On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets

Abstract

the positions they do fill are filled by foreign medical school graduates. It has been suggested that changes in the manner in which the clearinghouse treats hospitals and students might alter this situation.3 However it was shown in Roth [4] that any two outcomes that are stable-the relevant equilibrium notion4 for this kind of market-fill the same number of positions at any hospital. Since that paper also showed that the clearinghouse procedure yields a stable outcome, any change in procedure that preserves this property would thus have no effect on the perceived numerical maldistribution of physicians among hospitals. Here it is shown that any hospital that fails to fill all of its positions at some stable outcome will not only fill the same number of positions at any other stable outcome, but will fill them with exactly the same residents. Thus, while the staffs of other hospitals are determined by which of the multiple equilibria of such a market is reached, the situation of hospitals whose positions are not all filled remains unaffected. The maldistribution of phvsicians, and particularly of American educated physicians, is therefore a property of equilibria of this kind of market, and not an artifact of the particular equilibrium presently selected. The formal model:5 The agents in the hospital-intern market consist of two disjoint