This paper appears in full in
Roth, A.E. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory", Journal of Political Economy, 92, 1984, 991-1016.
Copyright 1984 by the University of Chicago. All rights reserved.

The following excerpt is reproduced with permission (#47508) from the University of Chicago Press.

What follows is the

Abstract and Introduction to:

The Evolution of the Labor Market for Medical Interns and Residents:
A Case Study in Game Theory

Alvin E. Roth

The organization of the labor market for medical interns and residents underwent a number of changes prior to taking its present form in 1951. The record of these changes and the problems that prompted them provides an unusual opportunity to study the forces at work in markets of this kind.

This paper begins with a brief history of the market, and then presents a game-theoretic analysis to explain the orderly operation and longevity of the current market, in contrast to the turmoil that characterized various earlier short-lived attempts to organize the market. An analysis is also given of some contemporary problems facing the market.

A subsidiary theme of the paper concerns the history of ideas: the problems encountered in the organization of this market, and some of the solutions arrived at, anticipated the discussion of such issues in the literature of economics and game theory.

Acknowledgements: I have profited from conversations and correspondence on this topic with David Gale, Gene Gruver, and John S. Graettinger, M.D., as well as from the comments of participants at seminars where I have presented parts of this work over the last four years, at Buffalo, Yale, Harvard, Northwestern, U. of Pennsylvania, VPI, Stanford, Minnesota, and Chicago. This work has been supported by grants from the National Science Foundation and the Office of Naval Research, and by Fellowships from the John Simon Guggenheim Memorial Foundation, and the Alfred P. Sloan Foundation.

1. Introduction

This paper concerns the labor market for medical interns and residents, and how it has evolved from the beginning of the century to the present time. The paper will discuss briefly the history of the various institutional procedures by which this market has been implemented, and present a formal theoretical analysis of what these procedures accomplished, and the problems they encountered.

The paper will describe how from the turn of the century until 1945, the market suffered from a prisoners' dilemma problem, in which competition by hospitals for interns manifested itself in a race to sign employment contracts earlier and earlier in a medical student's career. This problem was successfully resolved in 1945, after which the market suffered for several years from a "recontracting problem", in which the failure of the market to implement an outcome in the core made it difficult for the market to clear. This recontracting problem was closely related to an "incentive problem" that put a premium on strategic behavior by market participants, which manifested itself most clearly when a centralized market mechanism was introduced in 1950. All of these problems were apparently resolved, at least in large part, by the adoption of a different centralized market mechanism in 1951, which remains in use to this day.

It will be shown that this mechanism implements an outcome in the core of the market, and some of its other properties will be studied. Some modern problems this market mechanism has encountered and the theoretical issues they raise will also be considered. One of the most interesting of these concerns the transformation of the market into one containing dual-career households, as increasing numbers of medical school graduates are married to one another, and need to be employed in nearby locations. It will be shown that no core outcomes need exist in such markets.

A subsidiary theme that will be explored in this paper concerns the history of ideas. It will be noted that the practical problems encountered by the medical profession in the organization of this labor market, and some of the solutions proposed, anticipate by a number of years the discussion of similar issues in the literature of economics and game theory.

The remainder of this paper will be organized as follows. Section 2 briefly discusses the history of the market, and section 3 presents an analysis. Section 4 presents an analysis of some current problems facing the market. All proofs are presented in Sections 5 and 6, and section 7 concludes.

2. Some Institutional History

The internship was first introduced around the turn of the century as an optional form of postgraduate medical education. For students, internships offered a concentrated exposure to clinical medicine, and for hospitals they offered a supply of relatively cheap labor.

The number of positions offered for interns was, from the beginning, greater than the number of graduating medical students applying for such positions 1, and there was considerable competition among hospitals for interns.

One form in which this competition manifested itself was that hospitals attempted to set the date at which they would finalize binding agreements with interns a little earlier than their principal competitors. As a result, the date by which most internships had been finalized began to creep forward from the end of the senior year of medical school. This was regarded as costly and inefficient both by the hospitals, who had to appoint interns without knowing their final grades or class standings, and by the students and medical schools, who found that much of the senior year was disrupted by the process of seeking desirable appointments. Many resolutions were passed and much moral suasion was applied in efforts to remedy this state of affairs. A good idea of the situation in 1926 is conveyed in a letter to the Association of American Medical Colleges (Darrach, 1927), the body of which is quoted below in full.

For a number of years attempts have been made to defer the appointment of hospital internes until towards the close of the fourth year. The Association of American Medical Colleges, the Council on Medical Education of the American Medical Association, and the American Hospital Association have all passed resolutions favoring this idea. The difficulty has been in persuading someone to take the lead.

This is to inform you that it has been decided to defer the appointments of internes at the Presbyterian Hospital in the City of New York until some time in April.

It is earnestly hoped that other hospitals and schools will be able to act in a similar manner.

The advancement of the date of appointment was not halted, much less reversed, by these appeals and resolutions. A dozen years later, in an article devoted to the problem, Fitz (1939) referred to the above letter and wrote "For some unknown reason the Presbyterian Hospital soon abandoned its stand..." He reported that the results of a survey indicated that, in 1939, the bulk of intern appointments would be made during the Christmas holidays of the senior year, and many would be made earlier. He proposed that the problem could be solved if medical schools in the Association of American Medical Colleges (AAMC) would undertake not to give out before some agreed date any information to hospitals regarding students' abilities. This suggestion was not adopted, however.

The advancement of the date of appointment continued at an accelerating pace, and in an address to the AAMC on the problem in 1944, Turner (1945) reported that the standard appointment date "... has now been advanced on the school calendar to the beginning of the junior year and, indeed, inquiries now come to me even from sophomores." (emphasis added). Thus in 1944 the date of appointment had advanced to two full years before the internship would actually begin.

Turner proposed a number of steps to remedy this increasingly intolerable state of affairs. Most importantly, he again proposed that no information about medical students should be released by medical schools before some fixed date to be agreed upon. This proposal was adopted by the AAMC in consultation with the various hospital associations, and it was decided that neither scholastic transcripts nor letters of reference would be released prior to the end of the junior year, for students seeking internships commencing in 1946.

This proved to be an effective remedy for the problem it was intended to solve. Appointments for 1946 internships were largely made in the summer of 1945, and in subsequent years the dates at which information was released by medical schools was moved later into the senior year, and the date at which appointments were made followed in step. However a new problem appeared, and manifested itself in the waiting-period between the time offers of internships were first made, and the time students were required to accept them.

Basically, the problem was that a student who was offered an internship at, say, his third choice hospital, and who was informed he was an alternate (i.e. on a waiting list) at his second choice, would be inclined to wait as long as possible before accepting the position he had been offered, in the hope of eventually being offered a preferable position. Students who were pressured into accepting offers before their alternate status was resolved were unhappy if they were ultimately offered a preferable position, and hospitals whose candidates waited until the last minute to reject them were unhappy if their preferred alternate candidates had in the meantime already accepted positions. Hospitals were unhappier still when a candidate who had indicated acceptance subsequently failed to fulfil his commitment after receiving a preferable offer. In response to pressure originating chiefly from the hospitals, a series of small procedural adjustments were made in the years 1945 - 51. The nature of these adjustments, described next, makes clear how these problems were perceived by the parties involved.

For 1945, it was resolved 2 that hospitals should allow students ten days after an offer had been made to consider whether to accept or reject it. For 1946, it was resolved 3 that there should be a uniform appointment date (July 1) on which offers should be tendered (transcripts having been released on June 1), and that acceptance or rejection should not be required before July 8. 4 By 1949, the AAMC proposed 5 that appointments should be made by telegram at 12:01 AM (on November 15), with applicants not being required to accept or reject them until 12:00 Noon the same day. Even this twelve-hour waiting period was rejected by the American Hospital Association as too long: the joint resolution 6 finally agreed upon contained the phrase "no specified waiting period after 12:01 AM is obligatory," and specifically noted that telegrams could be filed in advance for delivery precisely at 12:01 AM. In 1950, the resolution again included a twelve-hour period for consideration, with the specific injunction that "Hospitals and/or students shall not follow telegrams of offers of appointment with telephone calls" until after the twelve-hour grace period 7.

By this time it was widely recognized both that there were serious problems in the last stage of the matching process, and that these problems could not adequately be resolved by compressing this last stage into a shorter and shorter time period. In order to avoid these problems and the costs they imposed, it was proposed, and ultimately agreed, that a more centralized matching procedure should be tried (Mullin, 1950; Mullin and Stalnaker, 1951).

Under this procedure, students and hospitals would continue to make contact and exchange information as before. 8 (It is worth noting in this regard that the complete job-description offered by a hospital program in a given year was customarily specified in advance; see e.g. Stalnaker, 1953. Thus the responsibilities, salary, etc. associated with a given internship, while they might be adjusted from year to year in response to a hospital's experience in the previous year's market, were not a subject of negotiation with individual job candidates.) Students would then rank in order of preference the hospital programs to which they had applied, hospitals would similarly rank their applicants, and all parties would submit these rankings to a central bureau, which would use this information to arrange a matching of students to hospitals, and inform the parties of the result 9. A specific algorithm was proposed to produce a matching from the submitted rankings, and this will be discussed in the next section.

It was agreed to try the proposed procedure in a "trial run" for the 1950-51 market, that would not be used to actually match students and hospitals in that year. Instead, participants were asked to submit rankings "as if" they would be used for determining the final matching, and the plan would be evaluated for actual use after this trial run had occurred. On the basis of the trial run, the relevant medical associations agreed to adopt the procedure for the 1951-52 market. The procedure was to be employed on a voluntary basis: students and hospitals were both free either to participate in the process or to seek internship appointments on their own.

After this was announced but before the procedure was implemented, objections by student representatives were raised to the algorithm used to produce a matching from the rankings submitted. Specifically, they observed that this algorithm made how adroitly a student composed his rank order list a matter of great importance. A student might suffer if he took a "flyer" and gave high rank to hospitals he preferred but had little chance of being matched with 10. That is, it was noted that a student who submitted a rank order of hospitals corresponding to his true preferences might receive a less preferable match than if he had submitted a different rank order. In response to these objections, a new algorithm was substituted for the old in the 1951-52 matching plan (Mullin and Stalnaker, 1952). This substitution was judged to be of sufficiently small import that its details were not widely disseminated, the announcements concerning the plan having already been distributed before the substitution was made.

In what follows, the initial algorithm will be called the "trial run algorithm", and the algorithm which replaced it will be called the "NIMP algorithm", where "NIMP" stands for National Intern Matching Program, the name adopted for this matching plan in 1953. The matching plan using the NIMP algorithm remains in use to this day, although the market which it serves has undergone considerable change in the intervening years 11. This longevity, and the very high levels of (voluntary) participation the system has attracted 12, are particularly surprising in view of the turmoil in this market in the years immediately prior to the establishment of the NIMP. Much of the theoretical analysis in the following section is intended to shed light on the causes of this success.

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[Click on note numbers to return to the text at the note.]

1. The number of positions offered for first-year medical graduates exceeded the number of eligible applicants until the mid 1970's, at which time the total of U.S. medical school graduates plus foreign graduates exceeded the number of first-year positions. However the number of positions offered continues to exceed the number of U.S. medical school graduates. (See Graettinger, 1976).

2. Unless otherwise stated, the resolutions discussed below are joint resolutions of the AAMC and the American Hospital Association. These resolutions were not legally binding on the member hospitals or on graduating students. For the first resolution, see Journal of the Association of American Medical Colleges, 20, 1945, pp. 192-4.

3. See J. AAMC, 21, 1946, p 178. Of the previous years resolution it is noted that "while not observed completely by a few medical schools and hospitals, [it] had been followed by most of the institutions in the country and had resulted in a very great advance in bringing order out of a chaotic situation."

4. "It was reported by a representative of the American Hospital Association that violations by hospitals was as high as 25 percent; nevertheless the American Hospital Association wants the system... to be continued." (J. AAMC, 22, 1947, pp 45-46).

5. (J. AAMC, 24, 1949, p 42.)

6. (J. AAMC, 24, 1949, pp 174-5.)

7. (J. AAMC, 25, 1950, pp 435-6.) Note that the injunction against telephone calls was two-way, in order to stem a flood of calls both from hospitals seeking to pressure students into an immediate decision, and from students seeking to convert their alternate status into a firm offer.

8. That is, the application and interviewing process would remain unchanged. (At this time Mullin (1950) states there were about 9300 interships being offered, to about 6,000 medical school graduates.)

9. Under the procedure being discussed here, hospitals actually ranked students in groups, rather than in a strict rank order, although in the procedure discussed next, hospitals as well as students submitted strict rank orders. Surveys of medical students (see eg. Rutkow and Glasgow, 1978) suggest that the most important factors determining student preferences over hospital programs have to do with their reputation as educational programs, with less importance being assigned to factors such as on-call schedule, patient population, and salary.

10. Cf. (Journal of Medical Education), 27, 1952, p 46.

11. In 1968 the National Intern Matching Program was renamed the National Intern and Resident Matching Program (NIRMP), and in 1978 renamed the National Resident Matching Program (NRMP), to reflect changes in the structure of postgraduate medical training.

12. In the first years, over 95% of eligible students and hospitals participated in the system (cf. Mullin and Stalnaker, 1952.) These high rates of participation continued until the early 1970's (see Checker, 1973), after which there was some decline, for reasons that will be discussed later.

13. The importance of the medical schools acting collectively in this regard was emphasized in 1945 by J.A. Curran @u(J. AAMC, 20, 1945, p 37) as follows. "While the Executive Council has already recommended that no letters of recommendation supporting internship applications should go out until after the end of the junior year, Dr. Turner's insistence that this be agreed on by all the medical schools is worthy of emphasis. Its importance may be illustrated by a situation created one year ago among the schools in New York City by such an agreement on a local basis. It was then discovered that in two neighboring cities all internship vacancies were being filled by students before the end of the third year. As a result, the New York schools were forced to abrogate hastily their rule against sending out earlier information."