In general, which hypotheses predict lots more short-term unemployment among the less educated, but among the long-term unemployed, a disproportionately high degree of older, more educated people? This stylized fact seems to point toward search and recalculation ideas, with some zero marginal products tossed in. Do aggregate demand theories yield that same data-matching prediction? I don't see it, at least not without being paired with a theory of concomitant real shocks.
1. I would say to be careful about what the "stylized facts" are these days. A lot of people have left the labor force, and that could skew things. A younger educated worker might leave the labor force to go to law school, rather than show up as long-term unemployed. The older educated worker faces different options.
2. Let us talk about the marginal product of worker i in occupation j. In most cases, this is indeed zero. My marginal product would be zero in fishing, medicine, and many other fields. In a complex economy, if you were to randomly assign workers to jobs, ZMP would be the norm, not the exception. The more complex the economy, the more carefully workers must be assigned in order to avoid ZMP.
3. When a manufacturer has excess inventory, production workers have effectively ZMP. But for the economy as a whole, that is consistent with an aggregate demand story.
In the 1930's, many agricultural workers became ZMP. This was due to a long-term trend of productivity rising faster than demand, a trend accelerated by the internal combustion engine, which reduced the amount of land under cultivation (with better transportation, you could grow the food where the land was best, even if it was far from cities). These ZMP workers came to cities, where they collided with other ZMP workers, as many manufacturers had excess inventories.
However, back when half the labor force (or more) was doing manual labor, if one worker was hired, the demand for goods and services from that worker's income served to increase the marginal product of workers elsewhere in the economy. The multiplier worked.
What I think Tyler Cowen means by ZMP is that even when demand at a firm whose workers are in occupation j is high, it does not need to hire additional occupation-j workers. The multiplier does not necessarily work.
4. The Garett Jones worker has a marginal product that is very subjective and lumpy. When you see expansions opportunities, you hire people to try to exploit them. When you see threats to the survival of your business, the short-term ZMP of such workers suddenly stares you in the face.
5. Older workers may suffer from a human capital vintage problem. Their education and experience may have become obsolete rather suddenly, because of globalization and technological change.
One way to summarize all this is that the capitalist calculation problem is to assign workers to jobs. Unless this is done correctly, ZMP results. A number of trends have made it harder to do this assignment correctly.
All that said, I am still optimistic that when employment starts to pick up, it will pick up very rapidly. The herd of employers who were motivated by contractionary fear will turn into a herd of employers motivated by expansionary greed.