In an interview with Businessweek's Josh Tyrangiel, Mitt Romney claimed, "government is the least productive—the federal government is the least productive of our economic sectors...The most productive is the private sector. The next most productive is the not-for-profit sector, then comes state and local governments, and finally the federal government." Thus, he argued, it makes sense for government to be shedding employees and cutting wages -- that's just what happens in an unproductive industry.
The standard measure of productivity is total economic output divided by hours spent on labor. The more output you produce in less time, the more productive you're being. This is kind of a funny way to evaluate the public sector. Teaching isn't especially productive, but then the point is not to create goods and services: it's to teach young people, which doesn't have a huge immediate effect on output (though obviously it spurs growth when those kids get jobs that use what their teachers taught them). So it may make sense to pay teachers a lot even if they don't have high raw productivity, both because there are good economic effects down the line and because we just value having a universally available education system, full stop, even if the market doesn't.
That said, the Bureau of Labor Statistics does keep data on productivity, so let's see how the sectors compare:
Until the 1990s, the government sector was actually more "productive," under the traditional measurement, than the private sector, both because it was very slowly declining and because private sector productivity was growing at a steady, linear clip, as is its wont. So he's right in the very narrow sense that the private sector produces $54.38 per hour worked and the government produces $37.29 per hour worked. Unfortunately, the BLS doesn't publish productivity numbers on the nonprofit sector, so I can't evaluate that part of Romney's claim. That said, productivity is kind of an odd metric there as well. A soup kitchen doesn't provide a whole lot of economic output but that doesn't mean it's not serving its purpose.
The other part of Romney's claim -- that wages and employment track productivity -- is actually false. Unpublished data from BLS, generously provided to me by the Economic Policy Institute's Larry Mishel and Nicholas Finio, shows that wages tracked productivity growth until about 1970. After that, wages stagnated even as productivity continued to grow. Here's EPI's graph on the matter:
Romney claimed in his interview with Tyrangiel, "higher productivity means higher wages for the American worker." No it doesn't, or at least it hasn't for the past 40 years.