This issue is particularly pressing in some specialized fields. When doctors graduate from medical school, for instance, they apply for their first jobs through a national clearinghouse in which both job-seekers and institutions express their preferences; a computer program determines the results. That means two-doctor couples are often fearful of not landing in the same geographic location.
Now a paper co-authored by an MIT economist sheds new light on the circumstances in which these job-placement programs can, in fact, accommodate married couples quite well.
“Our results provide justification for the current rules in practice,” says MIT economist Parag Pathak, who helped conduct the study to “try to understand how far we are from some kind of optimal system.”
In many cases, the answer appears to be: not far at all. If the method used is properly calibrated to the size of the job market, the researchers found, then the clearinghouse should work for nearly everyone, couples included.
Seeing if an ad-hoc system works
The paper, “Matching with Couples: Stability and Incentives in Large Markets,” published this month by the Quarterly Journal of Economics, was written by economists Fuhito Kojima and Alvin Roth of Stanford University, along with Pathak. All three scholars work in the field of “market design,” where they seek to devise rules bringing desirable outcomes to social systems. The paper blends theory and empiricism, bridging the gap between theoretical work suggesting these medical markets cannot work very well and recent data indicating that many clearinghouses do function quite efficiently.
In medicine, these mechanisms aim to create a set of “stable matching” results for each year’s applicant pool — that is, job placements in which, after preferences are listed, interviews are conducted, and mutual job decisions are made, there are no remaining pairs of doctors and hospitals who would sooner be matched with each other, but are not.
These job-market clearinghouses are built on a simple theory first formalized in 1962 by mathematicians David Gale and Lloyd Shapely. They designed an influential “deferred acceptance” algorithm showing how prospective market partners could pair off without any preferred matches being ignored. But in the medical job market, that theory breaks down when couples apply for jobs at the same time; the 1962 algorithm depends on everyone making decisions independently.
In medicine, the centralized job-placement system originated in the 1950s, and by the 1970s, it was increasingly common to find married couples entering the medical job market together. As a result, these clearinghouses began to change their mechanisms by the 1990s, allowing married couples to rank preferences for pairs of jobs.
However, “There had never been any real formal basis for those tweaks,” says Pathak, an associate professor in MIT’s Department of Economics. That meant it was not clear if there were a better system.
Moreover, some previous theoretical work in the field suggested that placing married couples in the same applicant pool as single doctors could make it impossible to find a stable matching. Mathematicians have shown that in some cases, even computing whether a stable matching exists is practically impossible.
“The theoretical results seemed to contradict the actual performance of the real-world markets,” Pathak says. Together, Kojima, Pathak, and Roth worked out the assumptions under which it is possible to reconcile the theory with the practice, and used data from the job market for clinical psychologists to test their theory.
Good test results for doctors
The researchers found that in order to find a stable outcome, the job market has to be fairly large; that married couples cannot constitute a large portion of the applicant pool; and that applicants must not rank every residency program.
And while it might seem intuitive that larger job markets will provide better opportunities, the researchers were able to arrive at some specific conclusions: If there are at least 2,000 jobs available in a given area, and if the number of couples equals the square root of the market size, then a stable matching will occur at least 96 percent of the time.
That corresponds with data from the job clearinghouse used by the Association of Psychology Postdoctoral and Internship Centers (APPIC) from 1999 to 2007, the researchers found that, on average, there were 3,010 single applicants and 19 pairs of married applicants annually.
Moreover, the APPIC data from those years did not record any instances of two-doctor couples who were unable to land in jobs in a stable outcome. The APPIC numbers also show that only 2 percent of the single applicants have had their preferences affected by the presence of married couples in the market.
Other scholars have started citing the study in their own work. Mark Braverman, a professor of computer science at Princeton University, calls it an “important” paper because it “showed a setting under which … you’ll be able to find a stable matching.”
At the same time, Braverman says of the search for a stable matching, “It’s not like a question you can just ask and answer and forget about.” The circumstances for stability may vary. In that vein, Braverman and Itai Ashlagi, of the MIT Sloan School of Management, have been refining their own algorithm involving couples in the medical job market, which may further ease the conditions under which married doctors can find jobs together.
In all, the positive prognosis for doctors is that current circumstances are helping their job-market clearinghouses work well. But for his part, Pathak also regards the paper as just one result in the larger scholarly effort to improve the methods employed in actual markets. The motivation of all such studies, he notes, is “coming up with practical solutions to real problems.”