Where do sheepskin effects come from?

From a loyal MR reader:

I’m very curious about the macroeconomics of the sheepskin effects. Traditional productivity forecast research tends to assume the wage premium is entirely human capital. Eg, Bosler/Daly/Fernald/Hobijn use a mincer equation with five education dummies http://www.frbsf.org/economic-research/files/wp2016-14.pdf   Jorgensen’s approach dividing workers into types also assumes this is not an issue.

If sheepskin effects are purely relative status effects, then the impact on total output and income should be zero, right? This implies increasing educational attainment will have a much smaller impact on productivity and output than typical productivity forecasts imply.

But it seems to me like showing you are “high ability”, if that’s all it does, makes you able to be slotted into higher ability jobs, and that this won’t simply give you a leg up on other workers but increase the number of higher ability jobs filled.

Anyway, I’m sort of thinking out loud but would be curious to read a blog of your thoughts on this, so consider this a bleg!

In the simplest Spence signaling model, the output goes to workers, and if one more worker sends the signal and boosts his or her wage, the non-signaling workers will receive an equal amount less.  That is an equilibrium condition, but it makes less sense as an account of dynamics.  As a practical matter, it’s not clear why the employers should revise their opinion downwards for the marginal products of these less educated workers.  You could say that competition makes them do it, but it’s tough to have good intuitions about an equilibrium that is hovering between/shifting across a varying degree of pooling and separating.

As a more general extension of Spence, a richer model will have market power and payments to capital and labor.  If one more worker finishes school, that worker is paid more and the higher wage serves as a tax on production.  Yet it is a tax the boss does not perceive directly.  The boss thinks he is getting a better worker for the higher wage, but in the counterfactual with more weight on the pooling solution, the boss would have hired that same person, with the same marginal product, at a lower wage.  The “whole act of production” will be and will feel more costly, including at the margin, but the boss won’t know how to allocate those costs to specific factors.  By construction of the example, the boss however will think that the newly educated laborer is the one factor not to be blamed.  So he’ll cut back on some of the other factors, such as labor and land.  Labor in the company will be relatively more plentiful, and the marginal product of labor in that company will fall.  So the incidence of a boost in the sheepskin effect falls on the land and capital that have to move elsewhere, plus to some extent the declining marginal products and thus wages for the remaining workers in the firm under consideration.  Note that outside firms are receiving some influx of capital and land, and so in those firms the marginal product of labor and thus its wage will go up somewhat.

Or so it seems to me.  The trick is to find some assumptions where the hovering between/moving across a varying degree of pooling vs. separation is not too confusing.