Pursuing this topic, here are some of the good or interesting papers I discovered:
This UK piece reframes the David Card IV literature in terms of signaling and with UK data estimates that signaling accounts for one-third of the educational wage premium. It uses a “compulsory” instrumental variable from earlier UK schooling reforms.
Here is the Hanming Fang paper (IER): “…productivity enhancement accounts for close to two-thirds of the college wage
premium.” It uses very different techniques, based on simulations, not IV and the like.
This paper shows that rank measure in class doesn’t affect earnings, contrary to what signaling theories should predict. This may be a puzzle for learning theories as well.
Here is a good piece (it ended up in the JPE) which shows signaling must have some import; it does not attempt to estimate how much of the educational wage premium is due to signaling.
This paper suggests that signaling may be especially important for MBAs.
This Carneiro, Heckman, and Vytlacil paper I found impressive. It redoes much of the IV Angrist and Card work with greater emphasis on heterogeneous agents and also heterogeneous margins. It seems to be the current peak of the IV approach and finds rates of return in the 15-20 percent range and that is for college. It also finds that lower ability individuals are harder to educate and therefore reap lower (though still high) marginal rates of return, contra some of the simpler IV papers.
This very interesting Kevin Lang paper argues that signaling theories do not diminish the case for education and also that they do not create particular problems for measuring the social rate of return on education.