Several years ago there was a book by Russell Jacoby, The Last Intellectuals that argued that unlike in the past public intellectuals today actually cluster in universities. Richard Posner's Public Intellectual's: A Study of Decline picks up on Jacoby's thesis and demonstrates how the requirement of disciplinary specialization narrows the scope of intellectuals to express informed judgement on a wide variety of topics.
In the Chronicle of Higher Education there is a nice discussion of professors who have the ability to speak on TV to issues related to their academic specilization and beyond. As I have pointed out before I have not excelled in this medium of communication. On the other hand, I have had some mild success as a teacher of economics --- as measured in students who have decided to go on to earn a PhD after studying with me, standard teaching evaluations and awards, and dissertation students who have established careers as teachers themselves. But teaching economics provides one with a captive audience, and being a graduate student advisor puts on in a unique position to impact people over time through intensive interaction. Being a successful public intellectual as represented in newspapers, radio and TV requires a different set of skills -- namely the ability to communicate clearly and with brevity.
As Milton Friedman once told my colleague Walter Williams --- if you cannot explain economics to the general public in 700 words or less perhaps you don't really know economics. Friedman is perhaps the most effective spokesman for economics as a public intellectual we had in the 20th century and perhaps is rivaled only by Frederic Bastiat in the history of our discipline. When Milton Friedman says something we all better listen, and in this case his challenge to economists to learn to write clearly, simply, and efficiently is certainly one we should take on in vocation of being economists as public intellectuals.