use data where they exist, e.g., on the likelihood of mismatches and positive crossmatches (see Table II). Where no data exist—on the willingness of patients and donors to trade a live donation for priority on the cadaver queue—we do robustness checks by simulating a wide range of preferences. IV.A. Patient and Donor Characteristics In addition to characteristics reported in Table II, for the HLA characteristics of the population, we use the distribution reported in Zenios [1996] using the UNOS registration data for years between 1987 and 1991. We assume that all HLA proteins and blood type are independently distributed following Zenios. For simplicity, we consider unrelated donor-patient pairs. About 25.3 percent all living-donor transplants were in this category in 2001. We use UNOS data to find the conditional distribution of the age of a nonspousal unrelated donor given that he is an adult. We assume that HLA and blood-type characteristics of the donor have the same distribution as the patients’, the characteristics of a nonspousal unrelated donor are independently distributed with the patient, and the characteristics of a spouse are independently distributed with the patient except his or her age. We assume that the spouse age is the same as the patient age. IV.B. Preference Construction The preferences of patients are determined using the survival analysis of grafts reported in Mandal et al. [2003]. This analysis uses data obtained from first-time kidney-only transplants between 1995 and 1998 in the United States Renal Data KIDNEY EXCHANGE 475 System (USRDS) database. We assume that the utility function of each patient depends on the number of HLA mismatches ( x) and the donor age ( y). In the “rational” preference construction, following Mandal et al., we assume that each patient younger than 60 has a utility function u( x,y) 0.514x y/10, and each patient 60 and older has a utility function u( x,y) 0.510x y/10. We also consider a “cautious” preference construction. Under cautious preferences, we assume that patient ti prefers donor TABLE II AMERICAN CAUCASIAN PATIENT AND LIVING DONOR CHARACTERISTIC DISTRIBUTIONS USED IN SIMULATIONS A. Patient ABO blood type Frequency O 45.6% A 39.5% B 11.1% AB 3.8% B. Patient gender Frequency Female 40.9% Male 59.1% C. Patient age Frequency 18 5.6% 18–34 13% 35–49 34.9% 50–64 38.9% 64 7.6% D. Unrelated living donors Frequency Spouse 53.5% Other 46.5% E. Living donor age Frequency 18 5.6% 18–34 13% 35–49 34.9% 50–64 38.9% 64 7.6% F. Positive crossmatch Frequency Female patient—husband 33.3% Other 11.1% The frequencies are obtained from the UNOS data for various years. Patients are the new wait-list additions recorded between January 1995 and April 2003, except the gender data. The gender and living donor data were recorded between 1992 and 2001. Based on UNOS/OPTN data and annual report as of 7/14/2003 retrieved from http://www.optn.org. Positive crossmatch probability is reported by Zenios, Woodle, and Ross [2001]. 476 QUARTERLY JOURNAL OF ECONOMICS kj Ki to his own donor ki only if kidney ki is not compatible with him, or if although kidney ki is compatible with him, it has more than an equivalent of one additional HLA mismatch than kidney kj has. Under both preference scenarios, the wait-list option may or may not be considered acceptable by a patient. Since the expected quality of HLA match is very low when a patient is given priority in the waiting list and since the graft failure rates are significantly higher for cadaveric kidneys than living-donor kidneys, we assume that a patient considers the wait-list option acceptable only if his donor is not compatible with him. We also assume that the patients who consider this option acceptable prefer any compatible living-donor kidney to this option. Because there are no reliable data available on the rate of patients who consider this option acceptable and because it depends on how priority is given, we consider two treatments, in which 0 percent and 40 percent of the patients with incompatible donors prefer the wait-list option to their own donors. IV.C. Simulated Mechanisms We consider four exchange mechanisms to contrast with the no-exchange regime: (1) paired-kidney-exchange mechanism, (2) TTC mechanism, (3) paired and indirect exchange mechanism, and (4) TTCC mechanism with the efficient and strategy-proof chain selection rule e. In our simulations we randomly simulate a sample of n donor-patient pairs using the population characteristics explained above. Then, we determine the preferences of patients over kidneys in the sample: for each patient ti, we first check whether a donor kj is ABO-compatible. If kj is ABO-compatible, then we check whether there is a positive crossmatch between ti and kj. If they test negative for crossmatch, then kj is in the compatible donor set Ki of patient ti. After finding the set of compatible kidneys for each patient, we obtain a preference ordering on this set, using the utility functions described above. We construct four sets of preferences for each patient using the rational or cautious preference construction and assuming that 0 percent or 40 percent of patients with incompatible donors consider the wait-list option acceptable. We simulate each of the five mechanisms under these four preference scenarios. We use a Monte-