was apparently just an imprecise and awkward way of saying the private sector is gaining.

The president went on to argue that an effective way to stem unemployment would be for Congress to borrow money and send it to state and local governments — who are generally prohibited from deficit spending — to help avoid public-sector layoffs.

So is it really the case that the public sector needs help more than the private sector? We are skeptical, to put it mildly. First, some context concerning unemployment in the public sector: It is well known that government employees enjoy considerably more job security than private workers. The steps required to fire tenured public workers are often so arduous that managers are loath even to try.

Consequently, unemployment rates have been consistently and substantially lower in the public sector than in the private sector. The recession and its aftermath are no exception. Last month, government workers had the lowest unemployment rate (4.2 percent) of any class of worker categorized by the Bureau of Labor Statistics (BLS). The next lowest unemployment rate, 4.9 percent, is for workers in the burgeoning energy industry. Construction workers, by contrast, are unemployed at nearly three times the rate of government workers.

Public employees tend to be more educated and experienced than the average private-sector worker, so one could argue that government workers just naturally have lower unemployment rates. The figure above tests this possibility, comparing public-sector unemployment rates with the unemployment rates of comparably skilled workers in the private sector over time. In other words, the private-sector line shows the unemployment rate that a typical public worker might face if he took his skills to the private sector.

Much of the difference between the two lines — an average of 3.3 percentage points over the past eleven years — is likely to reflect a perk of government work, one that public employees have enjoyed for a long time. That the gap narrowed slightly in 2011 — after exploding since 2008 — isn’t evidence that the private sector is “doing fine” and the public sector is ailing. In this context, arguing for a bailout of state and local governments seems rather shortsighted.

But even if we ignore the broader context about unemployment rates and focus instead on the impact of the recession, the private sector has still been hit much harder than the public sector. One way to see this is to look at the change in total wages, which captures the combined effects of conventional unemployment (people out of a job but looking for work), labor-force “dropout” (people out of a job and not even looking), and cuts in pay for those who have kept their jobs.

Our data run from the third quarter of 2007 — when the economy was near its cyclical peak — to the third quarter of 2011, the most recent data available from the Quarterly Census of Employment and Wages published by the BLS. Each sector increased total wages paid, if only because of inflation. But state and local governments saw greater payroll growth (10.8 and 8.5 percent respectively) than the private sector (6.4 percent), and the federal government grew most impressively of all (20.6 percent).

Once again, adding some context to the president’s comments goes a long way. Despite his warnings, the public sector hardly faces an employment crisis of any kind. To the extent that public employment decreased in recent months, it has only slightly diminished a long-standing gap that favors government employment.

Far from ailing, public-sector employees still experience lower unemployment rates and higher wage gains than private-sector workers. A slight reduction in the public sector’s advantage hardly justifies the argument for a bailout of state and local government finances.

Jason Richwine, a senior policy analyst at the Heritage Foundation, and Andrew G. Biggs, a resident scholar at the American Enterprise Institute, are authors of the recent paper “The Impact of Act 10 on Public Sector Compensation in Wisconsin.”