The deeper meaning can be seen in scattering problems. Sorry for the technical digression but in say a nuclear explosion one seeks certain fissionable materials that have a maximum scattering cross section, the get a better chance or probability of a collision and thus an explosion.
Then onto an exceptionally prescient piece by Mankiw, where he is looking at education and the top 1%. He states:
But it may be better to think of the return to education as stochastic.
Education not only increases the average income a person will earn, but
it also changes the entire distribution of possible life outcomes. It
does not guarantee that a person will end up in the top 1 percent, but
it increases the likelihood. I have not seen any data on this, but I am
willing to bet that the top 1 percent are more educated than the
average American; while their education did not ensure their economic
success, it played a role.
I would argue that the top 1% are not just well educated but were on the corner if you will or were where the scattering cross section was the greatest. Say Harvard. When at Harvard you are exposed to people who are brighter, well connected and who in life are most likely to build on that. You have thus put yourself in the best spot for that bus to stop.
Going to say Rutgers may not put you there, there are exceptions, but the scattering cross section would be much smaller. Going to MIT may not put you in the Harvard cross section but would most likely put you in another favorable cross section, the entrepreneurial one, where again you may have a chance at the 1%, if that is your goal, or a Nobel prize if that is a goal. In contrast the MIT education may actually be a negative for becoming a large corporate CEO due mainly to the development of independence and lack of group political finesse, yet that very cultural milieu may be ideal for a start up, as one would expect.
Mankiw continues:
I am inclined to think that education is important here in part
because the large increase in the share of the top 1 percent from the
1970s to the present occurred together with the increase in the rate of
return to education during this period documented by labor economists.
It is possible, of course, that the the two phenomena just happened to
occur simultaneously. But the timing suggests that the two trends--the
increasing value of education and the rising share of the top 1
percent--may be related
Education qua learning "stuff" is important but is not the sine qua non. Getting a PhD from say MIT in EECS will not in and of itself assure you of say entrepreneurial success. Thus possibly the stochastic element of Mankiw. However the culture combined with the contacts, fellow entrepreneurs, may establish a critical mass, a larger scattering cross section if you will, to get to that point.
I think Mankiw has hit onto something, a complex systems view of the process. Why work to get into MIT, why not default to say some other place, again Rutgers, I am picking that solely because it is down the road a piece and near Princeton. I really have no other reason, but say Rutgers. Most people there will seek jobs in well established firms most likely. Why, the scattering cross section for other options is small and thus the probability for such interaction is low, they are waiting on the wrong corner.
So is education a guarantee, not really, is going to Harvard one, not necessarily, it is an amalgam, but good schools raise the probability. One may be exposed to options and opportunities, as well as style and modus vivendi that may not have been known to the individual.
The Mankiw idea has some substantial merit, perhaps someone may pursue it further.
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