Since its publication, Thomas Piketty’s “Capital in the Twenty-First Century” has been criticized for a variety of reasons. The most recent wave has centered on his assertion that the share of income going to labor is on the decline. As the headline to a piece by the Wall Street Journal’s Greg Ip put it, “Thomas Piketty Says Labor’s Share of Income Is Declining, But Is It?

Ip highlights three different bits of research that question the declining trend in the labor share that Piketty (and others) have found. The first paper is by Benjamin Bridgman of the U.S. Bureau of Economic Analysis. Bridgman points out that the most-cited data about the labor and capital shares is “gross,” meaning it doesn’t account for the deprecation of capital goods. Because machinery and computers wear down over time, part of income must be plowed back into buying more equipment. If depreciation has increased, then the share of net income going to capital might not have increased and the labor share might not have declined. Bridgman’s analysis shows that depreciation has increased, which reduces the trend decline in the labor share of income. But that labor share still appears to be on the decline.

Other research finds similar trends when accounting for depreciation. Research by the University of Chicago’s Loukas Karabarbounis and Brent Neiman finds that the gross and the net labor share have both been on the decline. A paper by Piketty and the London School of Economics’ Gabriel Zucman looking at the capital share also accounts for depreciation as they note that they “always use net-of-depreciation income and output concepts.”

The second piece that Ip cites is a post by the Manhattan Institute’s Scott Winship that also raises the issue of depreciation in the measurement of the labor share. But Winship notes that there might be measurement issues related to the income going to the self-employed or proprietors. These payments are registered as capital in the official accounts, but most likely should be counted as labor income. This concern has been noted by previous research, specifically a paper by Michael Elsby, of the University of Edinburgh, Bart Jobijn, of the Federal Reserve Bank of San Francisco, and Aysegul Sahin of the Federal Reserve Bank of New York. Yet after accounting for the labor income of the self-employed, they still find that the U.S. labor share has been on the decline.

The final paper Ip highlights is by Massachusetts Institute of Technology PhD student Matthew Rognlie and was discussed last week as part of the Brookings Papers on Economic Activity. Rognlie makes two main contributions to the debate. The first is to point out that the increase in the net capital share of income is driven almost entirely by the housing sector. In other words, the form of “capital” that seems to receiving income instead of labor is housing. (As Ip notes, Rognlie isn’t the first to point this out.) The second is to show that outside of housing, the capital share seems to be driven by increases in “mark-up,” a term that describes increased profits due to monopolies in the U.S. economy.

On Rognlie’s first point, work by Piketty and Zucman does break down the capital share and does break out the contribution of housing. They find, like Rognlie, that housing capital is an increasing share of income. But if you take out housing, Piketty and Zucman find the capital share in the United States is still increasing.

Rognlie’s second point about market power and monopolies is the one that poses the biggest problem to Piketty’s famous “r > g” (the return on capital is greater than the rate of economic growth) inequality. Rognlie finds that the movement in the non-housing sector is not driven by changes in the value of capital, as Piketty states, but rather by monopoly profits.

Given that Piketty’s book is at its heart a prediction about the future, it’s impossible to disprove it in the here and now. Rognlie’s work and others might cast doubt on its predictions. But the future will be the final arbiter. For now, we simply have another story about what possibly drove inequality in the past and will drive it in the future.