Signaling in resident and fellowship matches to reduce interview congestion

An article by Dr. Joseph Bernstein in Clinical Orthopaedics and Related Research (December 2017, Volume 475, Issue 12, pp 2845–2849 ) argues that a signaling mechanism might help deal with congestion in the Orthopaedic Surgery match.
"Not the Last Word: Want to Match in an Orthopaedic Surgery Residency? Send a Rose to the Program Director," (gated)

I was invited to write the comment, below, which appeared along with two other (less favorable) comments from surgeons. (All of the comments appear, without titles, in the same Not the Last Word column at the link...)

Roth, Alvin E. “Congestion and signaling in residency matching,” Clinical Orthopaedics and Related Research, December 2017, 475: 2847, 2849

Now that applying to many residency programs is easy, programs receive so many applications that they have trouble deciding whom to interview, particularly because receiving an application is no longer as strong a signal of interest as it was when applying was harder [1]. The same could be said for how residents applied to colleges when they were younger, and how they will apply to fellowships when they are older. The internet and common application tools make sending applications easier, and evaluating them harder. (This is the common problem of congestion: e.g. it’s harder to use email when we get too many emails, etc.…)

In congested markets, in which not every interesting applicant can be interviewed, signals are important. An application itself is a signal about an applicant’s accomplishments. Like a peacock’s tail, it shows how desirable a candidate is, i.e. why the program should be interested in the applicant. When a program receives too many applications it becomes more costly to read them all, but each one continues to convey the applicant’s accomplishments.

What is lost when applications are easy to send is how interested the applicant is in the program. And, in a congested market, it helps to be able to signal not only how interesting you are, but also how interested, because programs that can’t interview every attractive applicant need to devote much of their interviewing to applicants who might ultimately be interested.

In Economics, the AEA’s signaling system allows each candidate to send no more than two signals of particular interest in being interviewed, for free [2].  Why [only] two? Because while it can be shown how one signal can unambiguously improve the process of selecting candidates for interviews [3], too many signals could harm the process.  Suppose we allowed 50 signals: then the absence of a signal would start to be a signal itself (“this candidate must not be interested in us at all if he didn’t even send us one of his 50 signals…”)  Signals get much of their value by being scarce. So when you can send only two, a program which receives one knows that you targeted them as one of only two recipients.

To which programs should a candidate signal? We advise candidates not to send either of their signals to the very top programs in their field. Those programs can simply interview the candidates they like best, since they have good reason to believe that every application signals genuine interest. Signals will do the most good if sent to programs that should be interested in the candidate, but to whom it might not be obvious that he or she is interested in them.

The resident match removes congestion from the process of making offers and accepting or rejecting them, since each participant can submit a long rank order list that is processed centrally [4]. But interviewing remains congested, because interviews take time. It is worthwhile considering how changes in the market design [5] could smooth the process.  Organizing a signaling system—and then monitoring how it works--seems like a promising step.

[1] Bernstein, Joseph, “Want to Match in an Orthopaedic Surgery Residency? Send a Rose to the Program Director,” this journal, this issue [?]

[2] Coles, Peter, John H. Cawley, Phillip B. Levine, Muriel Niederle, Alvin E. Roth, and John J. Siegfried, “The Job Market for New Economists: A Market Design Perspective,” Journal of Economic Perspectives, 24,4, Fall 2010, 187-206.

[3]  Coles, Peter, Alexey Kushnir and Muriel Niederle, “Preference Signaling in Matching Markets”, American Economic Journal: Microeconomics, 2013, 5(2), 99-134

[4] Roth, Alvin E.  “The origins, history, and design of the resident match,” JAMA. Journal of the American Medical Association, vol. 289, No. 7, February 19, 2003, 909-912.

[5] Roth, Alvin E. Who Gets What—and Why: The New Economics of Matchmaking and Market Design, An Eamon Dolan Book, Houghton Mifflin Harcourt, Boston, New York, 2015.