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Matching Markets in the Medical World

In May 1998, the National Resident Matching Program (NRMP) released a new matching program which paired entry-level physicians with eligible residency programs throughout the United States. Until then, the NRMP had been using the matching market algorithm designed in the 1950s. Future residents would rank the hospitals they wanted to be residents at in something called a Rank Order List, and the algorithm would match with the hospitals which needed a certain number of residents with a certain set of requirements. However, in the 1990s, people began to notice that the algorithm very clearly favored the residency programs and less the entry-level physicians who were applying. With the growth of the notion of trying to “cheat the system” by manipulating the order in which recent grads would rank the residency programs, NRMP pushed for a new design which could eliminate this inherent bias.

Alvin E. Roth and Elliot Peranson wrote an extensive paper about the development of this new matching algorithm and the effects it had on the NRMP after its deployment in mid 1998. The year long process ended with not only a better model, but several realizations about the realities of the matching process especially in the medical world. Among them, that the medical matching market was much more complex than the previous model had accounted for. For example, taking into account family situation, marriage status, etc. were important to incorporate into the new model. In addition, this new algorithm, based off the instability-chaining algorithm developed by Roth and John H. Vande Vate, was the first in the medical world to take more engineering and quantitative approaches into account in the design of the new NRMP.

The new design tried to produce more “stable matching as favorable as possible to applicants” (Roth and Peranson, 751). At its core, the model (both before and after the change) was a two-sided matching market. However, the original model viewed the process as a simple matching market, whereas the newer one developed it as a complex one. For example, there might be a married couple who both wanted to attend a residency program geographically close to each other. In other examples, certain entry-level physicians might have prerequisites that they would need to fill for future goals, etc.

In the end, the new algorithm did not affect the statistics of the matching process; about 0.1% of applicants were affected by this change and about 0.5% of programs were affected by the change. However, in this case, “affected” refers to the change of the number of rejected applicants or unfilled positions. With that said, the NRMP process almost always guarantees most of the applicants will get some position; it was the quality of the position that the new algorithm was trying to improve. The social benefit of the new algorithm, however, was not very well cited in the paper, though it speculated that the “associated change in welfare” is equally as small.



Roth, Alvin E. and Peranson, Elliott. “The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design.” The American Economic Review. September 1999. Vol. 89, No. 4 (pp. 748-780).


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