Evan Soltas
Sep 3, 2015

Inequality and Productivity

If you regularly read online about economics, you probably have seen this graph from Jared Bernstein and Larry Mishel so many times that you have lost count:

What it seems to say is that compensation had once kept pace with productivity but does not any longer -- in essence, that workers are getting a raw deal. And Mishel and Josh Bivens are back with a big, new update to the analysis. But there are some issues with the graph, despite the latest defenses.

Debating the divergence: some background

Let's review the debate. (My own contribution is towards the end of this post.) To an economist, the first red flag should be that this divergence looks nothing like the change in the labor share of income over the same period. The labor share was stable until about fifteen years ago, and since then has declined by about 10 percent, or about 6 percentage points. That translates to productivity having outgrown compensation by about 25 percent, not 140 percent as in the above graph.

So something is clearly strange here. That something, as James Sherk of the Heritage Institute has explained in a research memo, is a distinction in how productivity and compensation are adjusted for inflation. And that's a an important question -- why is the average price of consumption rising faster than the average price of output? -- but it's not at all an issue of workers not being compensated for rising productivity. It's a change in the terms of trade. Since workers buy a different basket of goods than businesses produce, the prices of those baskets can diverge.

Another key issue here is who counts as a worker: The above graph focuses only on compensation of production and non-supervisory workers. But supervisory workers are obviously part of the production process. While the graph certainly demonstrates inequality, in some vague sense, to compare the productivity of all workers against the compensation of a subset destroys the graph's ability to test the actual claim, which is that workers are not being compensated for their productivity.

What Mishel and others at the Economic Policy Institute have most recently argued, then, is that we should be focused on inequality within labor income. Even if, in an apples-to-apples comparison, mean labor compensation of all workers has kept up with productivity, median labor compensation hasn't. So what, they ask, explains the difference between mean and median labor compensation?

Mishel and Bivens's answer, in the latest study, is a "portfolio of intentional policy decisions" that have hamstrung labor. Capital deepening and broad gains in labor quality should lead us to believe that productivity has risen broadly, they say, and yet less than 10 percent of workers have seen their compensation keep up with productivity gains.

Inequality within labor compensation is a interesting place for the debate to have ended up. For one thing, it's where the academic conversation is: see, for example, Matt Rognlie's recent Brookings paper. Yet, on the other hand, it seems to make the key question -- are workers being compensated for rising productivity? -- intractable.

Why? Because it's hard to assess the productivity of individual workers. The whole debate over CEO pay, for example, has foundered on this issue. You can see that in Bivens and Mishel's recent paper on CEO pay, in which they concede that the evidence that CEO pay is untethered to productivity must be suggestive and circumstantial. In their latest, they again say it is hard to draw a link, and they're right.

It's easy to be pessimistic, then, about economists' ability to answer this productivity-compensation question. Mishel and Scott Winship at the Manhattan Institute have gone blue in the face, without any apparent resolution, arguing about how the productivity of the median worker has changed since the 1970s.

Another approach, then

It is important to concede up-front that there is, at the moment, no way to measure productivity at the individual level. But we can aggregate upwards, at least to the firm level, where there is a meaningful measure of output to be had. In this post, I'll use detailed industry-level data from the Bureau of Labor Statistics because firm-level data requires special clearances with the US government that I don't have.

The implication of this aggregation, however, is that I can't say anything about divergences between productivity and compensation within sectors. Which could be important. Critically, my results have no bearing on the debate about the very top of the income distribution; using sectors, I can only look at the body of the distribution. My industry breakdown, though, is reasonably granular: 246 industry categories.

With those caveats in mind, here's the big takeaway: Between 1987 and 2013, changes in sector-level labor productivity explain about a third of the changes in sector-level hourly labor compensation. And those productivity increases were paid as compensation to labor somewhat below the prevailing labor shares of income.

If you really want to know, 35 percent of the variance in the change between 1987 and 2013 in sector-level log hourly labor compensation is explained by changes in log labor productivity over the same period. A one-percentage point increase in productivity generated a 0.41-percentage-point increase in compensation. I've used 1987 and 2013 because this data was collected starting in 1987 and much of the data is still missing for 2014. As always, you can find my cleaned dataset here for your own analysis. [These results have been revised since the post went live. See below.]

We should ask if this result makes sense from a theoretical perspective. The key substance of labor economics has for decades circled around a key question: How true is the basic intuition that workers are paid their marginal product?

You might think it should be true. If workers aren't compensated for their productivity, it seems, they'll switch firms or industries. Yet there's a countervailing argument, associated with the economist William Baumol, which leads to the opposite result: If productivity rises more slowly in one industry than in others, its workers will demand wages in line with their opportunities in other industries -- and so, at the industry level, we shouldn't expect a link between productivity and compensation.

Whether the classical viewpoint or Baumol's is correct turns upon the strength of workers' "outside option" to exit industries where productivity growth is lagging and enter industries with faster productivity growth. If this outside option is weak, then workers' wages are determined by industry-level productivity; if this outside option is strong, then workers' wages are determined by the productivity of their best-alternative industry.

Mishel and Bivens, in their latest study, have argued that the industry-level approach doesn't make sense. Yet I don't think their critique really goes anywhere. (Read it yourself and be the judge.) Yes, measures of labor productivity reflect the average, not marginal, product of labor. Yes, workers in low-productivity industries could move to higher-productivity industries, so we can't say that low-paid workers are inherently and always unproductive.

Neither of these points, however, seems to have any bearing on the industry-level comparison. If labor productivity predicts labor compensation, then it seems fair to say that, at the industry level, workers have been compensated for their productivity gains.

My reading of the evidence, then, is distinctly different than that of Mishel and Bivens. We'd agree that, since 2000, the decline in the labor share of income is concerning. And we'd agree that some of the apparent divergence between compensation and productivity is attributable to changes in relative prices of consumption versus output, a phenomenon which isn't readily linked to inequality.

Where we differ is the extent to which changes in productivity explain changes in compensation. At least for the body of the income distribution, this evidence should lead us to explanations centered on productivity rather than on labor-market institutions.

Note: There was a data error in this post that has since been fixed. It weakens the conclusions relative to what was first posted, though there is still a robust relationship between productivity growth and compensation growth. Specifically, we go from an R2 of about 0.81 to 0.34 and a slope of nearly 1 to a slope of 0.41. See this post for more.