Gordon and Dew-Becker refer to "outsized" increases in CEO pay but scant attention is paid to the broader literature or to event studies. You don’t have to go as far as Jensen and Murphy (1.4 cents received for every $1000 of value created) to see that CEOs don’t capture the full value of their contribution to the corporation, or anything close to it. Read this survey, pp.33-38 in particular. That is, even in today’s "Gilded Age" successful CEOs are underpaid relative to their marginal product, or how much they affect the value of the firm.
What about pre-1970? The obvious interpretation is that "way back when" CEO compensation was held very low, relative to marginal product, by social conventions (and perhaps to some extent by the threat of law, especially in the 1930s and 40s). Once these social constraints were relaxed, CEO pay rose very broadly in step with the stock market. The elasticity of CEO pay, with respect to performance, has been rising sharply.
The citation of institutional factors may sound like a criticism of Gabaix and Landier, but nothing in their paper denies the influences of such forces. They simply point out a recent regularity between the value of what is controlled and how much one gets paid to control it. It’s a trivial point, but it stops being trivial when people start forgetting it.
We shouldn’t expect the elasticity of CEO pay to market capitalization, over most stretches of time, to be close to one, even if it is close to one for some time periods. I would expect fairly long lags at times and then lots of catch up, with an elasticity greater than one for those catch-ups; the data seem to show this. The CEOs, however productive they may be, are reaping rents relative to their leisure, and their ability to capture those collective rents need not fit any particular time path. (That said, when you do see a 1-1 ratio it makes perfect sense.) The data do indicate that a regime switch has led to much greater rent capture, bringing compensation closer in line with CEO marginal products but still falling short of marginal products.
So in my view the Gabaix and Landier results holds up quite well, especially if one is willing to admit the central role of cultural factors, pre-1970 or so, in limiting CEO pay.
I’m not persuaded by the Bebchuk-Grinstein result that observable factors explain only about half of CEO pay; in fact I am surprised that the observables explain as much as they do.
While I disagree with some of their interpretations, the Gordon and Dew-Becker paper is a very useful summary of much of the literature on income inequality.