This paper surprised me, but I believe this (while not the last word) is a promising path to explore:
There has been a remarkable increase in wage inequality in the US, UK and many other countries over the past three decades. A significant part of this appears to be within observable groups (such as age-gender-skill cells). A generally untested implication of many theories rationalizing the growth of within-group inequality is that firm-level productivity dispersion should also have increased. The relevant data for the US is problematic, so we utilize a UK panel dataset covering the manufacturing and non-manufacturing sectors since the early 1980s. We find evidence that productivity inequality has increased. Existing studies have underestimated this increased dispersion because they use data from the manufacturing sector which has been in rapid decline. Most of the increase in individual wage inequality has occurred because of an increase in inequality between firms (and within industries). [emphasis added by TC] Increased productivity dispersion appears to be linked with new technologies as suggested by models such as Caselli (1999) and is not primarily due to an increase in transitory shocks, greater sorting or entry/exit dynamics.
Here is the link. Here are non-gated versions. Does this mean that firm-linked inequality will smooth out over time as the loser firms (or their replacements) mimic the technologies and methods of the winner firms? Of course some sectors may have permanently become more "winner take all."
The paper has two further results of note. First, much of the increase in wage inequality has come from changes in productivity dispersion in the service sector, not manufacturing. Second, Norway and France haven’t had big boosts in wage inequality, and they also have not had comparable boosts in the inequality of productivity across firms.
Speaking of inequality, here is an interesting paper on the evolution of mobility and the American dream.