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By Bloomberg view

One of the best-loved stories about the squeeze on middle-class incomes in the U.S. concerns the long- term divergence between wages and productivity. This goes as follows: Wages have stagnated for decades even as output and profits kept going up. Owners of capital grabbed all the gains.

For those who tell this story, the issue is justice not growth. What's the point of striving for efficiency if the benefits don't flow to the living standards of everyday Americans? Instead, they argue, capital needs reining in. The U.S. should restore the bargaining power of labor -- with stronger unions, higher minimum wages, import barriers, taxes on profits, and so forth.

The narrative is so appealing that to remain popular it probably doesn't need to be true. That's just as well, because it turns out be wrong.

The evidence suggests that greater productivity makes a decisive contribution to living standards. Earlier this year, President Barack Obama's Council of Economic Advisers illustrated the point by comparing hypothetical scenarios. One asked what would have happened to living standards if everything had been the same except that inequality hadn't increased after 1973; another, if productivity growth had remained as strong in the 40 years after 1973 as it had been in the 25 years before. Unchanged inequality would have added $9,000 to the typical family's annual income, which is a lot. Sustained productivity growth would have added $30,000, which is a lot more.

The Wall Street Journal's Greg Ip adds that wages rose faster during administrations that presided over good growth in productivity (for instance, Bill Clinton's second term) than during administrations when productivity grew slowly (for instance, Clinton’s first).

Yet there's a puzzle: Despite the correlation between wages and productivity, standard measures of wage growth have shown disappointing results for years. And, especially if you exclude the higher-paid, wages have persistently lagged behind productivity. The picture in the chart below, or something like it, has become very familiar. Since 1970, output per hour has more than doubled, while the hourly wages of production workers, adjusted for inflation, stayed flat. Over time, an enormous gap has grown between wages and productivity.

In a note for the Peterson Institute of International Economics, Harvard's Robert Lawrence examines this much-cited divergence. He shows that, if you look more closely, it all but vanishes. He finds that, properly measured, the gap disappears for the period from 1970 to at least 2000. Possibly all the way up to 2008, growth in labor income matches growth in productivity.

Lawrence argues that to make a valid comparison, the figures need to be adjusted in four ways. First, you need to look at the wages of all workers, not just the production and nonsupervisory workers included in the usual series. Next, you need to measure total pay -- including health insurance and other benefits -- not just wages.

Third, to see whether workers are getting the share of output you'd expect, you have to adjust correctly for inflation. This means using the prices of goods and services that workers produce, not the prices of what they consume. Note: Judging whether workers' pay has changed in line with productivity is not the same as asking what's happened to their purchasing power. Measured this way, inflation has lagged behind the rise in the consumer-price index, again implying faster growth in real pay.

Fourth, you should look at net output not gross. The difference is depreciation -- capital that gets used up in production, which in turn reduces what can be paid out to owners and workers. Since 1970, net output has grown more slowly than gross output.

Combine all these and you find that between 1970 and 2008 pay went up roughly in line with productivity.

Now, the wedge between output per hour and workers' purchasing power (as opposed to "real product compensation") is an important issue in its own right, and much of that gap survives Lawrence's adjustments, as the second chart shows. From a policy point of view, it could stand closer attention.

If the prices of housing, health care and education continue to rise faster than other prices, they'll swallow the income gains due to productivity that most workers would otherwise enjoy. However, the reason for slow growth in living standards won't be a fundamental logical contradiction of capitalism or a breakdown in the social contract, but the peculiarities of those particular segments of the economy.

Has something bigger changed more recently? Doing the measurements correctly, you do see a gap between pay and productivity opening up around 2008 -- and the recovery from the Great Recession hasn't closed it. This too needs further study. In a more technical paper, Lawrence attributes it to weak investment combined with so-called labor-augmenting technological change. If he's right about this, the implication is the same as before: Policy makers whose priority is to help workers must be careful not to accidentally do the opposite by discouraging investment and making the shortfall even worse.

The main point to grasp, though, is simpler. For decades after 1970 -- contrary to one popular account -- labor incomes grew roughly in line with productivity. Over the long haul, far from being irrelevant to well-being, growth in productivity goes far to deciding how poor or prosperous ordinary Americans will be.

This column does not necessarily reflect the opinion of the editorial board or Bloomberg LP and its owners.