Productivity statistics are hardly exciting reading, but they are important. Our society is wealthy precisely because it can churn out products like automobiles, flush toilets and Google search algorithms at relatively low cost. Productivity slowdowns mean erosion of living standards over the long haul, and they also can lead to short-term crises. If productivity turns out to be much lower than expected, it often means that we have borrowed too much and taken on too much risk. Retrenchment can make a recession longer and deeper.

The overlooked piece of news came this month from the Bureau of Labor Statistics. In the second quarter this year, it reported, nonfarm business labor productivity fell by 0.3 percent, the second quarterly drop in a row. And it turns out that it rose only 0.8 percent from the second quarter of 2010. Over the last year, hourly wages have risen more quickly than productivity.

These factors have helped to keep the labor market sluggish and have thwarted a potential recovery.

Yet these numbers don’t capture the entire issue, and are themselves plagued by an array of problems. One bias in the economic statistics — which never shows up in published revisions — is embedded in the health care sector, where third-party payments, subsidies and care quality are hard to monitor and measure. A result is that a dollar spent on health care does not necessarily mean a true dollar’s worth of value added. The United States spends more per capita on health care than any other country, yet without producing measurably superior results. To the extent that some of these expenditures are wasteful, the gross domestic product and productivity numbers overstate economic growth.

Here’s another problem: Expenditures on the military and domestic security have risen since 9/11, but those investments are intended to neutralize external threats. Even if you agree with this spending, it generally doesn’t produce useful goods and services that raise our standard of living.

One of the most commonly cited productivity numbers describes per-hour labor productivity, but this, too, has intrinsic flaws. Labor force participation has been falling for more than a decade, and low-skilled workers are leaving the work force in disproportionate numbers. Taking some lower-paying jobs out of the mix will raise the measure for average productivity, which is hardly the same as increasing the economic gains from a given set of workers or, for that matter, from putting more people to work by making them more productive.

It is increasingly clear that many of our current economic problems predate the financial crisis, even if the crisis accelerated them or brought them into clearer view. A recent study by E. J. Reedy and Robert E. Litan, both researchers at the Kaufmann Foundation, found that sluggish job creation was a long-term trend. For instance, job creation from start-ups has fallen every decade since the 1980s, raising the specter of an America with an innovation shortfall.

Keynesians argue that the economy is suffering from a lack of spending or too little “aggregate demand.” That’s a valid point, but innovation is one means of stimulating demand. When the iPad and iPad2 arrived on the market, for example, the spending was there to support them, which suggests that more innovation could help turn around the business cycle.

One problem may be offshoring by American companies, as stressed in a study by Michael Mandel, chief economic strategist of the Progressive Policy Institute, and Susan Houseman, senior economist with the W. E. Upjohn Institute for Employment Research. Some productivity gains from the manufacturing of the iPad are captured by workers in China, who make important parts of the device, rather than by American workers. American companies often save on costs by finding lower wages abroad, not by enhancing the abilities of American workers. That would help explain why measured productivity has often been high over the last decade while despite year-to-year variation domestic wages and job creation have been flat.

My point is not to attack offshoring, which eases innovation and benefits poorer workers in the source countries. In any case, we cannot imprison capital in the United States. The relevant point is that even after the recent downward revisions, the domestic productivity statistics may be understating the bad news.

Finally, there is a growing realization that while the Chinese economy is wonderful for cutting costs and improving manufacturing methods, it will not soon be taking the lead in creating breakthrough products. For all the money spent on R. D. in China, Chinese scientific papers are not cited much abroad and Chinese patents are filed at a low rate internationally, suggesting that they are less than revolutionary. Dan Breznitz, a professor at the Georgia Institute of Technology, and Michael Murphree, a doctoral candidate there, have discussed the incremental nature of Chinese innovation in their new, illuminating book, “Run of the Red Queen.”

In other words, the next wave of major innovation will probably rely on the world’s current scientific leaders, many of whom are based in the United States. Recently, though, Americans have not been getting the job done, and it’s starting to sink in that the real story is the truth on the ground — not the published numbers.

Tyler Cowen is a professor of economics at George Mason University.

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