Geoff,

There is another side of the demand/supply issue with respect to graduate students: the demand for them on the part of science departments. These departments need graduate students to teach and perform research. The demand for teaching assistants is largely controlled by undergraduate enrollments in departmental classes. The demand for research assistants is largely controlled by external funding (though quite a few science departments have their own, or university-wide fellowships to buffer this). This IS the "supply" side that Romer and others refer to, but I think it's important to understand the demand structure that underlies this supply.

If Congress creates a large number of new, externally-funded fellowships it will allow science departments some flexibility in how graduate students are paid - but it will likely increase the number of graduate students at the same time. One result of such "external" funding would be that the holders of such (presumably desirable/prestigious) fellowships would gravitate to the best programs - because they would be in control of their own destiny and not beholden to the department for their funding. Science departments that were less successful in attracting these externally-funded fellows would still have the current supply of foreign S&E applicants to rely on.

We have a current example of externally-funded graduate fellowships: the NSF Graduate Fellowship program. I wonder if anyone has tabulated where these (prestigious and competitive) fellows have chosen to do their graduate work. I would guess that they would be highly concentrated in the top 10 departments of each field.

To control PhD production on the whole we will have to either teach less science at the undergraduate level (undesirable) or drive out the marginal programs that are competing for scarce research dollars (painful but, perhaps, inevitable). Alternatively, NSF or NIH could dictate which departments were "allowed" to support graduate students on research grants (though I'll live to be 1,000 to see that sort of micromanagement handed down from funding agencies!)

Peter