This is a very interesting article. Some thoughts. What does the Marx ratio indicate? According to the article, the Marx ratio is the ratio of profits per worker to median pay per worker. It we let P = profit and N = number of workers, then profits per worker is P/N. Now, median pay per worker is a measure of central tendency. It is not quite mean pay (it will be slightly lower than the mean), but for simplicity let's assume that the Marx ratio uses mean pay per worker. Letting L = total labor expenses, then mean pay is L/N.
So the Marx ratio becomes: (profits per worker) / ( median pay) ≈ ( P / N) / (L / N) = P / L
Thus the Marx ratio is a rough indicator of the ratio of profits to labor expenses.
What is interesting about the data, as you point out, is that the companies with high Marx ratios seem also to pay high wages. Tech companies like Facebook and Google are good examples. On the other end, low-wage companies like Walmart have fairly low Marx ratios.
First of all, this tells us something about how we intuitively think of exploitation. We see exploitation when companies like Walmart obviously attempt to keep wages down (by union busting ,etc). We don't see exploitation in Silicon Valley companies that pay very high wages.
Second, the Marx ratio appears to indicate that low-wage sectors like retail cannot achieve a high profit-to-wage ratio. The reasons why this is the case need to be explored.
Lastly, regarding exploitation. Marx's theory of exploitation rests entirely on the ability to discern how much value workers produce, and to measure the fraction that is appropriated by capitalists. But as Nitzan and Bichler show, this surplus value can never be measured. The Marx ratio would only measure exploitation if we assume a labor theory of value, in which all profits are produced by workers.
The problem with Marxist theory does not, however, diminish the empirical usefulness of the 'Marx ratio' -- a profit-to-wage ratio. Given the close relation between profits and capitalization, this ratio is likely related to Nitzan and Bichler's "power index", the ratio of the stock price index to average wages. http://bnarchives.yorku.ca/493/2/201611 ... wpcasp.pdf