On Wednesday, Jim Tankersley reported on a new study from the Heritage Foundation claiming that the apparent broken link between wages and productivity is actually just a statistical artifact.

Most of the report simply notes that compensation, not just wages, matters to American workers, that productivity and wage (compensation) growth are often calculated using different price deflators, and that one should take depreciation into account while calculating productivity.

All these are fair enough as matters of arithmetic (though we may have more to say on our interpretation of these issues, which differs a lot from the Heritage report ), and we have generally taken these factors into account in our work showing the growing gap between wages and productivity (and so have other careful analysts). So what’s the big difference between our work and the Heritage report? It’s something they spend a lot less time on.

At EPI, we don’t look simply at average compensation, but (generally) at median compensation, the compensation of a worker in the middle of the pack who makes more than half the workforce but less than the other half. This really matters; when, say, LeBron James walks into a bar average compensation rises a lot even though the compensation of the median person in the bar is likely unaffected.

So, average compensation does indeed track productivity growth much more closely (though not perfectly) than does median compensation. But this is just another way to make what is the entire point of the compensation/productivity gap analysis: rising inequality has kept typical Americans from seeing their compensation track productivity.

Average compensation, after all, includes every workers’ compensation—including those at the very top (and whose pay often include exercised stock options and bonuses paid to corporate executives). Median compensation, conversely, looks at the worker in the exact middle of the wage distribution. Therefore, rising inequality (i.e., compensation at the very top rising much faster than everybody else’s, say) will result in average compensation pulling away from median compensation, and hence a growing gap between median compensation and productivity.

The Heritage report hand-waves about this—but it’s the key issue. They argue that the failure of median compensation to track productivity growth is simply an efficient market rewarding skills (or not rewarding the lack of skills) correctly, and attributes this to “skill-biased technological change.” Needless to say, we don’t buy this—see the wages chapter of The State of Working America, 12th Edition for the pushback against the generic SBTC argument, and see this working paper (pdf) for pushback on more cutting-edge arguments in the SBTC oeuvre (ie, that the channel through which changing skill demands manifest is through changing occupational employment shares). Some of that working paper’s key arguments are summarized in blog-posts here, here, here and here.

Implicit in this whole argument is the view that the skills (and hence productivity) of the median worker over the past generation have badly lagged the average growth in skills. This seems hard to credit—there has been an enormous increase in both age and educational attainment over the entire labor force over the past generation (see Table 1 in this excellent paper by John Schmitt and Janelle Jones, as well as this table).

But let’s pretend for a second that we’re willing to credit this argument that half of the U.S. workforce is simply too poorly skilled to have been cut in on productivity growth over the past generation (even as this group got older and more-educated). It still raises another question—if half of U.S. workers are so poorly-skilled, just how high up the wage/compensation distribution must you go to see compensation growth track productivity growth? The Heritage report, for example, notes that “reducing the cost of higher education” as the only policy lever for boosting median wages, so, one imagines they think that at least all college graduates (a group that now account for about a third of the workforce) should have been cut in on the fruits of productivity growth, right?

After the tight labor markets of the late 1990s, not so much. The bottom seventy percent of college graduates have not seen a raise in ten years. Nor have wages risen for those in STEM occupations (workers in science, technology, engineering and mathematics)! One would presume they have skills that match the needs of the economy.

The figure below charts productivity growth against wage-growth for a number of points in the wage distribution. Yes, it is just wages—its Social Security data—but the interpretation still stands even if one assumes that compensation has cumulatively grown eight percent faster than wages over this time-period—which is the case in aggregate data (and assuming there’s been no rise in benefit-inequality over this time-period).

So what should you note? Well, the average wages of those below the 90th percentile have greatly lagged productivity. Ok, these are those low-skill people identified by the Heritage report, I guess. But look at wage-growth for those workers between the 90th to 95th percentiles—workers that earn more than at least 90 percent of the workforce. Surely there are some competent people in this group, no? After all, more than 10 percent of the U.S. workforce now has an advanced degree—some of them must be showing up here. And yet wage-growth cumulatively lags productivity growth by more than 30 percentage points for this group between 1979 and 2011.

It’s also worth noting that nearly two-thirds of the total cumulative wage-growth for this group of presumably highly-skilled workers can be accounted for by just five of the thirty-two years under discussion—the tight labor markets between 1997 and 2001 that lifted wages across the board. In short, for most of the past generation, the U.S. economy has been terrible at delivering wage growth even for half the workers above the 90th percentile. Skills shortage? Really?

So where does this leave us? Yes, average compensation growth has been close (not equal to, but close) to productivity growth over the past generation. In fact, since 2000 there has been a large divergence between productivity and average compensation. But compensation for not just typical workers, but for the vast majority of workers, has badly lagged productivity over this period. And it is awfully unconvincing to hang this on the interpretation that it’s just about their allegedly poor skills.

And, of course, it’s always worth noting the one group (see the figure below) that has been able to see wage-gains far in excess of productivity growth, and which kept the overall average wage-growth from lagging too far behind productivity growth.

Just as one example, Heritage assumes that the gap between compensation and productivity caused by difference in the price deflators used to calculate productivity of firms and used to calculate inflation-adjusted compensation should be seen simply as evidence that consumer price inflation is overstated. There’s an equally compelling interpretation (pdf) that this is instead evidence that we’re overstating the productivity of firms that can be translated into consumption growth, and hence that the last generation has been characterized not just by growing inequality, but by even worse overall economic performance than is commonly thought.

To make sure the interpretation is clear—the wages of the 90th-95th percentiles rose 36% cumulatively over this whole period, if this group saw non-wage compensation rise at the average rate, this means that their compensation growth rose eight percent faster, or, 39 percent over the period.