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In the book, Piketty relies on a paper by Loukas Karabarbounis and Brent Neiman that estimated a high marginal elasticity of substitution given two sets of facts: capital has gained national income at the expense of labor, and the price of capital inputs to production has been falling. The authors interpret the latter as the cause of the former, and again within the confines of neoclassical production theory, the only way to reconcile those two facts is with a high degree of factor substitutability: when capital becomes cheap, firms switch to using it, displacing workers. The labor displacement exceeds the increase in wages to workers who remain employed, thus reducing the total labor share of national income. That paper does not mention Piketty, but in a follow-up the next year, the same authors foreground the similar model proposed by Piketty."
Back in the '80s and '90s, a topic that I kept seeing was, "where is the productivity?" With companies spending huge money on technology and computerization, there should have been visible gains in productivity numbers, right? But, there weren't. What's up with that?
My thoughts, as a non-economist, when I saw that were of things like just-in-time inventory controls, which were new and entirely dependent on new technology. They needed massive structural changes, which may be why they didn't show up immediately, but still...they were there and the metrics and models of economists weren't capturing their effects until they had completely taken over.
Likewise, the elasticity of labor and capitol sounds very much like the effects of automation on industrial jobs.
"The aforementioned paper by Furman and Orszag argues that what Piketty (and Gabriel Zucman, in their joint work) identify as a high and invariant rate of return on capital in aggregate in fact reflects uncompetitively high rate of return on capital for a few specific, superstar firms in the economy, and the key task is not to manipulate aggregate macro equations, as Piketty (and neoclassical economists more generally) do, but rather to explain why these superstar firms do so much better than everyone else. The short version, according to Furman and Orszag, is rents—payments that some agents, superstar firms in this case, are able to extract from the rest of the economy either because they have successfully blocked any competitive pressure or because they have bought special treatment through the political system, or some combination of the two, in addition to other mechanisms."
Or perhaps we're talking about things like the FAANG set. the extracted payments are personal information---which is not captured in any economic theory I've ever seen---and the moat blocking competitive pressure is the combined result of network effects (bigger databases win) and extensive financial capitalization. (How do you fight a competitor to whom not only is additional capital effectively free but also has huge stocks of monetary capital just lying around in stacks on the floor?)