The word 'Establishment' isn't really as useful in the United States as it is in the nation where it was coined -- England. It works well in nations with an extremely narrow track of power (a couple specific schools, closely tied to the gov't, closely tied to industry) where you are either 'inside' or unable to ever get into power. France, Japan, and Korea, for example, have this kind of setup.
The purpose of the word is to reflect a tightly-interlocked set of social circles that wield disproportionate power ... ecclesiastical, academic, financial, social, political ... wound up together. This exists in more socialist nations, but the closest the U.S. came is the "WASP elite," which largely collapsed and died in the 1960s. Capitalism and immigration largely obliterated any ability to form a true Establishment long ago in the United States. This is, interestingly, one of the reasons why it's almost impossible to even be anti-Establishment. Capitalism is so dominant that things like elite academic institutions get crushed beneath its wheel just as easily as immigrant labor ... they are mere minor details.