ESSAYS ON THE ECONOMICS OF

ORGAN TRANSPLANTATION AND HEMODIALYSIS

By

Yeon Choi

A DISSERTATION

Submitted to

Michigan State University

in partial fulﬁllment of the requirements

for the degree of

Economics — Doctor of Philosophy

2020

ABSTRACT

ESSAYS ON THE ECONOMICS OF

ORGAN TRANSPLANTATION AND HEMODIALYSIS

By

Yeon Choi

Chapter 1. The Eﬀect of Broader Liver Sharing on Patient Outcomes and Oﬀer
Acceptance

This paper evaluates a liver allocation policy known as Share 35, which provides trans-
plant candidates facing high mortality risks with priority for livers obtained from relatively
distant geographic areas. Exploiting the variation in the access to liver transplants across
transplant candidates, I show that increasing access to liver transplants is an eﬀective way
to reduce mortality rates. Although the policy is well-targeted, I ﬁnd that the policy causes
unintended eﬀects on the quality of transplanted livers and transplant candidatesâ liver oﬀer-
acceptance incentives. Because the policy promotes liver sharing across areas, targeted candi-
dates receive a lower quality of livers due to longer liver transportation times. However, those
candidates receive a compensation on liver quality by receiving livers with better donor char-
acteristics. To further understand the mechanism of the compensation, I develop a strategic
liver search model and estimate the model with match-run data that contain oﬀer-acceptance
decision histories for all donated livers. I ﬁnd that the policy enables targeted candidates to
be more selective of liver and transfer some of their quality loss to others.

Chapter 2. The Role of Kidney Allocation Policy in Addressing Kidney Shortages

I examine whether prioritizing certain types of transplant candidates in deceased-donor
kidney allocation can increase the total number of kidney transplants. Transplant candidates
strategically choose one of the two kidney sources, namely, deceased-donor and living-donor
kidneys. While deceased-donor kidneys are available for all transplant candidates (similar
to public goods), living-donor kidneys are only available for the designated recipients by the
donors (similar to private goods). Using a regression discontinuity design, I show that trans-
plant candidates are less likely to choose living-donor kidneys when they have better access

to deceased-donor kidneys, which can be interpreted as a crowd-out eﬀect. Furthermore, I
ﬁnd that the size of the eﬀect varies substantially across race, blood type, and dialysis status
of transplant candidates. The result implies that prioritizing transplant candidates, who are
less prone to crowd-out, in deceased-donor kidney allocation could make policies designed to
increase the number of deceased donors more eﬀective.

Chapter 3. The Strategic Location Choice of For-proﬁt Hemodialysis Facilities in
the U.S.

In the last chapter, I identify key factors related to the location choice of for-proﬁt
hemodialysis facilities using a dataset from the United States Renal Data System (USRDS)
and structural methods. All patients with kidney failure need to receive hemodialysis treat-
ment regularly and permanently. Because dialysis treatments are homogeneous across facili-
ties, patients are likely to choose a treatment facility based on the distance from their homes.
The strategic model introduced by Seim (2006) involves a static and incomplete informa-
tion game among dialysis facilities for entry and positioning in a market. The estimation
results show that in choosing an optimal location, a tradeoﬀ occurs between local demand
and competition with potential entrants.

Copyright by
YEON CHOI
2020

To my parents,

my wife, Hyunjong Jong

and son, Hajin

v

ACKNOWLEDGEMENTS

First and foremost, I would like to express my deepest appreciation to my advisor
Todd Elder for his mentorship, constant support, encouragement and thoughtful com-
ments. I additionally thank Stacy Dickert-Conlin, Mike Conlin, and Mathew Reeves
for their invaluable help and advice. I would like to extend my sincere thanks to Ajin
Lee, Steven Haider, Jose Fernandez, Nikhil Agarwal, and Keith Teltser for their in-
valuable comments and feedback. I also like to express my appreciation for the oﬃce
staﬀ in the Department of Economics for their dedication to the economics graduate
students.

I would also like to thank seminar participants at the 2018, 2019 SEA annual
meeting, the 2018 WEA annual meeting, the 2018, 2019 Economics Graduate Student
Conference, the Grand Valley State University, and Michigan State University for their
helpful comments and discussion.

I am deeply indebted to my parents, Yangsoo Choi and Soonyi Lee, for encour-
aging me to follow my passions and their support. My son, Hajin, became the joy of
my life and have continually provided the requisite breaks and the motivation to ﬁnish
my degree with expediency.

Last but by no means least, my wife, Hyunjong Jong, has gladly endured a hard
time by my side during doctoral program. The completion of my dissertation would
not have been possible without her sacriﬁce and support. Thank you for being my
muse, editor, and proofreader. I owe you everything.

The data reported in Chapters 1 and 2 have been supplied by the Minneapolis
Medical Research Foundation (MMRF) as the contractor for the Scientiﬁc Registry of
Transplant Recipients (SRTR). The interpretation and reporting of these data are the
responsibility of the author(s) and in no way should be seen as an oﬃcial policy of or
interpretation by the SRTR or the U.S. Government.

The data reported in Chapter 3 have been supplied by the United States Re-
nal Data System (USRDS). The interpretation and reporting of these data are the
responsibility of the author(s) and in no way should be seen as an oﬃcial policy or
interpretation of the U.S. Government.

vi

TABLE OF CONTENTS

LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 1

The Eﬀect of Broader Liver Sharing on Patient Outcomes and Oﬀer
Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.2 Institutional Detail
1.2.1 Deceased Donor Liver Allocation Rule . . . . . . . . . . . . . . .
1.2.2 Regional Share 35 Policy . . . . . . . . . . . . . . . . . . . . . .
1.3 Data and Sample
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4 Empirical Framework . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.4.1 Fuzzy Regression Discontinuity . . . . . . . . . . . . . . . . . . .
1.4.2 Diﬀerence-in-Diﬀerences Estimation . . . . . . . . . . . . . . . .
1.5 Access to Liver Transplants and Mortality Rates . . . . . . . . . . . . .
1.5.1 Regression Discontinuity Estimates . . . . . . . . . . . . . . . . .
1.5.2 Diﬀerence in Diﬀerences Estimates . . . . . . . . . . . . . . . . .
1.6 Eﬀect on Posttransplant Outcomes . . . . . . . . . . . . . . . . . . . . .
1.6.1 Transplanted Liver Quality . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . .
1.6.2 Posttransplant Survival
1.7 Eﬀect on Liver Oﬀer-Acceptance Behavior . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.8 Robustness and Speciﬁcation Check . . . . . . . . . . . . . . . . . . . .
1.8.1 Placebo Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1.8.2 Sensitivity to Bandwidth and Polynomials . . . . . . . . . . . . .
1.8.3 The Assumption of a Common Trend . . . . . . . . . . . . . . .
1.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1.7.1 The Liver Search Model
1.7.2 Results

ix

xi

1
1
6
6
8
8
10
10
11
14
14
16
17
18
19
22
22
23
26
26
27
28
29

Chapter 2

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2 Institutional Details . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2.1 Treatments for Patients with Kidney Failure . . . . . . . . . . . .
2.2.2 A Candidate’s Choice between the Two Kidney Sources
. . . . .
2.2.3 Matching Donor Kidneys to Patients . . . . . . . . . . . . . . . .

The Role of Kidney Allocation Policy in Addressing Kidney Shortages 31
31
35
35
36
38

vii

2.2.4 Sensitization Points

. . . . . . . . . . . . . . . . . . . . . . . . .
2.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.4 Estimation Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.1 Trade-oﬀs between kidney sources
. . . . . . . . . . . . . . . . .
2.5.2 Mortality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.5.3 Heterogeneity . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.6 Robustness Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.7 Conclusions
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Chapter 3

The Strategic Location Choice of For-proﬁt Hemodialysis Facilities
in the U.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2.1 Treatments for Patients with Kidney Failure . . . . . . . . . . . .
3.2.2 Medicare and the Dialysis Industry . . . . . . . . . . . . . . . . .
3.3 Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.1 Market Deﬁnition . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.2 Dialysis Facilities . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.3.3 Local Demand for Dialysis Treatments . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . .
3.4.1 Location Choice . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.4.2 Identiﬁcation . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.5 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.6 Robustness Check . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.7 Conclusions

3.4 Model of Dialysis Facility Location Choice

39
41
43
46
46
48
50
53
55

58
58
62
62
63
64
64
65
66
67
67
69
70
72
73

75
APPENDICES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
76
Appendix A Tables and Figures for Chapter 1 . . . . . . . . . . . . . .
98
Appendix B Tables and Figures for Chapter 2
. . . . . . . . . . . . . .
Appendix C Tables and Figures for Chapter 3 . . . . . . . . . . . . . . 120
. . . . . . 128
Appendix D Validity Check for RD estimation in Chapter 1
Appendix E Variable Choice for Survival Prediction in Chapter 1
. . . 130
Appendix F Selection of Functional Form in Chapter 2 . . . . . . . . . . 132

BIBLIOGRAPHY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

viii

LIST OF TABLES

Table A.1 Descriptive statistics for liver transplant candidates . . . . . . .
76
Eﬀect of aM ELD ≥ 35 on patient outcomes, RD estimates
Table A.2
. .
77
Eﬀect of the Share 35 policy on patient outcomes, DD estimates
Table A.3
77
Table A.4
Eﬀect of the Share 35 policy on transplanted liver quality . . .
78
Eﬀect of the Share 35 policy on posttransplant survival . . . . .
Table A.5
78
Table A.6
Eﬀect of the Share 35 policy on liver oﬀer acceptance . . . . . .
79
[Placebo test] Eﬀect of aM ELD ≥ 35 on patient outcomes . . .
Table A.7
79
Table A.8 Diagnosis for exception MELD score . . . . . . . . . . . . . . .
80
Table A.9
Balance of covariates . . . . . . . . . . . . . . . . . . . . . . . .
80
Table A.10 Eﬀect of aM ELD ≥ 35 on patient outcomes . . . . . . . . . . .
81
Table A.11 Descriptive statistics for liver transplant recipients
. . . . . . .
82
Table A.12 Descriptive statistics for liver candidates in the match-run sample 83
. . . . . . . . . . .
Table A.13 Selected variables by LASSO (40 variables)
84
85
Table A.14 Comparison of the predictive power . . . . . . . . . . . . . . . .
Table B.1 Kidney allocation points . . . . . . . . . . . . . . . . . . . . . .
98
98
Scale of sensitization points (From December 4, 2014) . . . . . .
Table B.2
Summary statistics of outcomes . . . . . . . . . . . . . . . . . .
Table B.3
99
Table B.4
Balance of covariates . . . . . . . . . . . . . . . . . . . . . . . .
99
The eﬀect of sensitization points on kidney source choice . . . . 100
Table B.5
Table B.6
The eﬀect of sensitization points on waitlist mortality . . . . . . 101
The eﬀect of sensitization points on overall mortality . . . . . . 102
Table B.7
Heterogeneity of fuzzy RD results by candidates’ races . . . . . 103
Table B.8
Table B.9
Heterogeneity of fuzzy RD results by candidates’ blood types
. 104
Table B.10 Heterogeneity of fuzzy RD results by candidates’ dialysis status 105
Table B.11 Robustness to the exclusion of outermost observations
. . . . . 106
Table B.12 Diﬀerence-in-diﬀerences estimates . . . . . . . . . . . . . . . . . 107
Table B.13 Polynomial model selection . . . . . . . . . . . . . . . . . . . . 107
Table B.14 The eﬀect of sensitization points on patient mortality . . . . . . 108
Table B.15 Fuzzy RD results by candidates’ races
. . . . . . . . . . . . . . 109

ix

Table B.16 Fuzzy RD results by candidates’ blood types . . . . . . . . . . . 110
Table B.17 Fuzzy RD results by candidates’ dialysis status
. . . . . . . . . 111
ESRD patient distance to dialysis facilities . . . . . . . . . . . . 120
Table C.1
Table C.2 Market characteristics (81 sample markets)
. . . . . . . . . . . 120
Census tract-level characteristics
Table C.3
. . . . . . . . . . . . . . . . . 121
Table C.4
Parameter estimates . . . . . . . . . . . . . . . . . . . . . . . . 122
Robustness to the restrictions on the largest city within 20 miles 123
Table C.5
Table C.6
Robustness to the assumption on the size of potential entrants . 124

x

LIST OF FIGURES

. . . . . . . . . . . . . . . . . . . .
Eﬀect of the Share 35 policy on the liver transplant market . .

85
Figure A.1 DSAs and Regions in U.S.
Figure A.2
85
Figure A.3 Deceased donor liver allocation process under the Share 35 policy 86
Eﬀect of the Share 35 policy on patient outcomes
. . . . . . .
Figure A.4
87
Change in the access to liver oﬀers . . . . . . . . . . . . . . . .
88
Figure A.5
Sensitivity to bandwidth and polynomial
. . . . . . . . . . . .
Figure A.6
89
. . . . . . . . . . . .
Sensitivity to bandwidth and polynomial
90
Figure A.7
Event study, transplant and mortality for aM ELD ≥ 35
. . .
Figure A.8
91
92
Figure A.9
Event study, transplant and mortality for aM ELD < 35 . . . .
Figure A.10 Event study, transplantation quality for aM ELD ≥ 35 . . . .
93
Figure A.11 Event study, transplantation quality for aM ELD < 35
. . . .
94
Figure A.12 Event study, liver oﬀer acceptance for aM ELD ≥ 35 . . . . . .
95
Figure A.13 Event study, liver oﬀer acceptance for aM ELD < 35 . . . . . .
96
Figure A.14 aMELD distribution . . . . . . . . . . . . . . . . . . . . . . . .
97
Trends in the kidney transplant market . . . . . . . . . . . . . 112
Figure B.1
. . . . . . 113
Figure B.2
Net costs and beneﬁts of a living kidney transplant
Figure B.3 Kidney sensitization measure and sensitization points
. . . . . 114
Figure B.4
CPRA distribution . . . . . . . . . . . . . . . . . . . . . . . . 114
Figure B.5 Mean frequency test . . . . . . . . . . . . . . . . . . . . . . . . 114
Figure B.6 Discontinuities on predicted outcomes . . . . . . . . . . . . . . 115
Crowd-out eﬀect on the demand of living donor kidneys . . . . 116
Figure B.7
The eﬀect on patient mortality . . . . . . . . . . . . . . . . . . 116
Figure B.8
Figure B.9
Heterogentiy of the crowd-out eﬀect by candidates’ races
. . . 117
Figure B.10 Heterogentiy of the crowd-out eﬀect . . . . . . . . . . . . . . . 118
Figure B.11 Donut RD estimation . . . . . . . . . . . . . . . . . . . . . . . 119
Figure B.12 Sample of a diﬀerence-in-diﬀerence estimation . . . . . . . . . 119
Figure C.1
. . . . . . . . 125
Trend of ESRD incidences and dialysis facilities
Trend of ESRD incidence by age . . . . . . . . . . . . . . . . . 125
Figure C.2
Figure C.3
Trend of primary causes of ESRD . . . . . . . . . . . . . . . . 126

xi

Figure C.4
Figure C.5

Treatment choice within 1 year of ESRD incidence . . . . . . . 126
Trend of dialysis facilities . . . . . . . . . . . . . . . . . . . . . 127

xii

Chapter 1

The Eﬀect of Broader Liver Sharing on Patient Outcomes and

Oﬀer Acceptance

1.1

Introduction

A liver transplant is the ultimate treatment for patients whose livers are damaged,
potentially leading to better quality of life and improved patient survival. While many
patients are desperate for transplants, unfortunately considerable shortage of trans-
plantable livers exists in a system where the sale of human organs is illegal (National
Organ Transplantation Act, 1984). More than 12,000 candidates register on the liver
transplant waitlists every year, and roughly 1,200 candidates die while waiting for liver
transplants because only around 8,000 candidates receive liver transplants in a year1.
Thus, how to allocate scarce livers is an important issue in the liver transplant market.
A liver transplant recipient is jointly determined by a liver oﬀer via centrally-
managed liver allocation rules and a candidate’s decision to accept or decline the oﬀer.
The current liver allocation rule tries to minimize the mortality risk of transplant
candidates while not compromising the quality of donated livers. For the ﬁrst goal,
the sickest patients are prioritized in liver allocation, and the severity of liver disease
is measured by either Status 1A condition (the highest severity) or the model of end-
stage liver disease (MELD) score, which ranges from 6 (less ill) to 40 (severely ill).
However, the severity-based allocation may not guarantee the optimal liver allocation,
as livers cannot survive long outside of the body. Thus, the Organ Procurement and
Transplantation Network (OPTN) divides the country into 58 geographic allocation
units called donor service areas (DSAs), as shown in Figure A.1, and gives priority
to transplant candidates registered in the DSA where the donor hospital is located.
Finally, if a transplant candidate receives a liver oﬀer based on the allocation rule,
he/she strategically decides whether he/she will accept the oﬀer or wait for a higher
quality oﬀer.

1https://optn.transplant.hrsa.gov/data/view-data-reports/national-data,

web, last accessed on September 28, 2019.

information accessed on the

1

In June 2013, the OPTN introduced the Share 35 policy, which awards addi-
tional priority to transplant candidates with MELD scores of 35 or higher, to reduce
their mortality risks before receiving transplants, which is hereafter termed “waitlist
mortality”. As shown in Figure A.2, the policy increased the percentage of recipients
with MELD scores above 35 from 18 percent in the 4 years before 2013 to 26 percent
in the 4 years after 2013. Rather than increasing liver donations, the OPTN loosened
the distance-based allocation system explained above; namely, transplant candidates
with MELD scores above 35 have increased priority for livers obtained in their regions,
which consist of several adjacent DSAs, in addition to their own. Thus, the policy also
yields an increase in the share of livers transported to other DSAs from 20 percent in
the 4 years before 2013 to 29 percent in the 4 years after 2013. These changes show
that the Share 35 policy yields trade-oﬀs between access to liver transplants and the
quality of transplanted livers.

This paper examines impacts of the Share 35 policy on the two goals of liver
allocation policy, namely, mortality risk and liver quality, and oﬀer-acceptance incen-
tives. Speciﬁcally, I ﬁrst examine whether increasing access to liver transplants is an
eﬀective way to reduce mortality risk of transplant candidates. Then, I analyze unin-
tended impacts of the Share 35 policy on the quality of transplanted livers resulting
from the promotion of liver sharing across DSAs and liver oﬀer-acceptance incentives
of transplant candidates.

To estimate the causal impact of an increase in access to liver transplants on
patient mortality risk, I use a fuzzy regression discontinuity (RD) design exploiting the
variation around the MELD score 35 threshold, which determines eligibility under the
Share 35 policy. After the policy is implemented, transplant candidates with MELD
scores just above 35 are 13.6 percentage points more likely to receive liver transplants
within 90 days from the waitlist registration compared with those with MELD scores
just below 35. Using this result as the ﬁrst stage, I ﬁnd that a 10-percentage-point
increase in the likelihood of receiving a liver transplant signiﬁcantly decreases the
waitlist mortality rate by 4.4 - 6.5 percentage points. As the policy beneﬁt arises from
reallocating donated livers across transplant candidates not a supply shock that might
increase the number of liver donations, both transplant candidates with MELD scores

2

above and below 35 are aﬀected by the policy in an opposite direction. To separate the
eﬀect on each candidate group, I use the diﬀerence-in-diﬀerence (DD) estimation using
Status 1A candidates as a control group. DD estimates show that the policy decreases
the waitlist mortality rates for transplant candidates with MELD scores above 35
while not causing a signiﬁcant increase in the waitlist mortality rates for those with
MELD scores below 35. Additionally, I analyze the impact on overall mortality rates,
which refers to the likelihood of death irrespective of transplant status. Although I
do not ﬁnd any signiﬁcant impact of an increase in access to liver transplants on the
overall mortality rates in the RD design, DD estimates show that the Share 35 policy
signiﬁcantly decreases the overall mortality rates for transplant candidates with MELD
scores above 35.

Second, I estimate changes in the quality of transplanted livers and the probabil-
ity of posttransplant survival using a DD model. I ﬁnd that transplant recipients with
MELD scores above 35 are more likely to receive livers that are obtained from the other
DSAs and transported over longer times, which implies lower liver quality. However, I
ﬁnd that those recipients are more likely to receive livers with better donor character-
istics which could be interpreted as a compensation for the increased liver travel time.
The changes in the quality of transplanted livers result in a decrease in posttransplant
survival rates for both transplant recipient groups; MELD scores above and below 35,
although the latter group of candidates does not show longer transportation time after
the policy implementation.

Finally, to elucidate the mechanism of mixed eﬀect on the quality of transplanted
livers for candidates with MELD scores above 35, I examine how the policy aﬀects liver
oﬀer-acceptance behavior. I develop a liver search model that explains the strategic
liver oﬀer-acceptance behavior of transplant candidates. The model suggests that an
increase in access to liver oﬀers for a transplant candidate could increase the minimum
quality level of liver oﬀer acceptance. With this model in mind, I estimate the impact of
the Share 35 policy on the likelihood of accepting liver oﬀers using a DD speciﬁcation.
DD estimates show that the policy decreases the probability of accepting liver oﬀers for
transplant candidates with MELD scores above 35 by 10.2 percentage points, which
implies that those candidates become more selective of liver oﬀers. Exploiting the

3

increased access to liver oﬀers, those candidates could have chosen livers with better
donor characteristics although they more commonly received regionally shared livers.
The existing literature on the policy (Massie et al. 2015; Edwards et al. 2016;
Annamalai et al. 2015) agrees that the policy increases access to liver transplants
for transplant candidats with MELD scores 35 or greater. They show this result by
comparing the proportion of liver transplants for candidates with MELD scores above
35 before and after the policy. However, interpreting the results as causal should be
careful. Because donated livers are allocated based on the mortality risk of transplant
candidates, those with the highest mortality risk experience greater access to liver
transplants. Due to the reverse causality, the results in previous literature may not
show the causal eﬀect.

The results regarding the impact on waitlist mortality and posttransplant sur-
vival are mixed. For example, Massie et al. (2015) and Edwards et al. (2016) found that
the Share 35 policy led to a decrease in waitlist mortality of liver transplant candidates
with MELD scores above 35 using survival analysis. However, Annamalai et al. (2015)
found no signiﬁcant eﬀect of the policy on waitlist mortality for liver transplant candi-
dates with MELD scores above 35. Similarly, estimates of the eﬀect on posttransplant
survival rates are mixed. Edwards et al. (2016) found no signiﬁcant eﬀect of the Share
35 policy on 1-year posttransplant survival for liver transplant recipients with MELD
scores above 35 using the transplant recipient sample within 2 years before and after the
policy implementation. However, a recent study of recipients within 3 years before and
after the policy implementation revealed that Share 35 increases 1-year posttransplant
survival for transplant recipients with MELD scores above 35 (Kwong et al. 2018).

This paper contributes to the related literature in three ways. First, I estimate
the causal eﬀect of an increase in access to liver transplants on patient mortality risks.
I use a fuzzy RD design that uses the plausibly exogenous variation in access to liver
transplants across transplant candidates around the MELD score 35 threshold who
have similar characteristics.

Second, I propose a new liver quality model that predicts relatively long-term,
that is 5 years, posttransplant survival rates. As the Share 35 policy was not imple-
mented until 2013, currently available data have some limits in estimating the policy

4

impact on long-term posttransplant survival rates. Thus, the existing literature fo-
cuses mainly on 1-year posttransplant survival estimates (Edwards et al. 2016; Kwong
et al. 2018). My proposed model uses highly predictive variables for posttransplant
survival selected from Machine Learning (ML) algorithms, i.e., the Least Absolute
Shrinkage and Selection Operator (LASSO) algorithm. I ﬁnd that the predicted re-
sults show higher prediction power than the widely used Donor Risk Index (DRI) liver
quality measure (Feng et al. 2006).

Finally, I ﬁnd a liver oﬀer-acceptance mechanism through which the Share 35
policy aﬀects the quality of transplanted livers in other ways besides an increase in
transportation time. Although the existing literature examines the eﬀect of the Share
35 policy on posttransplant survival, few studies discuss the mechanism. For example,
Kwong et al. (2018) explained that transplant recipients with MELD scores above 35
show better posttransplant survival rates after the policy implementation thanks to
receiving higher-quality livers. However, they did not present the reason why those
variations in liver quality existed across transplant recipients. There are some studies
examining the eﬀect of the Share 35 policy on liver oﬀer acceptance. Washburn et
al. (2016) and Goldberg et al. (2017) showed that the number of liver oﬀer decline
for candidates with MELD scores above 35 increased after the policy implementation.
They interpreted the result as an evidence of ineﬃcient liver matching process without
discussing the relationship with the quality of transplanted livers.

This paper proceeds as follows. The following section provides additional back-
ground information on liver allocation and the Share 35 policy. Section 1.3 describes the
data used for estimation, while Section 1.4 discusses the identiﬁcation strategy. Section
1.5 presents estimates of the access to liver transplants and patient mortality. Section
1.6 and 1.7 investigate estimates of transplantation quality, posttransplant survival,
and oﬀer-acceptance behaviors. Section 1.8 provides key robustness and speciﬁcation
checks, and Section 1.9 concludes.

5

1.2

Institutional Detail

1.2.1 Deceased Donor Liver Allocation Rule

To manage organ shortages and improve organ matching, NOTA established the OPTN,
which is responsible for developing the allocation rule and distributing donated organs.
The OPTN has been operated by the United Network for Organ Sharing (UNOS), the
initial contractor since 1986 (Leppke et al. 2013). Under the OPTN allocation rule,
deceased donor livers are distributed based on geographical proximity to the donor
hospital and the medical urgency of the candidates2.

For a successful transplant, the donated liver should be transplanted before the
maximum preservation time, which is 8-12 hours3. Because of the time limit between
organ procurement and transplant, the distance between the donor hospital and the
patient’s residence is an important component of the liver allocation system. Thus,
the OPTN divides the United States into several areas and allocates organs based on
geographical proximity. As shown in Figure A.1, the country is divided into 11 regions
for organ allocation. Each region consists of several DSAs, and all U.S. transplant
centers belong to one of 58 DSAs. Each color in the ﬁgure represents a diﬀerent DSA.
The geographical boundaries of DSAs are diﬀerent from administrative boundaries
such as county and state boundaries. Hence, some DSAs include several counties in
one state, while others include an entire state or several states. In general, deceased
donor livers are allocated according to organ allocation area tiers (DSA → Region →
Nation). Once a liver is recovered from a deceased donor, the DSA administration
matches it to candidates listed in the DSA, where it becomes available ﬁrst. If there is
no suitable candidate, it passes to candidates in the region to which the DSA belongs.
If a proper candidate cannot be found or the liver is not accepted by oﬀered candidates
in the region, nationwide waitlisted candidates have a chance to obtain the liver.

2The allocation rule by organ is the same as below. Factors associated with kidney allocation are waiting
time, donor/recipient immune system incompatibility, pediatric status, prior living donor status, distance
from the donor hospital and survival beneﬁt. Factors associated with heart allocation are medical need
and distance from the donor hospital. Factors associated with lung allocation are survival beneﬁt, medical
need, waiting time and distance from the donor hospital.
(https://optn.transplant.hrsa.gov/learn/about-
transplantation/how-organ-allocation-works/, information accessed on the web, last accessed on June 23,
2019)

3Maximum organ preservation time for other organs are: heart or lung, 4-6 hours; pancreas, 12-
18 hours; kidney, 24-36 hours (https://optn.transplant.hrsa.gov/learn/about-transplantation/how-organ-
allocation-works/, information accessed on the web, last accessed on June 23, 2019)

6

Since February 27, 2002, the medical need of a liver transplant candidate has
been measured by the MELD score, which is highly correlated with 3-month mortality
of patients without liver transplants45. OPTN uses the allocation MELD (aMELD)
score determined by the calculated MELD (cMELD) score and the exception MELD
(eMELD) score (Massie et al. 2011).

aM ELD = max[cM ELD, eM ELD]

(1)

The cMELD score is based on three objective variables, namely, bilirubin, international
normalized ratio (INR), and creatinine, which can be obtained by a lab blood test and
ranges from 6 (less ill) to 40 (severely ill). The cMELD score is derived by using the
equation below and is rounded to the nearest whole number.

cM ELD = 3.78 ∗ ln[bilirubin] + 11.20 ∗ ln[IN R] + 9.57 ∗ ln[creatinine] + 6.43 (2)

To predict waitlist mortality risk more accurately, on January 11, 2016, sodium was
included as a cMELD score factor for candidates with previous cMELD scores higher
than 11 (Biggins 2015). All candidates active on the waitlist at the time of the new
policy implementation were aﬀected by this new cMELD score system6. The new
cMELD score is derived by using the equation below. The new cMELD score is still
capped at 40, similar to the previous cMELD score, and rounded to the nearest whole
number.

cM ELD(−N a) = M ELD(i)+1.32∗(137−sodium)−0.33∗M ELD(i)∗(137−sodium)
(3)
where M ELD(i) is the cMELD score calculated from the equation (2) and rounded to
the nearest whole number.

4Wiesner et al. (2003) showed that the 3-month mortality of patients without a liver transplant increases
when the MELD score increases. MELD < 9 : 1.9% / 10 - 19 : 6.0 % / 20 - 29 : 19.6% / 30 - 39 : 52.6 % /
> 40 : 71.3%

5Liver transplant candidates less than 18 years old at the time of registration are prioritized by the

Pediatric End-stage Liver Disease (PELD) score.

6Candidates who were Status 1A at the time of policy implementation were not aﬀected. In addition,
inactive candidates were not aﬀected. (https://www.transplantpro.org/news/technology/policy-and-system-
changes-adding-serum-sodium-to-meld-calculation/, information accessed on the web, last accessed on June
23, 2019)

7

However, it has been shown that the cMELD score does not accurately reﬂect
candidates’ need for liver transplants when they have certain liver-related diseases. To
solve this problem, OPTN assigns the eMELD score for certain recognized exceptional
diagnoses (RED), such as Cholangiocarcinoma and Cystic Fibrosis. (Table A.8).

The only measure of medical needs considered regardless of the aMELD score is
the Status 1A condition, which is assigned to patients with fulminant liver failures and
whose life expectancy without a liver transplant is fewer than 7 days. Since December
2010, the OPTN has provided them the beneﬁt of regional sharing for donated livers to
reduce the mortality risk of Status 1A candidates. That is, all the Status 1A candidates
receive the same priority in the liver allocation process irrespective of their DSAs if
they are registered in the same region.

1.2.2 Regional Share 35 Policy

Sharma et al. (2012) found that the waitlist mortality of transplant candidates with
aMELD scores 35 or greater is similar to that of Status 1A candidates. To promote
equity in liver allocation, on June 18, 2013, an extended regional liver sharing policy,
Share 35, was implemented. Figure A.3 shows the mechanism of the Share 35 policy.
Let us assume that Region 1 consists of three DSAs (A, B, and C) and a deceased
donor liver is recovered from DSA A. Regardless of Share 35 policy implementation,
Status 1A candidates registered in the Region 1 have priority for the liver over non-
Status 1A candidates. Under the allocation rule before Share 35, the liver, which was
not accepted by Status 1A candidates, was oﬀered to candidates in DSA A based on
their aMELD scores. If the liver was not matched to candidates in DSA A, candidates
registered in diﬀerent DSAs (B and C) received liver oﬀers. Since the implementation
of the Share 35 policy, however, the liver is oﬀered to candidates with an aMELD
score of 35 or higher registered in Region 1 before it is oﬀered to other candidates with
aMELD scores below 35 in the DSA A.

1.3 Data and Sample

This study uses data from the Scientiﬁc Registry of Transplant Recipients (SRTR).
The SRTR data system includes data on all donors, wait-listed candidates, and trans-

8

plant recipients in the US, submitted by the members of the Organ Procurement and
Transplantation Network (OPTN). The Health Resources and Services Administration
(HRSA), U.S. Department of Health and Human Services provides oversight to the
activities of the OPTN and SRTR contractors. The data include detailed individual-
level information such as liver candidate demographics and dates when and transplant
centers where each candidate was registered and underwent transplantation. The stan-
dard data also contain information on each liver candidate’s cMELD and eMELD score
histories. All candidates registered on the liver transplant waitlist must have a labora-
tory blood test regularly to update their aMELD scores. Each test result is reported
to SRTR, and this dataset contains all historical records.

When liver candidates receive donated liver oﬀers, they can decline the oﬀers
because of various reasons, such as their health status or donated liver quality without
any risk of penalty for the next liver oﬀer. Hence, the standard data, which contain
only the information on the ﬁnal acceptance that results in liver transplant, have limits
in the analysis of a liver candidate’s liver oﬀer acceptance. To overcome this limitation,
I use the potential transplant recipient data, which contain information on match runs
conducted for all the donated livers. The data include information on the donors
who donated livers, the candidates who received the liver oﬀers, and the decision on
whether the livers were accepted or declined by the candidates who received the oﬀers.
As the data indicate, donors and candidates with unique identiﬁers can be linked to
the standard data, which contain various demographics of donors and candidates.

This study examines adult liver transplant candidates and recipients who were
older than 18 years at the time of waitlist registration because the allocation rule
for younger candidates uses diﬀerent medical urgency measure, Pediatric End-stage
Liver Disease (PELD). I also restrict the sample to transplant candidates who were
registered on the transplant waitlist between January 2011 and June 2017. As explained
in Section 1.2.1, the policy that provides the beneﬁt of regional sharing with Status 1A
candidates was implemented on December 2010. Therefore, use of the analysis sample,
which includes transplant candidates waitlisted before December 2010 may result in
mixed results of two diﬀerent regional priority policies. Finally, I excluded transplant
candidates waitlisted for both liver and intestine transplants, because they are aﬀected

9

by a non-standard liver allocation rule.

1.4 Empirical Framework

1.4.1 Fuzzy Regression Discontinuity

To derive the causal eﬀect of an increase in access to liver transplants on mortality risk,
I use a discontinuous change caused by the Share 35 policy. As transplant candidates
with aMELD scores just above 35 are prioritized for donated livers in the waitlisted
regions, the likelihood of receiving liver transplants would discontinuously change at
the aMELD score 35 threshold. If an increase in the access to liver transplants reduces
the mortality risk of transplant candidates, we could expect a discontinuous decrease
in the mortality rates at the cutoﬀ. To examine this hypothesis, I use the following
local linear regression.

Yi = α + β1Share35i + β2Xi + β3Share35i × Xi + ui

(4)

where i denotes a liver transplant candidate. Yi is a binary variable that indicates
whether each candidate receives a deceased donor liver transplant (ﬁrst stage) or dies
while waiting for a liver oﬀer or after receiving a liver transplant (reduced form).
To minimize the eﬀect of the waitlist time variation across transplant candidates, I
focus on the outcomes occuring within a certain period from the waitlist registration.
Share35i is a binary variable equal to one if the aMELD score of candidate i is greater
than or equal to 35. Xi is a running variable that measures the diﬀerence between
the aMELD score of candidate i and the threshold. In the RD design, a continuous
running variable is desirable for a precise estimation (Jacob et al. 2012). However, the
aMELD score in the SRTR dataset only shows the value rounded to the nearest whole
number. Identiﬁcation with this discrete MELD score variable could make it diﬃcult
to derive precise results. To improve precision, I recover a continuous aMELD score
using historical records of 4 critical variables (serum bilirubin, INR, serum creatinine
and serum sodium) that are included in the cMELD score equation (2) and (3)7. The

7The reported eMELD is used, as it is originally a whole number. According to equation (1), each
candidate’s aMELD score is determined by comparing the cMELD and the eMELD scores. However, just
deriving each candidate’s historical aMELD score by simply comparing those two scores in the dataset is not

10

coeﬃcient of interest is β1, and it is reported in the tables with robust standard errors.
For bandwidth selection, I use the bandwidth selection method proposed by Calonico
et al. (2017), and the optimal bandwidths are reported in the bottom of the column
for each dependent variable.

With regard to the running variable, the aMELD score, because candidates
regularly have laboratory blood tests, each candidate has many historical records of
aMELD scores. Thus, the choice of an appropriate aMELD score is important for
obtaining precise estimation results. An intuitive choice could be the last aMELD
score valid at the time of transplantation or death. However, it is uncertain which
aMELD score should be used for transplant candidates who did not experience the
outcomes of interest during the analysis period. To apply consistent criteria across
transplant candidates, this paper uses the initial aMELD score, which is measured at
the time of waitlist registration, and set a relatively short analysis duration from the
registration. Additionally, using the initial aMELD score can minimize the incentive
of manipulation, which is the main assumption of the RD design, because transplant
candidates have little information about their previous aMELD scores.

For valid identiﬁcation using the RD design, transplant candidates should be
as good as randomly distributed around the cutoﬀ and not able to perfectly manip-
ulate their aMELD scores for the Share 35 beneﬁt. I examine whether any predeter-
mined characteristic of transplant candidates shows discontinuity around the cutoﬀ,
and whether the distribution of aMELD scores shows irregular heaps at the cutoﬀ.
The detailed results of validity checks are presented in , and I do not ﬁnd any evidence
of violations for the validity assumptions.

1.4.2 Diﬀerence-in-Diﬀerences Estimation

Although RD design is a well-known identiﬁcation strategy that elicits the causal eﬀect
of a treatment, there are several limitations in evaluating the Share 35 policy eﬀects.

appropriate. Some reported eMELD scores in a certain period are not used in aMELD score calculation for
various reasons. To derive the precise aMELD scores, a candidate’s exact eMELD scores in each period should
be considered. I calculate historical records of aMELD scores using a variable in the SRTR dataset that shows
the reason for the diﬀerence between the cMELD and the aMELD scores. If the aMELD score calculation
is not available for a certain period, I assigned the most recent aMELD score for each candidate up to that
period.

11

First, interpreting RD estimates as the policy eﬀect on the targeted candidates with
aMELD scores above 35 should be approached with caution. The Share 35 policy
takes livers that would be oﬀered to transplant candidates with aMELD scores below
35 and provides them to transplant candidates with aMELD scores of 35 or greater.
Thus, RD estimates, which compare outcomes between transplant candidates with
aMELD scores below and above the 35 cutoﬀ, could show aggregated results that
combine the positive and negative eﬀects in each candidate group. Second, due to data
restrictions, precisely estimating the policy eﬀect on posttransplant outcomes using
the RD design is not possible. Posttransplant outcomes can only be identiﬁable for
transplant recipients. Thus, transplant candidates who did not receive transplants are
excluded from the analysis sample. In this case, it is desirable to use the last aMELD
scores as the running variable, as I do not have to consider the choice of aMELD scores
for transplant candidates who did not receive transplants. However, continuous last
aMELD scores calculated using the blood test results are poorly matched to reported
last aMELD scores in the dataset due to missing information, and this mismatch may
result in imprecise RD estimates.

To overcome the above RD design limitations, I employ a DD approach for all
the outcomes of interest using the aMELD scores reported in the dataset. As discussed,
exploiting the transplant candidates whose aMELD scores are below 35 as a control
group is not desirable for studying the policy eﬀect on targeted candidates with aMELD
scores above 35. To identify positive and negative impacts on transplant candidates
with aMELD scores above or below 35 separately, I exploit transplant candidates with
Status 1A condition as an alternative control group and compare them with transplant
candidates with aMELD scores above or below 35. Before being oﬀered to transplant
candidates with aMELD scores, donated livers are oﬀered to those with Status 1A
condition registered at the regions where the livers are obtained (Figure A.3). As the
Share 35 policy only reallocates donated livers not accepted by the Status 1A transplant
candidates, I can reasonably assume that the Status 1A transplant candidates are not
aﬀected by the policy.

12

To assess the causal eﬀect of the Share 35 policy, I generate the following general

DD model:

Yicy = β0 + β1P osti + β2Above35i + β3P ost × Above35i + W (cid:48)
Yicy = β0 + β1P osti + β2Below35i + β3P ost × Below35i + W (cid:48)

i Γ + σc + τy + εicy

i Γ + σc + τy + εicy

(5)

(6)

where i denotes a liver transplant candidate, c denotes the waitlisted transplant cen-
ter, and y denotes the year of waitlist registration. After dividing the analysis sample
into three groups - Status 1A, aM ELD ≥ 35, and aM ELD < 35 -, I compare Status
1A transplant candidates with the other two treatment groups. Speciﬁcally, trans-
plant candidates with aMELD scores below 35 are excluded in the estimation using
the equation (5), and those with aMELD scores above 35 are excluded in the other
speciﬁcation. P osti is an indicator for dates after Share 35 policy implementation in
June 2013. Above35i is a binary variable that is one if the aMELD score of candidate
i is greater than or equal to 35, and zero if the candidate has Status 1A condition.
Below35i is a binary variable that is one if the aMELD score of candidate i is below
35, and zero if the candidate has Status 1A condition. Wi is a set of covariates of
transplant candidates, including blood types, gender, age, race, education level, and
payment sources. A set of year dummies, τy, and waitlisted center dummies, σc, capture
the changes ﬁxed over years and across transplant centers8.

Summary statistics of the covariates are shown in Table A.1. The table compares
the means and standard deviations (SD) of the control group, i.e. transplant candidates
with Status 1A condition, and the two treatment groups, i.e. transplant candidates
with aMELD scores above and below 35 measured at the time of waitlist registrtation.
On average, compared with Status 1A transplant candidates, the table shows that
transplant candidates in both treatment samples are older (52 years and 55 years),
more likely to be male (63 percent and 65 percent), and more likely to be white (82

8For the precise estimation, identiﬁcation of variable changes by outcomes of interest. (1) For the analysis
of the access to transplants and mortality, Above35i/Below35i are determined by the initial aMELD scores
measured at the time of waitlist registration, and yidentiﬁes the year of waitlist registration. (2) For the
analysis of the posttransplant outcomes, Above35i/Below35i are determined by the last aMELD scores mea-
sured at the time of liver transplants, and yidentiﬁes the year of liver transplants. (3) For the analysis of the
oﬀer-acceptance behavior, Above35i/Below35i are determined by the aMELD scores measured at the time of
liver oﬀers, and yidentiﬁes the year of liver oﬀers.

13

percent and 86 percent). In the control group, however, the average age is 44 years,
the proportion of males is 39 percent, and the proportion of recipients whose race is
white is 72 percent. Blood types, education levels, and payment sources of transplant
candidates are comparable.

1.5 Access to Liver Transplants and Mortality Rates

1.5.1 Regression Discontinuity Estimates

Panel (a) of Figure A.4 illustrates the likelihood of receiving liver transplants around
the aMELD score 35 threshold, which determines the eligibility for Share 35 treatment.
The x-axis shows transplant candidates’ initial aMELD scores, and the y-axis describes
the probability of receiving a deceased donor liver transplant within 90 days from the
waitlist registration. Each of the points in the ﬁgure shows the average outcome value
collapsed into equal-length bins. Consistent with the Share 35 policy beneﬁt, I ﬁnd
evidence of increased access to donated livers for transplant candidates with aMELD
scores greater than or equal to 35. Column (1) of Table A.2 Panel A presents RD
estimates analogous to the ﬁgures. It shows that the probability of receiving a liver
transplant discontinuously increases by 13.6 percentage points above the 35 threshold,
which implies an approximately 20 percent increase compared with the (baseline) mean
probability of 70.4 percent for candidates below the 35 threshold.

In panels (b) to (d) of Figure A.4, I explore the transplant candidates’ waitlist
mortality rates, which indicates the risk of losing a chance to receive a liver transplant
due to death while waiting for a liver oﬀer. As a liver transplant is the ultimate
treatment for liver failure, removal from the waitlist due to deteriorating conditions is
also considered as waitlist mortality (Massie et al. 2015; Edwards et al. 2016). The
ﬁgures indicate negative discontinuities at the aMELD 35 threshold, which shows lower
waitlist mortality rates for candidates with aMELD scores above 35 compared with
those with aMELD scores below 35. Corresponding RD estimates are presented in
columns (2) to (4) of Table A.2 Panel A. Although all results are negative, only the
estimates of 180-day and 1-year waitlist mortality are statistically signiﬁcant. The
180-day waitlist mortality rates for candidates with aMELD scores just above 35 is 7.4

14

percentage points lower than those for candidates with aMELD scores just below 35,
which implies an approximately 35 percent decrease compared with the baseline waitlist
mortality of 21 percent (column (3)). RD estimates of 1-year waitlist mortality rates,
-7.6 percentage points, in column (4) are similar to those of 180-day waitlist mortality
rates.

Fuzzy RD estimates that show the causal eﬀect of an increase in the access to
liver transplants on waitlist mortality rates using the above RD estimates are presented
in Panel B of Table A.2. For every analysis duration, I ﬁnd a statistically signiﬁcant re-
lationship between the probability of receiving a liver transplant and waitlist mortality
rates. A 10 percentage point increase in the probability of receiving a liver transplant
is associated with a decrease in waitlist mortality rates ranging from 4.38 percentage
points to 6.5 percentage points. Therefore, liver allocation policies increasing access
to liver transplants for transplant candidates facing extremely high waitlist mortality
risk could be eﬀective in reducing their waitlist mortality rates.

Although the waitlist mortality rate is a targeted outcome of the liver allocation
rule, the welfare of transplant candidates could be highly related to whether they
can survive until a certain period regardless of the receipt of liver transplants. As
some transplant recipients could die due to various reasons related to transplantation,
analysis of overall mortality risks, including deaths after receiving transplants, is also
meaningful. I examine the eﬀect of an increase in access to liver transplants on overall
mortality rates. In panels (e) to (g) of Figure A.4, there are still negative discontinuities
at the aMELD 35 threshold, but the magnitudes are smaller than those of waitlist
mortality outcomes. Corresponding RD estimates are presented in columns (5) to (7)
in Table A.2 Panel A. In all the analysis durations, transplant candidates with aMELD
scores just above 35 show lower overall mortality rates than those with aMELD scores
just below 35, but I ﬁnd little evidence of statistically signiﬁcant diﬀerences. Fuzzy RD
estimates that show the causal eﬀect of an increase in the access to liver transplants
on overall mortality rates are presented in columns (5) to (7) of Panel B. Compared
with the results of waitlist mortality rates, all the fuzzy RD estimates are smaller in
magnitude and insigniﬁcant.

15

1.5.2 Diﬀerence in Diﬀerences Estimates

By applying the DD approach to the same patient outcomes, we can examine the ro-
bustness of the RD estimates and separate the diﬀerent impacts of the Share 35 policy
on transplant candidates with aMELD scores above and below 35. Table A.3 shows
the eﬀect of the Share 35 policy on donor characteristics related to transplanted liver
quality. Eligibility for the Share 35 policy is identiﬁed based on initial aMELD scores,
and transplant candidates assigned Status 1A condition at the time of waitlist regis-
tration are used as a control group for each aMELD score group, aM ELD ≥ 35 and
aM ELD < 35. All columns are estimated with a full set of covariates, namely, trans-
plant candidate characteristics, waitlisted transplant center ﬁxed eﬀects, and waitlist
registration year ﬁxed eﬀects.

First, in column (1), I examine the impact of the Share 35 policy on the access
to deceased donor liver transplants. As donated livers are allocated based on the
waitlist mortality risk, on average, transplant candidates with aMELD scores greater
than or equal to 35 are more likely to receive liver transplants within 90 days from
the waitlist registration than those with aMELD scores below 35 (0.633 vs 0.301).
As the Share 35 policy reallocates donated livers between transplant candidates with
aMELD scores above and below 35, the coeﬃcients for each candidate group show
similar magnitudes but diﬀerent signs. Transplant candidates with aMELD scores
above 35 are 5.1 percentage points more likely to receive liver transplants after the
Share 35 policy implementation. However the policy lowers access to liver transplants
of transplant candidates with aMELD scores below 35 by 5.1 percentage points.

Second, columns (2) to (4) present the policy eﬀect on the waitlist mortality
rates within diﬀerent durations from the waitlist registration. On average, transplant
candidates with aMELD scores above 35 experience waitlist mortality rates more than
twice that of those with aMELD scores below 35. The DD estimates show that the
Share 35 policy reduces waitlist mortality rates of transplant candidates with aMELD
scores above 35 without causing signiﬁcant changes in waitlist mortality rates of trans-
plant candidates with aMELD scores below 35. For example, 90-day waitlist mortality
rates of transplant candidates with aMELD scores above 35 decrease by 8.4 percentage
points after the Share 35 policy implementation, and the coeﬃcient increases to 9.9

16

percentage points for 1-year waitlist mortality rates. However, I ﬁnd little evidence
of a statistically signiﬁcant change in waitlist mortality rates of transplant candidates
with aMELD scores below 35 after the Share 35 policy implementation.

Unlike the results regarding access to liver transplants and waitlist mortality,
with DD estimates similar to ﬁndings in RD models,
in the full sample, the DD
estimates showed a large decrease in overall mortality rates after the Share 35 pol-
icy implementation. Ninety-day overall mortality rates of transplant candidates with
aMELD scores greater than or equal to 35 decrease by approximately 10 percentage
points after the Share 35 policy, and the magnitude increases as the analysis duration
increases. However, DD estimates for transplant candidates with aMELD scores below
35 are small in magnitude and only show marginally signiﬁcant results for 1-year over-
all mortality outcome. The diﬀerence in the coeﬃcients between transplant candidates
with aMELD scores above and below 35 is approximately 9 percentage points, which
is larger than that of RD estimates.

1.6 Eﬀect on Posttransplant Outcomes

In this section, I assess the impact of broader liver sharing on posttransplant outcomes.
As discussed above, providing especially sick transplant candidates with the priority
for livers donated from the areas far from the transplant center could be eﬀective in
reducing their mortality risk. However, sharing livers in broader areas could worsen the
quality of transplanted livers, which could result in lower posttransplant survival rates
due to longer transportation time. To examine this hypothesis, this paper focuses on
the Share 35 policy to exploit the exogenous variation in the access to livers obtained
from areas further away. As posttransplant outcomes are only available for transplant
recipients, I limit the analysis sample to transplant recipients. The eligibility for the
Share 35 policy is identiﬁed based on the last aMELD scores, and transplant recipients
assigned Status 1A condition at the time of transplants are used as a control group for
each aMELD score group, aM ELD ≥ 35 and aM ELD < 35.

17

1.6.1 Transplanted Liver Quality

Table A.4 shows the eﬀect of the Share 35 policy on donor characteristics related to
transplanted liver quality. All columns are estimated with a full set of covariates,
namely, recipient characteristics, waitlisted transplant center ﬁxed eﬀects, and trans-
plant year ﬁxed eﬀects. First, I examine the donor characteristics directly aﬀected
by the Share 35 policy structure, which promotes frequent regional liver sharing across
DSAs for transplant candidates with aMELD scores greater than or equal to 35. As ex-
pected, I ﬁnd that the policy yields more liver sharing across DSAs, resulting in longer
distance and time of liver transportation. Column (1) shows that the likelihood of re-
ceiving a regionally shared liver, donated from diﬀerent DSAs in the waitlisted region,
increases by 35.9 percentage points for transplant recipients with aMELD scores above
35 after the Share 35 policy implementation. The result is consistent with the results
regarding distance and time of liver transportation in Columns (2) and (3). Exploiting
the location information of transplant centers, the distance and the cold ischemia time
(CIT) are 82.8 and 4.7 percent longer for transplant recipients with aMELD scores
above 35 than for Status 1A transplant recipients, respectively. However, transplant
recipients with aMELD scores below 35 do not exhibit a statistically signiﬁcant change
in those outcomes. DD estimates show that transplant recipients with aMELD scores
below 35 are less likely to receive regionally shared livers, and the transportation dis-
tance and time decrease after the policy implementation. The above results could be
interpreted as the trade-oﬀ between improving equity and eﬃciency in liver allocation.
As the current liver allocation policy balances equity and eﬃciency, improving equity
by reallocating donated livers across areas, i.e., loosening the proximity base allocation
rule, does not guarantee the best use of donated livers.

Additionally, I examine other donor characteristics pointed out as factors related
to worse posttransplant survival in the previous literature. For example, Busquets et
al. (2001) ﬁnd that livers from donors over 70 years old are negatively associated with
graft survival. Livers from donors with a body mass index (BMI) over 35 and donated
after the cardiac death are also described as factors that result in lower graft survival
(Perito et al. 2012; Taylor et al. 2019). Columns (4)-(6) of Table A.4 show whether
the above donor characteristics for transplant recipients with aMELD scores above

18

and below 35 change after the policy implementation. Most DD estimates do not show
a statistically signiﬁcant impact of the Share 35 policy, but the sign of coeﬃcients
is diﬀerent between the two transplant recipient groups. After the Share 35 policy
implementation, lower quality livers identiﬁed in Columns (4) to (6) are more likely to
be transplanted to recipients with aMELD scores below 35 rather than to those with
aMELD scores above 35.

1.6.2 Posttransplant Survival

In the liver transplant market, the quality of transplanted livers is meaningful, be-
cause it is highly related to the probability of survival without experiencing death or
other liver failures after receiving liver transplants, known hereafter as “posttransplant
survival”. In this section, I examine how the quality changes in transplanted livers af-
ter the Share 35 policy implementation aﬀect the posttransplant survival of transplant
recipients. Column (1) of Table A.5 shows the impact on the 1-year posttransplant sur-
vival rates. Although statistically insigniﬁcant, I ﬁnd that the posttransplant survival
rates of transplant recipients with aMELD scores above 35 increase by 3.9 percentage
points after the Share 35 policy implementation, while those of transplant recipients
with aMELD scores below 35 slightly decrease. Unlike the concern regarding the qual-
ity of livers transplanted to recipients with aMELD scores above 35, the impact on
posttransplant survival rates is better for those recipients than recipients with aMELD
scores below 35.

However, the analysis of 1-year posttransplant survival rates may not be suﬃ-
cient to show the impact on the overall posttransplant survival rates. Although ad-
ditional analysis of long-term survival rates is needed for accurate assessment, it is
diﬃcult to perform the test using observed posttransplant survival outcome. Because
transplant recipients whose maximal posttransplant duration by the end of the data
extraction date (June 2, 2017) is less than the analysis duration should be excluded
in the estimation, an increase in duration reduces the sample size and weakens the
explanatory power of the estimates. Therefore, I supplement the analysis using ex ante
liver quality measures highly related to long-term posttransplant survival.

19

The representative ex ante liver quality measure is the Donor Risk Index (DRI)
introduced by Feng et al. (2006). These scholars developed the index using donor char-
acteristics that were highly correlated with posttransplant survival rates; a higher index
shows that the donated liver has lower quality and predicts lower survival rates9. In
Column (2) of Table A.5, I examine the eﬀect of the Share 35 policy on the negative log
value of DRI of liver transplant recipients 10. The estimates show that recipients with
aMELD scores above 35 receive a 2.6 percent lower quality of livers than recipients with
Status 1A condition after the Share 35 policy implementation. Unlike the results in
Column (1), the negative impact of the Share 35 policy on transplanted liver quality is
smaller, -0.014, for transplant recipients with aMELD scores below 35. Based on these
results, we can expect that the Share 35 policy negatively aﬀects long-term posttrans-
plant survival of both transplant recipients groups, aMELD scores above and below 35,
and the magnitude of the impact is larger for the targeted recipients, aM ELD ≥ 35.
However, in explaining the long-term posttransplant survival rates, the DRI measure
has some limits. Although the likelihood of survival after receiving transplants is af-
fected not only by donor characteristics but also by the status of recipients at the time
of transplantation, the DRI measure mainly focuses on donor characteristics. Further-
more, coeﬃcients for DRI factors were derived using the transplant recipient sample
who received transplants before the usage of aMELD scores (1998-2002), which has
been the most important factor in the current liver allocation rule since 2002.

As an alternative liver quality measure, I propose a new match quality measure
that predicts long-term posttransplant survival rates, i.e., 5 years, using the infor-
mation of both donor and recipient characteristics. In the SRTR dataset, there are
approximately 100 available predictors, and the number of variables increases to sev-
eral thousand when I include interactions between predictors. Among these predictors,
some variables may not aﬀect posttransplant survival rates signiﬁcantly, and adding
too many variables in the prediction model could result in overﬁtting. To reduce the

9DRI = exp[(0.154 if 40≤age<50) + (0.274 if 50≤age<60) + (0.424 if 60≤age<70) + (0.176 if race =
African American) + (0.126 if race = other) + (0.066((170 - height)/10) + (0.079 if Cause of Death (COD) =
Anoxia) + (0.145 if COD = Cerebrovascular accident) + (0.184 if COD = other) + (0.411 if Donation after
Cardiac Death) + (0.422 if partial) + (0.010×Cold Ischemia Time) + (0.105 if Regionally shared liver) +
(0.244 if Nationally shared liver)]

10To avoid confusion in interpreting the sign of coeﬃcients with other survival outcomes in the table, I use

the negative sign on the log value of DRI outcome.

20

n(cid:88)

ˆβ = argmin

k(cid:88)

dimension of the prediction model, I use an ML algorithm, LASSO, which chooses the
variables with the highest predictive power for posttransplant survival rates by adding
a penalization term λ to the OLS objective function (Belloni et al. 2014).

(yi − x(cid:48)

iβ)2 + λ

| βj |

(7)

i=1

j=1

To incorporate the eﬀect of aMELD scores on posttransplant survival rates, the
sample used for variable selection is restricted to transplant recipients waitlisted after
February 2002. Recipients whose maximal time period, i.e., the diﬀerence between the
date of transplant surgery and the end of data collection in June 2017, is less than 5
years are excluded for precise estimation. The LASSO algorithm selects 40 variables,
and the prediction results using these variables show the highest predictive power. (see
for details about how variables are selected using LASSO algorithms and prediction
performances are compared).

The DD estimates of predicted posttransplant survival rates for diﬀerent analy-
sis durations are shown in Columns (3)-(5) of Table A.5. The probability of survival
after receiving transplants is calculated using the coeﬃcients obtained by taking a logit
estimation with LASSO-selected variables. On average, as analysis duration increases
from 1 year to 5 years, posttransplant survival rates decrease for both transplant recip-
ient groups. Although average 1-year posttransplant survival rates in Column (3) are
similar to those in Column (1), DD estimates for transplant recipients with aMELD
scores above 35 are diﬀerent in sign. In Column (3), predicted 1-year posttransplant
survival rates decrease by approximately 0.8 percentage points after the policy imple-
mentation. Although the sign is diﬀerent, both results in Column (1) and (3) suggest
that the negative impact on posttransplant survival rates of transplant recipients with
aMELD scores below 35 is bigger in magnitude than that of transplant recipients with
aMELD scores above 35. This ﬁnding is consistent with DD estimates for the 3- and
5-year predicted posttransplant survival rates in Columns (4) and (5). For all analysis
durations, transplant recipients with aMELD scores below 35 are around 1 percentage
point less likely to survive after receiving transplants, and all results are statistically
signiﬁcant.

21

When we consider the Share 35 policy structure, negative impacts of the Share
35 policy on transplanted liver quality and posttransplant survival rates for transplant
recipients with aMELD scores above 35 could be intuitive. However, explaining neg-
ative and even larger impacts on those outcomes for recipients with aMELD scores
below 35 could be diﬃcult. To further elucidate the mechanism, I hypothesize that
transplant candidates with a higher chance of receiving liver oﬀers become more se-
lective of liver oﬀers, which could transfer some loss in donor liver quality to other
transplant recipients. To examine this hypothesis, I analyze the impact of the Share
35 policy on the liver oﬀer-acceptance pattern in Section 1.7.

1.7 Eﬀect on Liver Oﬀer-Acceptance Behavior

1.7.1 The Liver Search Model

I develop a simple liver search model with an exogenous quality of donated livers
in continuous time following the search model proposed by Rogerson et al. (2005).
Consider an economy with individuals who are risk-neutral, live inﬁnitely long, and
discount the future at rate r. Without receiving a transplant, liver candidates face a
high mortality risk. With probability δ, liver candidates die while waiting for a liver
oﬀer. Surviving candidates receive donated liver oﬀers at rate λ, and the quality of the
liver, q, is randomly drawn from a known distribution function F (q). If a liver oﬀer
is accepted, the candidate receives a utility w until he/she experiences a transplanted
liver failure. The likelihood of liver failure is a decreasing function of transplanted liver
quality, p(q), with p(cid:48)(q) < 0. When not receiving a transplant, the candidate receives
a utility b smaller than w. Thus, Bellman equations in discrete time can be deﬁned as

VT (q) = w +

1

{1 − p(q)}VT (q)

1 + r
(1 − δ)[λ

1

VU = b +

1 + r

(cid:90) ∞

0

max{VU , VT (q)}dF (q) + (1 − λ)VU ]

(8)

(9)

where VT (q) is the payoﬀ from receiving a donated liver with quality q. VU is the payoﬀ
from searching for a deceased donor liver: earning base payoﬀ, b, and waiting for the
next liver oﬀer. When I allow the length of the time period to be (cid:52) and (cid:52) → 0, I can

22

generalize the above two Bellman equations in continuous time.

{r + p(q)}VT (q) = w

(r + δ)VU = b + λ

(cid:90) ∞

max{0, VT (q) − VU}dF (q)

(10)

(11)

0

If VT (q) is strictly increasing, there is a unique reservation liver quality qR that makes
VT (qR) = VU. A liver candidate rejects a liver when q < qR and accepts it when q ≥ qR.
Solving equation (10) for VT (q) and substituting in equation (11) yields the reservation
liver quality equation

p(qR) = [

b

(r + δ)w

+

(cid:90) ∞

λ

r + δ

qR

{

1

r + p(q)

−

1

r + p(qR)

}dF (q)]−1 − r.

(12)

In this model, an increase in the rate of a liver oﬀer, λ, yields a higher reservation
liver quality, qR, which makes a liver candidate more selective. The Share 35 policy
increases the chance of receiving liver oﬀers for transplant candidates with aMELD
scores greater than or equal to 35 by providing them with the regional priority. Based
on the above liver search model, we can expect that transplant candidates treated by
the Share 35 policy would become more selective, and show lower oﬀer-acceptance rates
given the quality of liver oﬀers.

1.7.2 Results

As not all livers are accepted at the ﬁrst oﬀer, some transplant candidates have multiple
liver oﬀer histories and a diﬀerent aMELD score for each oﬀer. I treat each liver oﬀer
of a transplant candidate as a distinct observation to consider the incentive changes
resulting from a diﬀerent aMELD score. As a candidate’s oﬀer-acceptance decisions
could be related to each other, standard errors clustered at the individual level are
reported. I limit the analysis sample to transplant candidates who received at least
one liver oﬀer while waiting since liver oﬀer-acceptance outcome is only avaiilable when
transplant candidates receive liver oﬀers. Additionally, I limit the sample to liver
candidates ranked in the top 5 positions for each liver oﬀer (Goldberg et al. 2017).

23

Candidates ranked in a very low position could refuse liver oﬀers due to their ranks
rather than the quality of oﬀered livers. Refusals from other candidates with higher
rank may present a bad signal about the condition of the oﬀered liver and yield lower
acceptance regardless of the quality of livers.

First, I examine whether transplant candidates with aMELD scores greater than
or equal to 35 are more likely to receive liver oﬀers after the Share 35 policy imple-
mentation. Identifying the causal eﬀect of the policy on the access to liver oﬀers is
diﬃcult because the change in oﬀer-acceptance rates after the policy implementation
also aﬀects the access to the liver oﬀer. When a liver becomes available, a transplant
candidate ranked in second position can receive a liver oﬀer only if the top-ranked can-
didate declines the oﬀer. If transplant candidates become more selective and decline
liver oﬀers more due to an increased access to liver oﬀers, access to liver oﬀers for
transplant candidates ranked in a lower position would also increase. Thus, an overall
increase in the access to liver oﬀers in the analysis sample, which includes transplant
candidates ranked in the top 5 positions, may overestimate the causal eﬀect of the Share
35 policy. Although restrictive, we can avoid the eﬀect of change in oﬀer-acceptance
rates and guess the change in access to liver oﬀers by focusing on the ﬁrst liver oﬀers
matched to top-ranked transplant candidates. Figure A.5 shows the frequency of ﬁrst
liver oﬀers for each aMELD score at the time of liver oﬀers, and I ﬁnd that the Share
35 policy increases liver oﬀers for transplant candidates with aMELD scores above 35
and reduces oﬀers for those with aMELD scores below 35.

Table A.6 presents the DD estimates for the impact of the Share 35 policy on the
likelihood of liver oﬀer acceptance. The eligibility for the Share 35 policy is identiﬁed
based on the aMELD scores at the time of liver oﬀers, and transplant candidates
assigned Status 1A condition at the time of liver oﬀers are used as a control group
for each aMELD score group, aM ELD ≥ 35 and aM ELD < 35. All columns are
estimated with a full set of covariates, namely, donor and candidate characteristics,
waitlisted transplant center ﬁxed eﬀects, and year of liver oﬀer ﬁxed eﬀects. Column
(1) shows the DD estimates without donor characteristics. Transplant candidates with
aMELD scores greater than or equal to 35 are 12.4 percentage points less likely to accept
liver oﬀers after the Share 35 policy implementation. The estimate is an approximately

24

22 percent decrease in the oﬀer-acceptance rate given that the average acceptance rate
of candidates with aMELD scores above 35 before the Share 35 policy implementation
was 56 percent. However, the result in Column (1) may not show the causal eﬀect
of an increased chance of receiving a liver oﬀer (λ in equation (12)) under the Share
35 policy on a liver candidate’s oﬀer-acceptance behavior (qR). If the Share 35 policy
changes not only the likelihood of receiving a liver oﬀer but also the quality of the oﬀer
(F (q)) for the treated candidates, the result in Column (1) could reﬂect the impact
of both changes. In particular, the change in liver quality could be negative, as the
Share 35 policy yields more regional liver sharing and longer transportation times. In
this case, the results could overestimate the eﬀect of the change in λ, as transplant
candidates with lower quality liver oﬀers would be more likely to refuse them. To
isolate the eﬀect of an increased chance of receiving a liver oﬀer, I controll for donor
characteristics, and the results are presented in Column (2). The oﬀer-acceptance rates
for transplant candidates with aMELD scores above 35 decrease by 10.2 percentage
points after the Share 35 policy implementation. As expected, the magnitude of the
estimates in Column (2) is smaller than that in Column (1).

As shown in Figure A.5, the Share 35 policy reduces access to liver oﬀers for
transplant candidates with aMELD scores below 35. Thus, we can expect that those
candidates would be more likely to accept liver oﬀers after the Share 35 policy imple-
mentation. However, although statistically insigniﬁcant, DD estimates in Columns (1)
and (2) for transplant candidates with aMELD scores below 35 are negative in sign,
which implies more declines of liver oﬀers. The results that diﬀered from expected
results could be explained by the forward-looking behavior of transplant candidates.
As transplant candidates update their aMELD scores regularly, some candidates with
aMELD scores just below 35 could expect that they will be eligible for the Share 35
policy in the next aMELD score update and decline liver oﬀers based on expectations
rather than current aMELD scores. Because each candidate’s expectation of aMELD
score is unobserved, I use various aMELD score update frequencies across transplant
candidates as a proxy. A transplant candidate’s aMELD score update frequency is
regulated by OPTN’s rule. Transplant candidates with aMELD scores ranging from 15
to 18 are updated every 3 months, and those with aMELD scores ranging from 19 to 24

25

are updated every month. If a transplant candidate has an aMELD score greater than
25, his/her aMELD score should be updated every week. As transplant candidates
with aMELD scores close to the aMELD score 35 cutoﬀ update their aMELD scores
more frequently, we can expect that those candidates could be more forward looking
and become more selective of liver oﬀers. Columns (3) - (5) show the estimates for dif-
ferent subgroups based on the aMELD scores at the time of liver oﬀer. In Column (3),
transplant candidates whose aMELD scores ranging from 25 to 34 are 3.8 percentage
points less likely to accept liver oﬀers, representing a statistically signiﬁcant diﬀerence.
As aMELD scores are farther from the aMELD score 35 cutoﬀ, DD estimates imply
that transplant candidates are less likely to become selective of liver oﬀers after the
Share 35 policy implementation. As shown in Column (5), transplant candidates with
aMELD scores ranging from 15 to 18 are around 0.8 percentage points more likely to
accept liver oﬀers. As a result, the negative estimates, that we observed in Columns (1)
and (2) could be a result of transplant candidates who become selective of liver oﬀers
due to their forward-looking behaviors although their aMELD scores are less than 35.

1.8 Robustness and Speciﬁcation Check

1.8.1 Placebo Tests

In the analysis of access to liver transplants and patient mortality (Section 1.5), I
assume that the observed discontinuities in the outcomes are caused by the Share 35
policy.
If similar discontinuities exist at the aMELD score 35 threshold in the pre-
Share 35 periods, it would be diﬃcult to argue that the RD estimates are caused
by the policy. To address this concern, I repeat the RD estimation using transplant
candidates waitlisted before the Share 35 policy implementation. I deﬁne the pre-Share
35 sample as candidates whose registration was completed between January 2011 and
June 201311.

The placebo test results for the access to liver transplants within 90 days from
the waitlist registration are shown in Column (1) of Table A.7. Unlike the positive

11If I only deﬁne the Pre-Share 35 sample with the date of registration, there could be an overlap of
candidates between Pre- and Post-Share35 periods, as I am interested in the transplant outcomes within the
analysis period (90 days from registration). To avoid this overlap, I exclud candidates whose 90th day from
registration exceed June 18, 2013.

26

and statistically signiﬁcant results in the post-Share 35 period, transplant candidates
with aMELD scores greater than or equal to 35 are 8.4 percentage points less likely to
receive liver transplants within 90 days compared with candidates with aMELD scores
below 35. The results for waitlist mortality rates and overall mortality rates are shown
in Columns (2)-(4) and Columns (5)-(6), respectively. For both outcomes, although
the magnitude of RD estimates for 90-day and 180-day outcomes is large, they have
opposite signs to those of the results in the post-Share 35 period, with statistically
signiﬁcant diﬀerences. However, RD estimates for 1-year waitlist mortality rates are
relatively small in magnitude. The above results with the opposite sign suggest that
the signiﬁcant eﬀect on access to liver transplants and waitlist mortality rates found
in the post-Share 35 period could be caused by the Share 35 policy implementation.

1.8.2 Sensitivity to Bandwidth and Polynomials

As a speciﬁcation check, I examine whether the RD estimates in Table A.2 are sen-
sitive to bandwidths and the degree of the polynomials. Figure A.6 and A.7 present
the RD estimates and point-wise 95 percent conﬁdence intervals for the estimated co-
eﬃcients based on all bandwidths from 1 to 4 in 0.25 aMELD score increments. The
vertical red line in each ﬁgure shows the data-driven optimal bandwidths (Calonico
et al. 2017). Additionally, I compare the local linear estimates with estimates using
quadratic polynomials. In all ﬁgures, the distance between the upper and lower bounds
decreases as the bandwidth increases, which indicates an increase in precision due to
an increase in sample size. Panels (a) and (b) in Figure A.6 present the results of the
likelihood of receiving a liver transplant within 90 days from the waitlist registration.
They show that the RD estimates are robust to the bandwidth selection and the degree
of the polynomials. The results of the waitlist mortality rates are shown in panels (c)
- (h), and those of the overall mortality rates are shown in panels (a) - (f) in Figure
A.7. Overall, the ﬁgures suggest that the RD estimates for mortality outcomes are not
sensitive to the bandwidth choices and the degree of polynomials.

27

1.8.3 The Assumption of a Common Trend

For the causal interpretation of the estimates driven from a DD estimation strategy, a
parallel pre-trend assumption is needed. Under the assumption, the change in outcomes
of transplant candidates with aMELD scores above 35 or below 35 would have been
the same as that of Status 1A transplant candidates in the absence of the Share 35
policy. I use an event study approach to assess whether the DD estimates in this paper
correspond to this the assumption. For the event study analysis, I add interaction
terms of a treatment dummy variable and the series of a time dummy variable using
the year prior to the time of Share 35 policy implementation in the DD equation. If
the assumption holds, I would expect insigniﬁcant coeﬃcients for interactions terms
before the Share 35 policy implementation.

Figure A.8 displays the estimates from the event study model for access to liver
transplants and mortality rates for transplant candidates with aMELD scores greater
than or equal to 35. Most ﬁgures support the parallel pretrend assumption, but I ﬁnd
a positive and statistically signiﬁcant results for the 90-day overall mortality rates,
panel (e), at the 10 percent signiﬁcance level. Figure A.9 shows the estimates for the
same outcomes for transplant candidates with aMELD scores below 35. 90- and 180-
day overall mortality outcomes show positive and statistically signiﬁcant pretrends at
the 5 percent signﬁcance level. The results suggest that we need to be cautious in
interpreting the causality of the impact on the overall mortality rates based on the DD
estimates.

Figures A.10 and A.11 show the event study results of posttransplant outcomes
for transplant recipients with aMELD scores above 35 and below 35, respectively.
Regarding the outcomes of transplant recipients with aMELD scores greater than or
equal to 35, I do not ﬁnd any evidence of a violation in the parallel pretrend assump-
tion. However, in Figure A.11 for transplant recipients with aMELD scores below 35,
there are three outcomes that have statistically signiﬁcant estimates at the 10 percent
signiﬁcance level: the likelihood of receiving regionally shared livers (panel (a)), the
likelihood of receiving livers from donors whose BMI is over 35 (panel (e)), and the
negative log value of DRI (panel (h)).

28

Finally, the event study results for liver oﬀer-acceptance rates for transplant
candidates with aMELD scores above and below 35 are shown in Figures A.12 and A.13.
None of the ﬁgures show statistically signiﬁcant estimates before the implementation of
the Share 35 policy, which supports the parallel trend assumption of the DD estimates.

1.9 Conclusion

As the price mechanism, which allocates scarce resources based on willingness to pay,
does not exist in the liver transplant market, every donated liver is distributed by the
allocation rule of the OPTN. Following the Final Rule (2000)12, the current liver allo-
cation rule prioritizes medically urgent candidates while trying to maintain the quality
of donated livers. To improve access to liver transplants for transplant candidates
who have similar mortality risk to Status 1A transplant candidates, in June 2013, the
OPTN implemented the Share 35 policy. Under the policy, transplant candidates with
aMELD scores above 35 are prioritized for livers donated in their regions over local
candidates with aMELD scores below 35 registered in the same DSA as the donor
hospital.

This paper studies the impact of the Share 35 policy on transplant outcomes
and transplant candidates’ liver oﬀer acceptances. Using the variation in the eligibil-
ity for the policy at the aMELD score 35 threshold, I found that waitlist mortality
rates decrease signiﬁcantly when the access to liver transplants increases, although the
signiﬁcance of the impact on the overall mortality rates is not clear in the RD re-
sults. Additionally, I found that the Share 35 policy could result in several unintended
impacts on posttransplant outcomes and oﬀer-acceptance incentives of transplant can-
didates. The policy could worsen liver quality by increasing transportation time, but
some amount of the quality loss is transferred to untargeted recipients with aMELD
scores below 35. DD estimates suggest that the negative impact on posttransplant
survival rates is larger for untargeted recipients with aMELD scores below 35 than tar-
geted recipients. To explain the compensation for the transplanted liver quality loss for
the targeted recipients, I propose a mechanism in which the Share 35 policy aﬀects the

12https://optn.transplant.hrsa.gov/governance/about-the-optn/ﬁnal-rule/,

web, last accessed on June 23, 2019.

information accessed on the

29

liver oﬀer-acceptance behavior of transplant candidates. With a proposed liver search
model, I found that transplant candidates with MELD scores above 35 become more
selective of liver oﬀers when the likelihood of receiving a liver oﬀer increases under the
Share 35 policy and choose livers of better quality.

Currently, the OPTN is preparing a new liver allocation system that allocates
donated livers based on the distance from the donor hospitals regardless of previous ge-
ographic boundaries, DSA and Region13. Although the areas of distribution according
the new allocation rule will change dramatically from those in the Share 35 policy, the
liver-sharing model used to prioritize targeted candidates in the Share 35 policy still re-
mains. For example, under the new allocation rule, transplant candidates with MELD
scores of 37 or greater registered at transplant centers within 250 nautical miles (nm) of
the donor hospital are prioritized under the new allocation rule over those with MELD
scores below 37 registered at transplant centers within 150 nm14. Although there are
active discussions about the new allocation system, the topic is mainly focused on how
many donated livers each DSA or region will lose or gain. As shown above, changes
in areas where donated livers will be shared will also cause changes in donated liver
quality and strategic oﬀer-acceptance behavior of transplant candidates. Therefore,
the results found in this study could also be meaningful for evaluating the possible
impact of the new allocation rule before its implementation.

13https://unos.org/policy/liver-distribution/, information access on the web, last accessed on June 23,

2019.

14This allocation rule is applied for livers from non-DCD donors younger than 70. Livers from DCD donors
older than 70 are allocated to candidates with MELD scores of at least 15, ﬁrst within 150 nm, then within
250 nm, then within 500 nm (https://unos.org/policy/liver-distribution/, information accessed on the web,
last accessed on June 23, 2019).

30

Chapter 2

The Role of Kidney Allocation Policy in Addressing Kidney

Shortages

2.1

Introduction

Kidney transplant is a treatment that prolongs the lives of patients with kidney failure.
Although many patients with kidney failure are eager to receive kidney transplants,
a large and rapidly increasing excess demand exists because the transplantable kid-
ney supply depends only on altruistic deceased and living donations according to the
National Organ Transplant Act (NOTA, 1984), which bans the sale of organs.15 Fig-
ure B.1 shows the trends in the kidney transplant market from 1997 to 2016. The
number of candidates added to the waiting list for deceased donor kidneys is always
greater than the number of candidates receiving kidney transplants, which results in a
dramatic increase in the number of candidates remaining on the waiting list each year.
As there is no market that distributes scarce organs using the price mechanism,
Organ Procurement and Transplantation Network (OPTN) manages the organ dona-
tion and allocation process. According to their strategic plan16, OPTN aims to achieve
“equitable allocation” while also improving transplantation quantity and patient out-
comes, speciﬁcally mortality. The current kidney allocation system emphasizes equity
by placing a high priority on individual waiting time for transplantation. Because al-
location based on waiting time does not guarantee the best use of donated kidneys,
OPTN has supplemented the allocation system by prioritizing certain types of candi-
dates to improve patient outcomes.17

15NOTA (1984) bans the sale of human organs. It states that it is “unlawful for any person to knowingly
acquire, receive, or otherwise transfer any human organ for valuable consideration for use in human trans-
plantation”. Because allocation based on candidates’ willingness to pay is not applicable, the government is
obliged to allocate donated kidneys on behalf of the market. In the United States, the Organ Procurement
and Transplantation Network (OPTN), established by NOTA, manages donated kidney allocations.
information access on the web,

16https://optn.transplant.hrsa.gov/governance/strategic-plan/,

last ac-

cessed on March 27, 2019.

17For example, pediatric candidates younger than 18 years of age, whose expected post-transplant survivals
are longer than those of adult candidates have received priority for young deceased donor kidneys since 2005.
In 2014, OPTN started to include the pre-waitlist registration dialysis time in a transplant candidate’s waiting
time as the duration of dialysis is highly related to patient survival.

31

However, to date, the role of the allocation system in increasing transplant quan-
tity has received relatively little consideration. Instead, OPTN has focused on increas-
ing the supply of organ donors. Representative examples of this approach include
ﬁrst-person consent legislation (Levin 2014), the provision of ﬁnancial incentives for
living organ donors such as tax deductions, paid leave (Wellington et al. 2011) and
educational programs (Siminoﬀ et al. 2009). Although policies regarding organ supply
would be a direct method to increase the number of transplants, designing a kidney
allocation system helpful in achieving this goal might be still meaningful under the
current large kidney shortages.

In this paper, I ask whether prioritizing certain types of candidates in a kidney
allocation system can increase the number of kidney transplants while achieving an
improvement in patient mortality. To identify the types of candidates, this paper
focuses on the problem of candidates choosing a kidney source between deceased and
living donor kidneys. In the U.S., most living donors designate the recipients of their
kidneys, while most deceased donors do not designate recipients. Hence, deceased donor
kidneys can be matched to all waitlisted candidates based on the kidney allocation
policy, while living donor kidneys beneﬁt only the designated recipients. When the
chance of receiving a deceased donor kidney increases, some candidates may change
their preference from a living donor kidney to a deceased donor kidney (crowd-out) to
avoid using kidneys from a known person. However, the living donor kidney cannot
be used for other kidney candidates as it is only available for the designated recipient,
which limits an increase in the total number of transplants. Hence, if a kidney allocation
policy prioritizes candidates who are less likely to be on the margin between a deceased
and living donor transplant, then the number of total kidney transplants may increase
nearly one-for-one with an increase in the number of deceased donor kidneys.

I also examine the heterogeneous eﬀect of kidney transplantation on the mortal-
ity risk of candidates as a measure of patient outcomes.18 If candidates who are less
likely to be crowded out also experience small improvements in mortality in comparison

18In the OPTN strategic plan,

reducing waitlist mortality and increasing

survival

tient
the
(https://optn.transplant.hrsa.gov/governance/strategic-plan/goal-5/,
last accessed on March 27, 2019).

in achieving

key metrics

are

set

as

improvement

information access

graft
of patient

and pa-
outcomes
on the web,

32

to candidates who are more likely to be crowded out, then overall mortality outcomes
would be worsened when we prioritize the former candidates. Hence, an optimal allo-
cation policy would target kidney candidates who are less likely to be crowded out and
show relatively large mortality improvements in response to positive supply shocks of
deceased donor kidneys.

I use restricted-use data from the Scientiﬁc Registry of Transplant Recipients
(SRTR), which contains detailed information on the universe of kidney transplant can-
didates, donors, and transplants in the U.S. I focus on the variation in the likelihood
of receiving a deceased donor kidney across individuals resulting from a kidney allo-
cation policy - a sensitization point policy - that prioritizes candidates with a highly
sensitive immune system. As transplantation is a surgery that replaces a patient’s
damaged organ with another person’s organ, whether the recipient’s immune system
regards the transplanted organ as a target of removal is important for the success of the
surgery. The sensitivity of an individual’s immune system is measured by a calculated
panel reactive antibody (CPRA) value that ranges from 0 to 100. As it is diﬃcult to
ﬁnd compatible donor kidneys for highly sensitized candidates with high CPRA val-
ues, since 2009, OPTN has prioritized candidates with a CPRA value of 80 or greater
by assigning them additional kidney allocation points, which increases their rank on
the transplant waitlist. Using the plausibly exogenous variation around the CPRA 80
threshold, I compare candidates with CPRA values above and below the sensitization
point policy cutoﬀ using a fuzzy regression discontinuity (RD) design.

First, I ﬁnd that an increase in access to deceased donor kidneys signiﬁcantly
reduces a candidate’s likelihood of receiving a kidney from a living donor. My central
estimates show that a 10 percentage-point increase in the probability of receiving a
deceased donor kidney decreases the likelihood of opting for a living donor kidney by
approximately 1.7-1.9 percentage points. This result is similar to those of Fernandez
et al. (2013), Howard (2011), and Sweeney (2010), who focus on identifying the trade-
oﬀs between kidney sources.19 To address the endogeneity of the kidney source choice

19Fernandez et al. (2013) show that one additional cadaveric kidney donation reduces living kidney donation
by 0.2 to 0.5 units. Howard (2011) ﬁnd that a decrease of ﬁve cadaveric kidney donations is correlated with
an increase of one living kidney donation. Sweeney (2010) show that a 10 percentage-point increase in the
likelihood of receiving a deceased donor kidney reduces the probability of receiving a living donor kidney by
2-3 percentage points.

33

problem, Fernandez et al. (2013) and Howard (2011) use geographic variation, i.e.,
traﬃc safety laws and kidney transplantation wait time, respectively. Regarding the
identiﬁcation strategy, my paper is closely related to that of Sweeney (2010), who
examines the trade-oﬀs between kidney sources with RD estimation by exploiting the
variation caused by a traditional sensitization point policy in a sample obtained between
1997 and 2006. The prior research, however, focuses only on identifying the existence
of overall trade-oﬀs between kidney sources and provides little understanding of the
heterogeneity across candidate subgroups and the eﬀect on mortality risks.

Second, I derive the causal eﬀect of the additional chance of receiving a deceased
donor kidney in reducing mortality risks. I ﬁnd that the probability of death before
receiving a kidney transplant - known hereafter as “waitlist mortality” - within 2 years
decreases by 2.8 percentage points when kidney candidates receive the sensitization
point beneﬁts. This is a substantial eﬀect, implying a 43 percent decrease compared
to the baseline mortality rate of 6.5 percent. Although OPTN focuses on waitlist
mortality, presumably a more important issue for patients is the overall mortality rate,
i.e., unconditional on whether they receive a kidney transplant. This eﬀect can be
captured when we assess both the waitlist mortality and deaths after receiving a kidney
transplant within the same period. I ﬁnd evidence that the sensitization point beneﬁt is
also eﬀective in reducing overall mortality. The overall mortality rate within 2 years20
decreases by 2.53 percentage points when kidney candidates receive sensitization point
beneﬁts, which implies a 34 percent decrease compared to the average mortality rate
of 7.4 percent.

Finally, I examine whether the RD estimates on trade-oﬀs between kidney sources
and mortality rates diﬀer across candidates with diﬀerent demographics. Kidney can-
didates with blood type O, who are African-American, and who are currently receiving
dialysis treatment are relatively unlikely to switch kidney sources from living donor
kidneys to deceased donor kidneys when access to a deceased donor kidney increases.
Also, these candidates groups show relatively large reductions in waitlist and overall
mortality rates when access to deceased donor kidneys increases. These heterogeneous
results imply that prioritizing these candidates in deceased donor kidney allocation
20Though insigniﬁcant, the eﬀect on the overall mortality rate within 1 year (0.7 percentage points) is also

sizable and implies a reduction of 26 percent compared to the baseline mortality rate.

34

would result in a larger number of kidney transplants while improving candidate mor-
tality rates.

This paper proceeds as follows. The following section provides background in-
formation on the U.S. kidney transplant system and the sensitization point policy.
Section 2.3 describes the data sources, while Section 2.4 explains the main identiﬁca-
tion strategy. Section 2.5 shows the estimation results, Section 2.6 tests the robustness
of the results, and Section 2.7 concludes.

2.2

Institutional Details

2.2.1 Treatments for Patients with Kidney Failure

Kidneys remove waste from the blood and control the body’s ﬂuid balance. Kidney
damage and improper function (kidney failure21) increase the risk of the accumulation
of blood wastes in the body, which results in death without treatment. There are two
types of treatment, namely, dialysis and kidney transplantation, that enable patients
with kidney failure to live prolonged lives. Dialysis treatment ﬁlters patients’ blood
using artiﬁcial tools that substitute for the function of their own kidneys.22 Although
it is a relatively low-risk treatment, patients need to receive dialysis at least three times
a week permanently, and each treatment takes a long period of time (approximately
four hours), which limits patients’ quality of life. As the duration of dialysis treatment
increases, the risks of infection (Ronco et al. 2006) and mortality (USRDS 2018) also
increase.

The other treatment is kidney transplantation. As the transplanted kidney per-
forms the work of the patient’s failed kidney, no other treatment for kidney failure is
needed except for the permanent use of immunosuppressants, which reduce the risk of
rejection of the transplanted kidney by suppressing the transplant recipient’s immune
system. There are two sources of transplantable kidneys, living donors and deceased
donors. In living kidney donations, donors give one of their two kidneys while they

21The status that less than 15 percent of the kidney is working.

(National Institute of Diabetes and

Digestive and Kidney Diseases, NIDDK)

22NIDDK categorizes dialysis into two groups, hemodialysis and peritoneal dialysis, based on the dialysis
process (https://www.niddk.nih.gov/health-information/kidney-disease/kidney-failure, information access on
the web, last accessed on March 27, 2019).

35

are alive. By contrast, deceased kidney donation is the process of kidney donation at
the time of the donor’s death. These two kidney donation types also diﬀer in terms
of the donor’s relationship with the recipient. In most cases, living donors designate
the candidates who will receive their kidneys and have a close relationship with the
recipients, such as parents, spouses, children, and friends. However, most deceased
kidney donors do not designate the recipients of their kidneys.23 All of the donated
kidneys for which recipients are not designated are allocated to patients on the waitlist
for deceased donor kidneys using OPTN’s allocation rules. Hence, the eﬀect of the
allocation rules is highly related to deceased donor kidney transplants.

2.2.2 A Candidate’s Choice between the Two Kidney Sources

In this section, I establish a simple conceptual framework that illustrates that a candi-
date’s kidney choice depends on the transplant beneﬁts and costs of receiving a living
donor kidney transplant. Let us assume that a candidate has a potential living donor
willing to donate a kidney when it is needed. The kidney candidate chooses whether
he will continue waiting for a deceased donor kidney oﬀer on the waitlist or receive
a living donor kidney. The net beneﬁts of choosing a living donor kidney instead of
waiting for a deceased donor kidney are twofold. First, there is little or no wait time
for a living kidney transplant. As time on the waitlist increases, a candidate’s quality
of life worsens, and the candidate’s preference for a living donor kidney with little
wait time could increase (Howard 2011; Segev et al. 2007). Moreover, previous studies
have shown that the survival outcomes of living donor kidney recipients are better
than those of deceased donor kidney recipients, which implies a higher quality of trans-
planted kidneys (Roodnat et al. 2003; Weitz et al. 2006). This quality diﬀerence does
not depend on the candidate’s wait time. Hence, the overall net beneﬁts of receiving a
living donor kidney transplant increase over the candidate’s wait time.

The cost of waiting for a deceased donor kidney includes the expenses of the
dialysis treatments. While waiting for a deceased donor kidney, dialysis treatment is

23Directed deceased donation is legally authorized by the Uniform Anatomical Gift Act (UAGA) and by
most states anatomical gift laws. The exact number of directed deceased donations is not available in the SRTR
dataset. However, according to OPTN, approximately 100 of the more than 100,000 transplants each year
are directed donations (https://optn.transplant.hrsa.gov/news/optn-information-regarding-deceased-directed-
donation/, information access on the web, last accessed on March 27, 2019).

36

an inevitable procedure to prolong the candidate’s life. However, when the candidate
decides to receive a living donor kidney at a certain time (t), he needs to receive dial-
ysis treatments until that time. Hence, there is no diﬀerence in dialysis treatment
costs between the two options. Moreover, living donor kidney recipients face “emo-
tional costs” for potential living donors. In contrast to deceased donors, who donate
their kidneys after their death, living donors need to undergo a surgery to extract a
kidney while they are alive. Although the medical costs are covered by the recipient’s
health insurance, coverage of lost wages and transportation and lodging costs is not
guaranteed. Additionally, as the expected health risks for kidney donors are uncertain
(Young et al. 2008; Mjøen et al. 2014; Muzaale et al. 2014) , a candidate would be
concerned about a closely related living donor’s future health status. If the candidate
decides to use a living donor kidney, then emotional costs will always exist, and the
amount would be constant over the wait time.

Panel (a) of Figure B.2 shows how the net costs and beneﬁts determine the
candidate’s kidney source choice. The quality beneﬁt and emotional costs of using a
living donor kidney are represented as α and β, respectively. The candidate’s preference
for a living donor kidney transplant relative to waiting for a deceased donor kidney
oﬀer increases over the wait time, and he decides to use a living donor kidney at t∗,
when the net beneﬁts equal the costs. It is uncertain when a kidney candidate receives
an acceptable deceased donor kidney oﬀer, and we assume a bell-shaped deceased
donor kidney oﬀer density over the wait time. A candidate who receives an acceptable
deceased donor kidney oﬀer before t∗ receives a deceased donor kidney transplant (A),
but another candidate who does not receive an oﬀer until t∗, switches to a living donor
kidney (B). Unlike panel (a), if a candidate’s emotional cost (β) is smaller than the
quality beneﬁt of using a living donor kidney (α) at the initial point (t = 0), then he
will receive a living donor kidney without registering on the waitlist.

Not all kidney candidates have potential living donors when they are waitlisted
for deceased donor kidneys as we assumed in the framework. Although I relax this
assumption and allow kidney candidates to ﬁnd their potential living donors while
waiting for deceased donor kidneys, these candidates’ kidney source choice problem
still can be explained (panel (b)). Until they ﬁnd potential living donors, their only

37

option is waiting for a deceased donor kidney. Hence, the framework can be modiﬁed
as the initial time (t = 0) of the kidney source choice changes to the time when kidney
candidates ﬁnd their potential living donors (t = t0).
In that case, the cutoﬀ time
when candidates switch kidney sources will increase (t∗ ⇒ t∗∗).

With this framework, we can explain why increased access to a deceased donor
kidney crowds out the choice of living donor kidneys. An allocation policy that prior-
itizes certain groups of waitlisted candidates increases their rank on the waitlist and
the probability of receiving a deceased donor kidney oﬀer earlier. Then, the density of
receiving a deceased donor kidney oﬀer moves left as shown in panel (c). Some candi-
dates who would choose living donor kidneys without the policy would receive deceased
donor kidney oﬀers before t∗ under the policy, which implies crowd-out of living donor
kidney choices. Hence, the amount of crowd-out depends on the net beneﬁt and cost
of choosing a living donor kidney instead of waiting for a deceased donor kidney oﬀer
and the availability of potential living donors, which are the key factors that determine
t∗.

2.2.3 Matching Donor Kidneys to Patients

Not all donated kidneys can be transplanted to candidates. Only kidneys donated
by compatible donors can be transplanted to the patient, and the compatibility is
determined by blood tests, blood type, tissue type, and cross-matching. First, the
blood type should be compatible. There are 4 basic blood types: A, B, O, and AB.
A patient with type A blood can receive a kidney from a donor with type A or O
blood. A patient with type B blood can receive a kidney from a donor with type B
or O blood. A patient with type AB blood can receive a kidney from a donor with
any blood type. On the other hand, a patient with type O blood can only receive a
kidney from a donor with the same blood type. Second, a donor should have similar
body tissue types as a patient. When a patient-donor pair shares many tissue types,
the transplanted kidney is more likely to adapt well in the recipient’s body. Third,
the antibodies of a patient should be less likely to attack a transplanted kidney. This
factor is important in minimizing the risk of rejection of the transplanted kidney and
medical tests check the sensitivity of a patient’s antibodies to a potential donor’s tissue

38

types.

When a living donor’s kidney is compatible with the characteristics of a des-
In the case of a deceased
ignated recipient, he or she receives the donated kidney.
donor kidney not designated to a certain recipient, OPTN ranks the kidney transplant
candidates for the kidney and allocates the kidney to the highest ranked and most
compatible candidate. OPTN allocates deceased donor kidneys based on geographical
proximity from the transplant center where the kidney is recovered and the kidney
points. The distance from the donor hospital is important because a longer period of
time between kidney discharge from the donor and transplant surgery might lead to
worse transplant results (Salahudeen et al. 2004). For allocation based on geographical
proximity, the United States is divided into 58 donor service areas (DSAs), and all
transplant centers belong to one of the DSAs. Additionally, there are 11 regions, and
each region consists of several DSAs. If a deceased donor kidney becomes available,
kidney transplant candidates registered in the DSA where the donor is located receive
higher priority. If the kidney is not compatible with any candidate waitlisted in the
DSA, candidates registered in the region where the donor DSA is included are matched
to the kidney. Lastly, a kidney that could not be accepted by candidates in the region
is matched to candidates registered in the U.S. The other factors that rank candidates
in each geographical category are the kidney points. The kidney points are determined
by each candidate’s age, waiting time, history of prior living donation, and value of
sensitization (OPTN 2017). Detailed points are presented in Table B.1. Candidates
who are younger, better matched, waitlisted longer, and more sensitized are more likely
to have higher kidney points.

2.2.4 Sensitization Points

Among the factors in the kidney points in Table B.1, this study focuses on the value
of sensitization. Although a kidney transplant is the ultimate treatment for patients
with kidney failure, not all transplants are successful because of infection caused by the
surgery or failure of the transplanted kidney, i.e., kidney rejection. Kidney rejection
occurs when the recipient’s immune system recognizes the transplanted kidney as an

39

invader and attacks the kidney.24 Rejection is more likely to happen for patients with
a high level of antibodies, i.e., sensitized candidates. Although the reason for sensitiza-
tion varies across candidates, OPTN describes representative cases, such as pregnancy,
previous transplants, previous blood transfusion, and viral/bacterial infections.25 Be-
cause it is diﬃcult to ﬁnd kidney donors compatible with sensitized candidates, waiting
times for these candidates are likely to be longer than those of candidates with low
sensitization. To compensate for this disadvantage, OPTN’s kidney allocation system
provides sensitized candidates with additional kidney points that increase their rank
on the waitlist and allow greater access to deceased donor kidneys.

Figure B.3 shows the history of the sensitization measure and sensitization point
policy changes. As of October 1, 2009, the panel reactive antibody (PRA), which ranges
from 0 to 100, was used to measure the sensitivity of candidates. This value was derived
by testing a patient’s blood against lymphocytes (white blood cells) obtained from a
panel of approximately 100 randomly chosen blood donors.26 If the test result shows 90
reactions, the likelihood of acute rejection is 90 percent when a donor in the 100 donor
pool is available. In the PRA era, candidates with a PRA score of 80 or greater received
an additional 4 kidney points. According to Table B.1, 4 kidney points can be achieved
when a candidate waits for 4 years on the kidney transplant waitlist, which implies a
large beneﬁt when we consider that the median wait time for kidney transplants is
approximately 4 years (USRDS 2018).

The CPRA value has been used as a new sensitization measure since October 1,
2009.27 Antibodies protect our body by attacking invaders from the outside (antigens).
The relationship between an antibody and an antigen is similar to that between a key
and a door lock. A certain type of antibody (a key) can only attack antigens with
matched tissue types (a door lock). If a candidate has various antibody types, then
many tissue types in a transplanted kidney would be matched with the candidate’s

24http://columbiasurgery.org/kidney-transplant/organ-rejection-after-renal-transplant, information access

on the web, last accessed on March 27, 2019.

25https://optn.transplant.hrsa.gov/resources/allocation-calculators/about-cpra/, information access on the

26https://optn.transplant.hrsa.gov/resources/allocation-calculators/about-cpra/, information access on the

27CPRA was introduced on December 5, 2007, but the original PRA was used in deceased donor kidney

web, last accessed on March 27, 2019.

web, last accessed on March 27, 2019.

allocation until 2009.

40

antibodies and the probability of rejection increases. By comparing a candidate’s
antigen types with the frequency of the tissue types of more than 12,000 previous
donors, each candidate’s CPRA value shows how diﬃcult it will be to ﬁnd donors whose
kidneys are less likely to be rejected. Similar to the PRA, this measure has a value
ranging from 0 to 100, but the meaning of the value is slightly diﬀerent. The probability
of ﬁnding a well-matched donor for the candidate when n donors are considered is
1 − (CP RA)n28 (Keith et al. 2016). Although the sensitization measure was changed
in 2009, candidates with a CPRA value of 80 or greater continued to receive an 4
additional kidney points. On December 3, 2014, the sensitization point policy changed
to a sliding scale as shown in Table B.2.

2.3 Data

This study used data from the Scientiﬁc Registry of Transplant Recipients (SRTR).
The SRTR data system includes data on all donor, wait-listed candidates, and trans-
plant recipients in the US, submitted by the members of the Organ Procurement and
Transplantation Network (OPTN). The Health Resources and Services Administration
(HRSA), U.S. Department of Health and Human Services provides oversight to the
activities of the OPTN and SRTR contractors. The data were extracted on June 2,
2017, and contain individual-level information, such as age, gender, race, blood type,
education level, and primary source of insurance. As all the transplant centers’ pre-
evaluation tests for waitlist registration include blood tests, the dataset includes the
initial CPRA values for all candidates placed on the waitlist. However, candidates who
receive living donor kidneys without being placed on waitlists do not have CPRA val-
ues in the dataset, and I exclude these candidates from the analysis. Each transplant
center has its own plan for registered candidates’ antibody screening, and candidates’
CPRAs are updated whenever transplant centers report the most recent unacceptable
tissue types using their antibody type information (OPTN 2017). Hence, the SRTR
dataset contains all CPRA values as a history of each candidate. However, the up-
dating term of CPRA varies among transplant centers, as there is no national rule of

28If CPRA is 90 percent, then the probability of ﬁnding a well-matched donor when the candidate is

matched to 100 donors is not 10 percent but rather 99.997 percent.

41

updating frequency by the OPTN.

To exploit the eﬀect of a sensitization point policy that provides 4 additional
kidney points to candidates with CPRA values of 80 or greater, I restrict the sample
to candidates registered from October 1, 2009 to December 3, 2014. As the dataset
was extracted on June 2, 2017, there is a gap between the end of the analysis period
and the end of the dataset. The health outcome status, such as transplant or death, of
some candidates registered during the analysis period might have changed during the
gap. If I treat these outcomes in the same way as the other outcomes that occurred
during the analysis period, the result would be biased, as these outcomes are aﬀected
by the new sliding scale sensitization point policy. Hence, this study does not include
health outcome changes that occurred after the end of the analysis period.

I exclude candidates who are registered on the waitlist for multiple organs and
who are less than 18 years old because they receive additional beneﬁts in the deceased
donor organ allocation.29 I include only ﬁrst-time transplant candidates because, all
else being equal, the choice between the two kidney sources is similar for candidates
without prior transplants as for the other candidates. Additionally, candidates with
prior living donor kidney transplants have a diﬀerent living donor pool compared to a
ﬁrst-time transplant as the donor cannot donate his kidney again.

After the above sample restrictions, there are 152,247 candidates who have ever
joined kidney transplant waitlists during the analysis period and more than 68 per-
cent of candidates have zero CPRA. When I estimate the ﬁtted line using RD, this
large number of candidates with zero CPRA may drive the estimation results too much.
Hence, I exclude the candidates with zero CPRA from the estimation sample. The ﬁnal
sample includes 49,055 kidney transplant candidates. Table B.3 shows the summary
statistics of the key variables of the sample. In the analysis period, 23 percent of can-
didates received kidney transplants and 2/3 of transplant recipients received deceased
donor kidneys. A total of 18 percent of candidates were removed from the waitlist
because of sickness or death before receiving kidney transplants, and the mortality

29Under the deceased donor kidney allocation rules by OPTN, candidates under 18 receive priority in the
following ways. (1) pediatric kidney allocation points (Table B.1) (2) match classiﬁcation priority for zero-
ABDR mismatches (3) match classiﬁcation priority for donated kidneys at the local, regional, and national
levels.

42

rate increases to 20 percent when I include deaths after receiving kidney transplants.
Columns (2) and (3) show the summary statistics of the CPRA subgroups. Unsur-
prisingly, compared to kidney transplant recipients with a CPRA less than 80 (column
(2)), transplant recipients with a CPRA value of 80 or greater (column (3)) are less
likely to receive living donor kidneys. This overall diﬀerence can be explained by two
mechanisms. First, according to the deﬁnition of CPRA, it becomes more diﬃcult to
ﬁnd compatible donors when a candidate’s CPRA increases, and ﬁnding compatible
living donors is much more diﬃcult than ﬁnding compatible deceased donors as the size
of the available living donor pool is smaller than that of deceased donors. Moreover,
due to the sensitization point beneﬁt, some candidates with a CPRA value of 80 or
greater would switch their kidney source to deceased donor kidneys from living donor
kidneys.

2.4 Estimation Strategy

To identify the causal eﬀect of an increase in access to a deceased donor kidney on
living donor kidney choice and mortality risk, I exploit the discontinuity at the CPRA
80 resulting from the sensitization point policy. I estimate the eﬀects using the fuzzy
RD approach using the CPRA as the running variable.30 The estimation equation is
shown below.

Yi = α + β0CP RA80i + f (Xi) + ui

(13)

where i denotes a kidney transplant candidate. Yi is the outcome of interest in
the study, the likelihood of receiving a deceased or a living donor kidney and mortality
rate. CP RA80i is a binary variable with a value of one if the CPRA of a candidate i is
80 or greater.31 Xi is a running variable that measures the diﬀerence in CPRA from the
threshold. β0 is the coeﬃcient of interest that shows the discontinuity of the outcomes
between the candidates just around the CPRA 80 threshold. As explained in Section

30D. S. Lee et al. (2010) showed that the treatment eﬀect in the fuzzy RD design can be interpreted as the

local average treatment eﬀect (LATE) in the instrumental variables setting.

31According to OPTN (2017), CPRA values are rounded to the nearest one-hundredth percent. Hence,
candidates with a CPRA of 79.995 or greater receive the sensitization points. I use the 79.995 threshold to
derive the diﬀerence from the threshold of the policy.

43

2.2, each candidate has many CPRA histories that have been measured since their
waitlist registration. Hence, the choice of a proper CPRA is important for a precise
analysis. In the CPRA era, the eligibility for the sensitization points is determined by
the most recent CPRA, and this study also used the most recent CPRA as the running
variable. The function f (Xi) represents the relationship between the running variable,
CPRA and the outcome variables. In this study, I use the parametric approach, which
uses the whole sample in the identiﬁcation with quadratic polynomials and interactions
(see Appendix E for details about how I chose the functional form).

The main identiﬁcation assumption of my RD design is that candidates do not
have precise control over the running variable, CPRA (lee2008regression; D. S. Lee
et al. 2010). When additional kidney points that increase the likelihood of receiving
a deceased donor kidney oﬀer are awarded to candidates with a CPRA value of 80
or greater, candidates placed just below the CPRA threshold have an incentive to
manipulate their CPRA to receive the beneﬁt. As explained in Section 2.2.4, the
CPRA value depends on the variety of unacceptable tissue types matched to and likely
to be attacked by each candidate’s various types of antibodies. However, I argue that
manipulating the running variable, CPRA, would be diﬃcult in my context. For CPRA
manipulation, candidates must be able to adjust their antibody types precisely rather
than adjusting the amount of antibodies, which would be diﬃcult to do. Moreover,
a slight adjustment of antibody types may result in a large change in unacceptable
tissue types for a candidate and for the CPRA value. Each antibody binds to a speciﬁc
portion of the tissue, an epitope, when it attacks a tissue. As some tissues share
epitopes across tissue types, an antibody can attack multiple types of tissues that
share epitopes (Keith et al. 2016). Hence, increasing antibody types precisely for the
sensitization point beneﬁt would be diﬃcult, and the beneﬁt could be oﬀset by a large
increase in the CPRA value, which would limit the probability of ﬁnding compatible
donors.

To examine evidence of CPRA manipulation, I plot the distribution of the CPRA
values in Figure B.4. Panel (a) presents the overall CPRA distribution with a 0.1-bin
width. There is a large cluster at the lowest level of CPRA values, although I exclude
candidates with a zero CPRA, which implies that most kidney candidates do not face

44

restriction in ﬁnding compatible donors. Kidney candidates are also clustered at the
highest CPRA values. Since an antibody can be matched to multiple tissue types be-
cause tissues share epitopes across types, most tissue types become unacceptable even
though a patient does not have all types of antibodies. However, no large cluster is
present around the CPRA 80 threshold, which would be evidence of CPRA manipula-
tion for sensitization point beneﬁts. To determine the existence of a cluster around the
threshold in detail, panel (b) shows the histogram within a narrower window (band-
width 3 from the threshold, 0.01 bin width). No large cluster is present at the CPRA 80
threshold, except for a cluster around CPRA 81. Additionally, Figure B.5 presents the
mean frequency test results in which each circle is the number of observations in each
bin, and the line is the predicted plot. The ﬁgure shows no signiﬁcant discontinuity of
observation frequencies at the CPRA 80 threshold.

To further test the validity of the RD design, I examine whether the observed
predetermined covariates are similar around the CPRA 80 threshold. As it is diﬃcult to
manipulate the CPRA precisely, predetermined characteristics of kidney candidates are
unlikely to be discontinuous around the threshold. Table B.4 shows the RD estimates
of the covariates. Among 18 covariates, there are only 2 characteristics, male and
high school education, that show signiﬁcant discontinuities at the threshold. With a
large number of characteristics, it is possible that a few are signiﬁcantly discontinuous,
although candidates located on either side of the threshold have a similar distribution.
However, it should be noted that the existence of signiﬁcant discontinuities can weaken
my RD estimation results. One noteworthy result is the RD estimate of gender. In the
analysis sample, there exists a highly negative correlation between the share of males
and the CPRA value, and this relationship can be explained by the occurrence of
pregnancy32 (Hönger et al. 2013; Hyun et al. 2012). Although pregnancy is eﬀective in
increasing the CPRA value, it is diﬃcult to believe that the signiﬁcant discontinuity in
gender covariates is evidence that female kidney candidates with a CPRA value below
the threshold become pregnant to achieve the sensitization point beneﬁt. As dialysis
treatment for patients with kidney failure changes the status of anemia and hormones,

32Approximately 30∼50 percent of women with three or more pregnancies have a high level of antigens,
which results in high CPRA (https://optn.transplant.hrsa.gov/resources/allocation-calculators/about-cpra/,
information access on the web, last accessed on March 27, 2019).

45

many women of childbearing age may experience irregular menstruation periods and
have unhealthy eggs33, and pregnancy among women on chronic dialysis accounts for
only 1-7 percent of dialysis patients (Sachdeva et al. 2017).

Additionally, I test whether the changes in the predetermined characteristics af-
fect the discontinuities of the outcomes at the CPRA 80 threshold. The discontinuous
eﬀect may call into question the causality of the identiﬁed results using the RD estima-
tion, because the eﬀect could be driven by changes in the predetermined characteristics.
For the test, I use the equation below.

Yi = α + β0Xi + β1X 2

i + γ(cid:48)Wi + ui

(14)

where i denotes a kidney transplant candidate. The equation is similar to the
identiﬁcation equation (13). To check the discontinuities of the outcomes driven by
the predetermined characteristics, I exclude the binary variable terms, CP RA80i, and
include the vector of predetermined characteristics, Wi. After deriving the predicted

outcomes, (cid:98)Yi, using the above equation, I plot the predicted outcomes against the

CPRA running variables as shown in Figure B.6. As I predicted each outcome without
using the binary variable terms, CP RA80i, smoothly continuous graphs would be
desirable for the validity of the RD design. As expected, all the graphs in Figure B.6
show smooth patterns around the CPRA 80 threshold.

2.5 Results

I show the trade-oﬀs between the two kidney sources in Section 2.5.1. Section 2.5.2
shows how a candidate’s mortality risk changes as his or her access to deceased donor
kidneys increases, while Section 2.5.3 tests heterogeneity by characteristics of candi-
dates to identify the types of candidates who can be prioritized in the kidney allocation.

2.5.1 Trade-oﬀs between kidney sources

In this section, I examine whether an increase in access to deceased donor kidneys
reduces the likelihood of receiving living donor kidneys. Panel A of Table B.5 shows

33https://www.kidney.org/atoz/content/pregnancy, information access on the web, last accessed on March

27, 2019.

46

the RD estimates of the probability of receiving deceased donor kidneys, and panel
(a) of Figure B.7 presents the corresponding ﬁgure. There is a positive and signiﬁcant
discontinuity of access to a deceased donor kidney at the CPRA 80 threshold. In col-
umn (1) of Table B.5, the likelihood of receiving a deceased donor kidney increases by
23 percentage points just above the CPRA 80 threshold, which implies a 165 percent
increase compared to the unadjusted mean probability of receiving a deceased donor
kidney (13.9 percent) in the sample below the CPRA 80 threshold. Column (2) shows
the RD estimate identiﬁed with control variables. The RD estimate with control vari-
ables is 0.227, similar to the result in column (1). Although several variables, including
gender and education level, show statistically signiﬁcant discontinuities at the threshold
in the validity check, those discontinuities do not substantially aﬀect the RD estimate.
For precision, I repeat the estimation that controls the waitlist registration year ﬁxed
eﬀects (column (3)) and the waitlisted DSA ﬁxed eﬀects (column (4)). The magnitude
of each RD estimate is similar to that of the previous two RD estimates. After the
large jump at the threshold, however, the probability of receiving a deceased donor
kidney shrinks quickly as the CPRA increases. When a candidate’s CPRA increases,
the probability of ﬁnding compatible donors decreases exponentially. Although the
sensitization point provides high-CPRA candidates with priority for deceased donor
kidneys, the beneﬁt is focused on candidates with CPRAs just above the threshold,
and candidates with very high CPRAs still struggle to receive a deceased donor kid-
ney. This problem illustrates why OPTN modiﬁed the sensitization point system to a
sliding scale (Table B.2) in 2014.

Panel (b) of Figure B.7 presents the eﬀect of sensitization points on the prob-
ability of receiving a living donor kidney. There is a negative gap at the CPRA 80
threshold, although the gap is smaller than that in panel (a), and the correspond-
ing RD estimate is -0.0399 (Column (1) of Table B.5 Panel B), which implies a 43
percent decrease compared to the mean probability of 9.2 percent. The results show
evidence of crowding out in the kidney transplant market. Candidates with CPRAs
above the threshold are less likely to choose living donor kidneys as their access to
deceased donor kidneys increases. The crowd-out eﬀect can be derived by using the
fuzzy RD estimation, and the results are shown in column (1) of Table B.5 panel C.

47

A 10 percentage-point increase in the probability of receiving a deceased donor kidney
reduces the probability of receiving a living donor kidney by 1.73 percentage points,
and the estimate is statistically signiﬁcant. The fuzzy RD estimates are similar even
though I control for predetermined characteristics, year ﬁxed eﬀects, and waitlisted
DSA ﬁxed eﬀects in columns (2) to (4), -0.179 to -0.191.

These results show evidence that kidney candidates behave strategically when
they choose between two kidney sources: a deceased donor kidney and a living donor
kidney. The sensitization points improve the kidney candidate’s rank on the waitlist
and increases the probability of receiving a deceased donor kidney oﬀer earlier. The
fuzzy RD estimates above can be considered as the probability of receiving an accept-
able deceased donor kidney oﬀer before the waiting time threshold (t∗) in Figure B.2
and switching the kidney source from living donor kidneys to deceased donor kidneys.

2.5.2 Mortality

The second measure of evaluating a deceased donor kidney allocation policy is the
eﬀect on patients’ outcomes. In particular, reducing the waitlist mortality of kidney
candidates, which indicates the deaths before receiving kidney transplants, has been
suggested as a key metric of improving patient outcomes in OPTN’s strategic plan.34 To
ﬁnd the types of candidates who can be prioritized in deceased donor kidney allocation
to increase the transplant quantity while improving mortality, understanding the causal
eﬀect of increased access to deceased donor kidneys on patient mortality is necessary.
In the waitlist mortality outcome, I include removal from the waitlist due to
severe sickness, as these patients also face a high risk of mortality. Table B.6 shows
the RD estimates of the waitlist mortality analysis, and panels (a) and (b) of Figure
B.8 present the corresponding ﬁgures. As the mortality risk could be highly correlated
with the waiting time, I estimate the eﬀect within ﬁxed durations, 1 and 2 years, from
the waitlist registration. I exclude candidates whose maximal waiting time by the end
of the analysis period, December 3, 2014, is less than the length of each duration.
In Figure B.8, there are negative discontinuities at the CPRA 80 threshold, and the

34https://optn.transplant.hrsa.gov/governance/strategic-plan/goal-5/, information access on the web, last

accessed on March 27, 2019.

48

magnitude of discontinuity increases as the duration increases. The corresponding RD
estimate, in column (1) of Table B.6 panel A, increases as the duration increases from
1.13 percentage points (1 year) to 2.83 percentage points (2 years).35 Compared to
the baseline waitlist mortality rate of candidates with CPRAs below the threshold, the
waitlist mortality rate decreases by approximately 43 percent, a sizable reduction. In
columns (2) to (4), which control for covariates, the magnitude of the RD estimates is
similar for each duration. Panel B of Table B.6 shows the fuzzy RD estimates using
the ﬁrst-stage results in the above section.36
In column (1), a 10 percentage-point
increase in the likelihood of receiving a deceased donor kidney signiﬁcantly reduces the
1-year waitlist mortality rate by 0.4 percentage points and the 2-year waitlist mortality
rate by 1 percentage point. Similar to the reduced-form results, the RD estimates in
columns (2) to (4) are not signiﬁcantly diﬀerent from the result in column (1).

Although waitlist mortality is a widely used mortality risk measure, it may un-
derestimate kidney candidates’ mortality risk from waitlist registration. The measure
shows the risk of losing a chance of receiving kidney transplants rather than the risk
of death because deaths after receiving kidney transplants are not considered. Hence,
when a kidney policy increases access to donated kidneys and reduces waitlist mortal-
ity, interpreting the result as evidence of improvement in mortality risk from waitlist
registration requires caution.

To address this concern, I examine the overall mortality measure which considers
both deaths before receiving kidney transplants and after receiving kidney transplants
within 1 and 2 years from waitlist registration. The RD estimates of the overall mor-
tality are shown in Table B.7, and related ﬁgures are presented in panels (c) and (d)
in Figure B.8. Compared to waitlist mortality outcomes, the magnitude of discontinu-
ity is relatively small, but the negative discontinuity at the CPRA 80 threshold still
increases as the duration increases. In panel A of Table B.7, baseline overall mortality
rates are slightly greater than baseline waitlist mortality rates because people who die
after receiving kidney transplants are now considered. Although the RD estimates for

35As the sample size for the mortality analysis in each duration is diﬀerent, direct comparisons of RD
estimates may not accurate. I repeat the RD estimation using the same sample size for each duration and the
results are shown in Table B.14.

36For each duration, I derived the RD estimates with the same sample restriction as the reduced-form

estimation.

49

1-year overall mortality analysis are negative, I do not ﬁnd any signiﬁcant discontinuity
at the CPRA 80 threshold. When I extend the analysis duration to 2 years, the RD
estimates become signiﬁcant. In column (1), I ﬁnd evidence that kidney candidates
who receive sensitization point beneﬁts experience a signiﬁcant decrease in overall mor-
tality rates by 2.53 percentage points. Compared to the baseline overall mortality rates
(7.4 percent), the magnitude of RD estimates implies a roughly 34 percent decrease.
The eﬀect on overall mortality is stable controlling for covariates in columns (2) to (4).
Panel B presents the fuzzy RD estimates of the overall mortality outcome. I do not
ﬁnd any signiﬁcant evidence that an increase in the probability of receiving a deceased
donor kidney reduces the overall mortality within 1 year (column (1)), but the results
become signiﬁcant for the overall mortality results within 2 years. When the probabil-
ity of receiving a deceased donor kidney increases by 10 percentage points, the overall
mortality rate within 2 years decreases by approximately 0.9 percentage points, and
the results are similar controlling for covariates.

2.5.3 Heterogeneity

I ﬁnd evidence that an increase in access to deceased donor kidneys partially crowds
out kidney candidates’ living donor kidney choices and improves both waitlist mortality
and overall mortality. It is possible, however, that the magnitude of the eﬀects would be
heterogeneous across kidney candidates with the diﬀerent characteristics. In the kidney
source choice problem discussed in Section 2.2.2, the net beneﬁts or costs of receiving
a living donor kidney instead of waiting longer for a deceased donor kidney oﬀer may
vary among candidates. In addition, the availability of potential living donors could
be diﬀerent across kidney candidates. When the magnitude of the crowd-out eﬀect is
heterogenous across kidney candidates, prioritizing candidates with smaller crowd-out
eﬀects would help increase the number of kidney transplants.

Table B.8 shows the fuzzy RD estimates across race for kidney candidates. In
column (1), both groups of candidates show a signiﬁcant crowd-out of living donor kid-
neys when access to deceased donor kidneys improves; however, the magnitude of the
RD estimates is signiﬁcantly diﬀerent between the two races. When the probability of
receiving a deceased donor kidney increases by 10 percentage points, white candidates

50

are 2.55 percentage points less likely to receive a living donor kidney and the amount of
crowd-out decreases to 1.19 percentage points when I restrict the sample to candidates
who are African-American. Based on the ﬁndings of previous studies, this diﬀerence
could be caused by knowledge about the net beneﬁt of living donor kidney transplants
or the potential living kidney donor pool. Due to relatively limited access to healthcare,
African-American kidney candidates tend to have little knowledge about the beneﬁt
of living donor kidney transplants compared to white kidney candidates (Purnell et
al. 2013). In addition, they are less likely to ﬁnd potential living donors than white
kidney candidates because of a lack of skills to recruit potential donors (Rodrigue et
al. 2014; Weng et al. 2010). Both reasons result in a longer cutoﬀ time until kidney
candidates switch the kidney source from a living donor to a deceased donor, as shown
in Figure B.9, and this diﬀerence could cause heterogeneity in the crowd-out eﬀect
when access to deceased donor kidneys increases. In the eﬀect on mortality outcomes
(Columns (2) to (4) in Table B.8)37, African-American kidney candidates show signiﬁ-
cant RD estimates. When the likelihood of receiving a deceased donor kidney increases
by 10 percentage points, the waitlist mortality rate and overall mortality rate decreases
by approximately 1 percentage point. However, I do not ﬁnd any signiﬁcant eﬀect on
the mortality outcomes of white kidney candidates, and the diﬀerence in RD estimates
is statistically signiﬁcant for 1-year mortality outcomes. The smaller crowd-out eﬀect
but larger mortality reduction of African-American kidney candidates implies that pri-
oritizing African-American candidates would increase the number of transplants while
improving the mortality of kidney candidates.

Another characteristic highly related to the heterogeneous size of the compatible
donor pool is blood type. For successful kidney transplantation, the compatibility of
blood types between kidney candidates and donors is important. Candidates with
blood types A or B can receive donor kidneys with blood type O in addition to donor
kidneys with the identical blood type. On the other hand, candidates with blood type
O can only receive donor kidneys with the identical blood type. Hence, compared to
the other blood types, kidney candidates with blood type O face a restriction in ﬁnding

37As the sample size for the mortality analysis in each duration is diﬀerent, direct comparison of RD
estimates may not be accurate. I repeat the RD estimation using the same sample size for each duration and
the results are shown in Table B.15 - B.17.

51

potential donors. Using a similar logic with race analysis, limited access to the kidney
donor pool results in a longer cutoﬀ time, and we can expect a smaller crowd-out
eﬀect for candidates with blood type O(Panel (a) of Figure B.10). Table B.9 shows
the fuzzy RD estimates of the above outcomes across blood types.
In column (1),
kidney candidates with blood types A and B show large and signiﬁcant crowd-out in
the probability of receiving living donor kidneys. When the probability of receiving a
deceased donor kidney increases by 10 percentage points, candidates with blood type
A are 2.73 percentage points less likely to receive a living donor kidney (blood type B:
2.82 percentage points). However, as expected, I do not ﬁnd any signiﬁcant evidence of
crowd-out for kidney candidates with blood type O. In the mortality analysis (Columns
(2) to (4) in Table B.9), the eﬀect of increased access to deceased donor kidneys is
heterogeneous across blood types. I do not ﬁnd any signiﬁcant improvement for kidney
candidates with blood type A. Blood type B candidates show signiﬁcant reductions in
2-year mortality outcomes, waitlist mortality (-0.219) and overall mortality (-0.222),
and blood type O candidates show signiﬁcant estimates in waitlist mortality outcomes:
1 year (-0.0713) and 2 years (-0.126). Although the magnitude of the RD estimates for
blood type B candidates is larger than that for blood type O candidates, the diﬀerences
are not statistically signiﬁcant. Hence, blood type O kidney candidates, for whom a
smaller crowd-out eﬀect is observed, can be considered for prioritization.

Finally, I examine the heterogeneity of kidney candidates’ dialysis status. Pa-
tients with kidney disease can register on the kidney transplant waitlist even though
their kidneys have not failed yet. As the waiting time for deceased donor kidney trans-
plants increases, the risk of kidney failure increases, and candidates would need to start
dialysis treatments after failure. Hence, compared to kidney candidates already receiv-
ing dialysis treatments, candidates who are not receiving dialysis would place greater
value on living donor kidneys, which does not have to wait for an oﬀer, as the waiting
time increases. This diﬀerence is illustrated by the steeper slope of the net beneﬁt and
shorter cutoﬀ time in panel (a) of Figure B.10. Hence, we can expect a larger crowd-
out eﬀect for candidates who are not receiving dialysis treatment. The heterogeneity
results by dialysis status are presented in Table B.10. As expected, candidates who
are not receiving dialysis treatments are more likely to switch living donor kidneys to

52

deceased donor kidneys. When the probability of receiving a deceased donor kidney
increases by 10 percentage points, candidates not receiving dialysis treatments are 3.04
percentage points less likely to choose living donor kidneys, while the result for candi-
dates receiving dialysis treatments is 1.21 percentage points. The results for mortality
outcomes show that kidney candidates receiving dialysis treatments can be eligible for
prioritization. Although they show a smaller crowd-out eﬀect, the increased access to
deceased donor kidneys reduces their waitlist mortality and overall mortality signiﬁ-
cantly, and I do not ﬁnd any evidence of a signiﬁcant mortality eﬀect for candidates
who are not receiving dialysis treatments.

2.6 Robustness Check

This section presents a series of analyses to test the robustness of the main ﬁndings.
First, in Figure B.11, I re-estimate the main results, crowd-out and mortality outcomes
using donut-RD models that exclude observations close to the CPRA 80 threshold. The
estimation results are stable, which supports the idea that some clusters around the
threshold in panel (b) of Figure B.4 do not drive the main ﬁndings. The magnitudes
of the mortality results for 1 year and 2 years slightly increase at the larger exclusion,
but the diﬀerences in the donut-RD estimates are insigniﬁcant.

Second, if the identiﬁed RD estimates are driven by the discontinuity around
the CPRA 80 threshold, then the RD estimates that exclude observations far from the
threshold are expected to have similar values. In Table B.11, I repeat the RD estimation
with the samples that exclude 1 percent, 5 percent, and 10 percent of the analysis
sample far from the threshold. Column (1) shows the crowd-out eﬀect on the choice
of a living donor kidney. Although I exclude the outermost sample, the signiﬁcance
of the RD estimate still holds, and all the results are similar in magnitude. Columns
(2) to (4) present eﬀects on candidates’ waitlist mortality. In each duration, the RD
estimates show similar values. However, in a 1-year analysis, the signiﬁcance of the RD
estimate is removed when I exclude the 5-percent and 10-percent outermost samples.
Although insigniﬁcant, the coeﬃcient is indistinguishable from the other results with
diﬀerent sample restrictions. In columns (5) to (7), which present the eﬀect on the
overall mortality, the magnitudes of the RD estimates are also similar in all durations.

53

However, the eﬀect on the overall mortality within 2 years of registration becomes
insigniﬁcant when I restrict the 5-percent outermost sample. Although 2 mortality
outcomes are insigniﬁcant when I restrict the outermost sample, the magnitudes of
the RD estimates do not chang substantially, which supports the argument that the
identiﬁed eﬀects are robust to the outermost sample restrictions.

Finally, the RD estimates focus on the discontinuities of candidates close to the
threshold and may not be applied to other candidates. To address this, I re-estimate
the eﬀect of receiving the sensitization point beneﬁt assigned to kidney candidates
with a CPRA value of 80 or greater using a diﬀerence-in-diﬀerence (DD) model and
compare the results with the RD estimates. Although CPRA was introduced as a
new sensitization measure in December 2007, the traditional PRA was used to assign
the sensitization point beneﬁt until October 2009. Hence, in the DD framework, I
use the sample whose most recent CPRAs are available between December 2007 and
December 2014, and the candidates are categorized as shown in Figure B.12. For an
accurate analysis using a DD framework, an additional 2 groups of candidates should
be excluded from the analysis. First, inclusion of candidates with a traditional PRA
of 80 or greater may cause an underestimation of the eﬀect of the sensitization point
policy. Kidney candidates with a traditional PRA of 80 or greater (groups III and
IV in Figure B.12) could receive the sensitization points even though their CPRAs
are lower than 80. Hence, I exclude these kidney candidates because they are treated
not by CPRA but by the traditional PRA. Second, inclusion of candidates who were
registered in the pretreatment period but did not receive kidney transplants until the
end of the pretreatment period may also cause an underestimation of the policy eﬀect.
They are deﬁned as pretreatment period samples but may receive sensitization point
beneﬁts if their CPRAs are 80 or greater because the beneﬁt eligibility is determined
by the most recent CPRA. Hence, candidates whose waiting periods overlap between
the pre-treatment and post-treatment periods are excluded from the analysis.

54

In the following regression, β2 is the coeﬃcient of interest

Yit = α + β0CP RA80i + β1postCP RAt + β2(CP RA80× postCP RA)it + Witγ + ηt + uit
(15)
where i denotes a kidney transplant candidate. postCP RAt is a binary variable
with a value of one if candidates are registered on the waitlist in the post-treatment
period when the sensitization point beneﬁt is assigned based on the CPRA. CP RA80i
is the same binary variable as the RD estimation, which shows the eligibility for the
sensitization point beneﬁt and Wit is a vector of predetermined characteristics. I include
the waitlist registration year ﬁxed eﬀect (ηt) and standard errors are clustered at the
waitlisted DSA level.

Panel A of Table B.12 shows the estimates from the DD model. All ot the co-
eﬃcients are similar to the RD estimates, although the magnitudes become slightly
larger. The probability of receiving a deceased donor kidney increases by 24.8 per-
centage points after the introduction of a sensitization point policy using the CPRA
measure. In addition, the probability of receiving a living donor kidney decreases by 4.7
percentage points, which shows the existence of a crowd-out eﬀect. The DD estimates
for mortality, waitlist mortality and overall mortality, are negative and similar in mag-
nitude to the RD estimates. The standard errors of the DD estimates are larger than
those of the RD estimates, which results in some insigniﬁcant results, even though the
level of coeﬃcients is stable. The larger standard errors could be driven by a relatively
small sample size in the pretreatment period due to the exclusion of candidates with
traditional PRAs greater than 80.

2.7 Conclusions

Given the absence of the price mechanism due to the stipulations of NOTA in 1984,
which bans the sale of organs, the problem of transplantable kidney shortages has be-
come more severe in recent decades. As not all kidney candidates receive transplants
in the year of waitlisting, the number of waitlisting candidates increases dramatically
every year: roughly 95,000 kidney candidates are currently waiting for kidney trans-

55

plants on the waitlist.38 To date, OPTN has mainly tried to reduce organ shortages by
increasing kidney donations, but the role of kidney allocation rules in kidney shortages
has received much less attention. As kidney candidates choose kidney sources strate-
gically, a change in kidney allocation rules aﬀects candidates’ kidney source choices
between deceased and living donor kidneys. I propose a model in which kidney candi-
dates choose kidney sources by comparing the net beneﬁt and costs of receiving living
donor kidneys rather than waiting longer for deceased donor kidneys. The model im-
plies that an increase in access to deceased donor kidneys could result in the crowd-out
of living donor kidney choices only available to designated recipients.

Exploiting the variation in eligibility for kidney sensitization points, which in-
crease access to deceased donor kidneys for candidates with CPRA values of 80 or
greater, I ﬁnd that an increase in access to deceased donor kidneys crowds out the
choice of living donor kidneys. When the probability of receiving a deceased donor
kidney increases by 10 percentage points, the likelihood of receiving a living donor kid-
ney decreases by approximately 1.7-1.9 percentage points. Additionally, the crowd-out
eﬀects are diﬀerent across demographic subgroups, i.e., races, blood types, and dialysis
status. Candidates who are African-American or receiving dialysis treatments are less
likely to switch to deceased donor kidneys from living donor kidneys when access to
deceased donor kidneys increases. Among the blood type subgroups, blood type A
and B candidates show greater crowd-out than blood type O candidates. Using the
kidney source choice model, I show that diﬀerences in knowledge about the quality
diﬀerence between deceased and living donor kidneys, the opportunity cost of waiting
for deceased donor kidneys, and the availability of potential living kidney donors could
be reasons for the heterogeneous crowd-out eﬀects.

The heterogeneous results provide implications for the allocation of deceased
donor kidneys. When allocation policies prioritize subgroups that show smaller crowd-
out eﬀects, we may expect an increase in the number of overall transplants, thereby
ameliorating kidney shortages. In addition, kidney candidates with smaller crowd-out
in the choice of living donor kidneys show relatively large improvements in waitlist
mortality and overall mortality, which implies that prioritizing these candidates would
38https://optn.transplant.hrsa.gov/data/view-data-reports/national-data, information access on the web,

last accessed on March 27, 2019.

56

not worsen the mortality of kidney candidates.

This paper considers only three candidate characteristics because previous re-
search has shown how the net beneﬁts and costs in the choice of kidney sources vary
across these characteristics. In order to identify the kidney candidate groups who can
be prioritized in deceased donor kidney allocation, further research on the sources of
heterogeneity in crowd-out and kidney candidates’ mortality is needed. For patients
with kidney failure, a kidney transplant is a key treatment to prolong their lives and
improve their quality of life.
In addition to increasing the supply of altruistic kid-
ney donations, future policies should consider the role of kidney allocation rules in
delivering the eﬃcient allocation of donated kidneys.

57

Chapter 3

The Strategic Location Choice of For-proﬁt Hemodialysis Facil-

ities in the U.S.

3.1

Introduction

The kidneys are a pair of organs in the human body that remove waste from the
blood and control the body’s ﬂuid balance. When both kidneys fail, blood wastes
accumulate in the patient’s body and the risk of death increases. Two representative
treatments for patients with kidney failure are kidney transplants and dialysis. Unlike
transplants, which place a healthy kidney in a patient’s body, dialysis uses a machine
that substitutes the work of the kidneys. Due to the high shortage of transplantable
kidneys, in 2016, more than seventy percent of 726,331 patients with kidney failure were
dependent on dialysis treatment for survival (United States Renal Data System 2018).
As depicted in Figure C.1, with the steady increase in the incidence of kidney failure
and demand for dialysis treatment, the dialysis industry has expanded. In 2016, there
were approximately 7,100 dialysis facilities in the United States, four times the number
of facilities in 1988. Furthermore, because Medicare covers nearly all populations with
kidney failure regardless of age, the ﬁnancial burden of the government for supporting
those patients is high. According to United States Renal Data System (2018), although
less than 1 percent of patients covered by Medicare had kidney failure in 2016, these
patients accounted for approximately 7 percent of Medicare fee-for-service coverage.

Despite the fast growth of the dialysis industry and the huge ﬁnancial burden
on Medicare, little is understood about how dialysis facilities decide whether to enter
a certain market and where to locate within the market. In the general market, proﬁt-
maximizing ﬁrms wish to diﬀerentiate their products by lowering prices or improving
quality to appeal to consumers and gain more proﬁts. However, the dialysis industry
has characteristics that make product diﬀerentiation diﬃcult. First, the price of dialysis
is fully controlled by the government because most patients with kidney failure are
eligible for Medicare. Additionally, the performance of dialysis treatment is somewhat

58

homogeneous across facilities because most of the dialysis process is performed using
a dialysis machine. Therefore, the location of dialysis facilities could be the most
important factor allowing for product diﬀerentiation.

The goal of this paper is to identify key factors that aﬀect dialysis facilities’
strategic decisions for market entry and location choice by using a structural model.
First, dialysis facilities are likely to choose a location where the demand for dialysis
treatment is high. However, they also need to consider the expected competition with
other facilities that might choose the same location. Because of the limited options
for diﬀerentiating the product, namely, dialysis treatment, across facilities in the same
location, higher competition will lower a facility’s expected proﬁts.

This paper applies the structural methods from modern industrial organization
to study dialysis facility behaviors. The analysis of ﬁrm entry and location decisions is
based on the literature on discrete entry games proposed by Bresnahan et al. (1991) and
Berry (1992). These studies show that the level of competition aﬀects the entry decision
of ﬁrms because an additional entrant in a market reduces proﬁts in an oligopolistic
market structure. More recent studies (Mazzeo 2002; Seim 2006) extend this literature
by incorporating the product diﬀerentiation concept. In Mazzeo (2002)’s model, ﬁrms
not only determine whether to enter a market but also select product types under the
complete information assumption. That is, ﬁrms do not have the information on the
proﬁt shocks of the other competing ﬁrms. On the other hand, in Seim (2006)’s model,
video rental stores determine their market entry and their location under the assump-
tion of homogeneous product type and incomplete information status. I contribute to
this literature by examining the dialysis industry using the estimation model of Seim
(2006).

To date, literature on the hospital competition has focused on the eﬀect of
competition on the quality of health care services. In many situations, prices for health
care services are administered by regulators such as Medicare. Hence, hospitals are
likely to compete for quality and empirical studies support this. Kessler et al. (2000)
ﬁnd higher one year mortality rates for Medicare patients with acute myocardinal
infarction (AMI) and lower expenditures in less concentrated markets. Two studies
(Cooper et al. 2011; Gaynor et al. 2013) also ﬁnd similar results and identify lower

59

mortality rates among AMI patients in less concentrated markets by using a reform in
the English National Health Service (NHS) that promotes competition among hospitals.
Using the same set of data from the English NHS, Propper et al. (2010) ﬁnd that
having more local competitors has a large impact on hospital management quality
based on Bloom et al. (2007). I contribute to this literature by suggesting that facility
location could also be a factor that allows health care providers, i.e., dialysis facilities,
to diﬀerentiate their quality.

Several studies have analyzed the spatial competition in the dialysis industry.
Wilson (2016) studied diﬀerences in the entry and exit patterns of for-proﬁt and non-
proﬁt dialysis facilities. Exploiting 20 years of longitudinal data on dialysis facilities in
the U.S., this author ﬁnds that for-proﬁt facilities are quicker to enter growing markets
and slower to exit declining ones compared to non-proﬁt facilities. Additionally, the
existence of for-proﬁt facilities in a market has a larger impact on the entry and exit
of competitors. Eliason (2017) estimates an entry game where dialysis facilities choose
both the capacity and quality, and he ﬁnds that dialysis facilities can compete more
eﬀectively in terms of capacity rather than quality because increasing quality is very
costly to dialysis providers and patients may not be responsive to the quality. Al-
though these studies consider the market entry decision of dialysis providers, they do
not consider location selection upon entry in their estimation models. Wilson (2016)
uses counties as their market unit, and Eliason (2017) exploits Core-Based Statistical
Areas as a market deﬁnition. This paper contributes to this literature by analyzing
the location choice problems in a census tract-level assuming that competing dialysis
facilities are symmetric.

Detailed information on the dialyis market in the United States is obtained from
the United States Renal Data System (USRDS). The data contain the exact locations
of dialysis facilities and the demographic characteristics of patients with kidney failure,
including their zip code-level residence information. Information on the socio-economic
status of each census tract-level location, such as the per capita income, education level,
median gross rent, etc., is obtained from the 2015 American Community Survey (ACS).
The estimation results show that dialysis facilities are usually located in areas
with a larger number of patients with kidney failure. A 10 percent larger number of

60

patients with kidney failures increases the location choice probability by 2.01 percent.
In terms of competition, I ﬁnd that the expected probability of having competitors
in the location reduces proﬁts signiﬁcantly and makes ﬁrms avoid locations in which
high competition is expected. This result supports the idea that dialysis facilities use
spatial diﬀerentiation to diﬀerentiate their products.

When dialysis facilities consider future local demand more than the current
demand, the eﬀect of local demand variables increases while the competition eﬀect
shrinks. I use the number of population with age 65 years and above and socioeconomic
status as the measures of future local demand and ﬁnd that a 10 percent increase in
the elderly population increases the location choice probability by 3.85 percent. As
socioeconomic status is negatively related to kidney failure incidence, the estimation
results show that dialysis facilities prefer locations with lower socioeconomic status.

This evidence of the strategic location choice of dialysis facilities is meaningful for
the discussion on the relationship between proﬁt status and patient outcomes. Previous
literature (D. K. Lee et al. 2010; Brooks et al. 2006) ﬁnds longer hospital days per
patient but no evidence of an eﬀect on patient mortality in for-proﬁt dialysis facilities.
To address the possible bias in a patient’s choice of dialysis facility, those studies use an
instrumental variable regression method with the relative proximity of dialysis facilities
to the patient’s residence as the instrument. The evidence of strategic location choice
of for-proﬁt dialysis facilities implies that the relative distance instruments may not
fully address the selection biases. For-proﬁt dialysis facilities are more likely to be
located in areas with low socioeconomic status, and patient outcomes in those areas
could be diﬀerent from those in the other areas.

The rest of the paper is organized as follows. The following section provides
background information on dialysis and the dialysis industry. Section 3.3 describes the
data used for the estimation, while Section 3.4 discusses the estimation model. Section
3.5 presents the parameter estimates of key factors that aﬀect the location choice of
dialysis facilities. Section 3.6 provides key robustness factors, and Section 3.7 presents
the conclusions.

61

3.2 Background

3.2.1 Treatments for Patients with Kidney Failure

When a person’s kidneys are no longer able to work on a permanent basis, he/she
is diagnosed with the end-stage renal disease (ESRD)39. As shown in Figure C.2, the
number of ESRD occurrences has increased steadily from 1988 to 2016. In 1988, there
were 28,927 incidences of patients newly diagnosed with ESRD in the United States,
although this ﬁgure increased to 101,334 in 201640. The ﬁgure shows that the increase
in ESRD incidences is driven primarily by people aged 65 and older. This result
could be related to an increasing number of elderly people thanks to medical advances
(Administration on Aging 2018). Figure C.3 shows the share of primary causes among
patients with ESRD. The most common causes of ESRD are diabetes (48%, 2016) and
hypertension (29%, 2016). Stevens et al. (2010) shows that the prevalence of these
conditions is higher for elderly individuals than for middle-aged adults41.

ESRD patients need to receive either a kidney transplant or dialysis treatments
to prolong their lives. A kidney transplant is a surgery that places another person’s
kidney into the ESRD patient’s body. Unlike patients with other organ failures, ESRD
patients can survive by undergoing dialysis treatments without receiving a kidney trans-
plant. Dialysis is a treatment that ﬁlters ESRD patients’ blood using a machine that
performs the work of the kidneys. As blood wastes and ﬂuids continuously accumu-
late after each dialysis, ESRD patients regularly need to receive dialysis, which takes
approximately 4 hours, and is usually performed three times a week. Previous studies
have shown that patients who receive kidney transplants may have better outcomes
in terms of survival and quality of life on average than those who continue receiving
dialysis (Schold et al. 2014; Wolfe et al. 1999; Overbeck et al. 2005). However, Figure
C.4 shows that most ESRD patients choose dialysis and do not even register for kid-
ney transplant waitlists. The share of patients who are waitlisted for deceased donor

39https://www.cms.gov/Medicare/Coordination-of-Beneﬁts-and-Recovery/Coordination-of-Beneﬁts-and-

Recovery-Overview/End-Stage-Renal-Disease-ESRD/ESRD

40This paper excludes ESRD occurrences in U.S. territories - Puerto Rico (PR), Virgin Islands (VI), Guam
(GU), Northern Mariana Islands (MP), American Samoa (AS) -, and with unknown age, race, sex, zip codes,
and proﬁt status of the dialysis center.

41Approximately 11% of middle-aged adults have diabetes and 33% have hypertension, with the prevalence

of these conditions increasing to 23% and 66%, respectively, by age 60.

62

kidneys or receive living donor kidneys within 1 year after ESRD diagnosis is less than
10 percent.

3.2.2 Medicare and the Dialysis Industry

If the cost of dialysis treatment is high42, many patients will not receive the treatment
and the mortality risk of ESRD patients will increase. In the United States, Medicare
plays an important role in ﬁnancing dialysis treatment. The Social Security Amend-
ments of 1972 provided Medicare coverage to nearly the entire U.S. population with
ESRD regardless of age43. On December 31, 2015, more than 80 percent of ESRD-
prevalent patients were receiving dialysis treatments covered by Medicare (Kirchhoﬀ
2018). Since 2011, Medicare has reimbursed the dialysis facilities using a prospec-
tive payment system (PPS) that provides a bundled amount of money per patient per
treatment for dialysis and necessary support, such as tests and medications (Collins
2012). As the amount of the reimbursement is determined in advance (the base rate
in 2020 is $239.334445), and beneﬁciaries pay coinsurance equal to 20 percent of the
Medicare-approved amount; the price of dialysis treatment for the majority of ESRD
patients is stable across dialysis facilities.

As the number of ESRD patients has increased, with certain Medicare payments,
the number of dialysis facilities has steadily increased since 1988. Figure C.5 shows
that there were approximately 1,800 dialysis facilities in 1988, and this ﬁgure increased
to approximately 7,100 in 201646. Dialysis facilities can be classiﬁed as either hospital-
based or freestanding units, i.e., units not aﬃliated with a hospital (Center for Medicare
and Medicaid Services 2019). Additionally, the facilities are operated on either for-
proﬁt or not-for-proﬁt bases, similar to other health care providers. The growth in

42Childers et al. (2019) found that the cost of dialysis varies across insurers of ESRD patients. For-proﬁt
dialysis facilities charge $248 per treatment when the government is the insurer, compared with $1,041 per
treatment for private insurance.

43When a patient enrolls in Medicare based on ESRD, Medicare coverage usually starts at 90 days from

the ESRD diagnosis (https://www.medicare.gov/manage-your-health/i-have-end-stage-renal-disease-esrd).

44https://www.federalregister.gov/documents/2019/11/08/2019-24063/medicare-program-end-stage-

renal-disease-prospective-payment-system-payment-for-renal-dialysis

45Actual amount of reimbursement is driven by adjusting multiple factors, such as patient characteristics,
facility-level characteristics, etc. Detailed information on the reimbursement amount calculation is available
in Kirchhoﬀ (2018).

46This paper counts only Medicare-certiﬁed hospitals and outpatient dialysis facilities and excludes facilities

with unknown for-proﬁt status.

63

the number of dialysis facilities in each category is shown in Figure C.5. The ﬁgure
implies that the major growth in the dialysis industry has been driven by freestanding
and for-proﬁt dialysis facilities. The share of this category increased from 51 percent
(1988) to 84 percent (2016).

3.3 Data

3.3.1 Market Deﬁnition

In the dialysis industry, dialysis treatment is somewhat homogenous. As most ESRD
patients are eligible for Medicare coverage, the treatment cost is well controlled by the
government and similar across dialysis facilities. Furthermore, the process of dialysis
treatment is performed by the dialysis machine, which provides standardized care. To
recruit more patients, dialysis facilities tend to compete in terms of amenities, such as
TVs and heated chairs. However, as ESRD patients need to receive dialysis regularly (at
least 3 times a week) and permanently, they are likely to choose dialysis facilities close
to their residences; thus the eﬀect of distance may dominate the eﬀect of amenities.
Therefore, dialysis facilities may primarily compete against other facilities located in
a local area and choose a location that could be the most proﬁtable. Table C.1 shows
these characteristics of the dialysis industry derived from the USRDS data. Column
(1) reports that the median distance between their preferred dialysis facility and their
residence among patients diagnosed with ESRD from 1988 to 2016 was only 7.404
miles. Columns (2) to (5) show the median distance to diﬀerent subgroups of dialysis
facilities classiﬁed according to the proﬁt status or aﬃliation with a hospital. Although
the distance to for-proﬁt and freestanding facilities (7.236 miles) is shorter than that
to the other types of facilities (7.636 - 8.269 miles), the diﬀerence is not great.

Because ESRD patients are sensitive to the distance from their residence, this
paper focuses on mid-sized cities to identify well-deﬁned markets. Using 2015 popula-
tion data from the United States Census Bureau, this paper focuses on mid-sized cities
and groups of small cities close to each other with populations ranging from 50,000 to
300,000. All cities within 5 miles from a city boundary are categorized as the same mar-
ket, and the distance between cities is calculated using population-weighted centroids

64

of census tracts47 located in each city boundary. To minimize the eﬀect of neighbor-
ing markets on the dialysis facility choice of ESRD patients, I only include markets
whose largest neighboring market within 20 miles had a population below 25,000. Af-
ter this process, eighty-one markets are deﬁned as the sample markets for the analysis.
In Table C.2, the market size by population ranges from 56,548 to 304,016, with an
average of 127,485 people. On average, there are 30 census tracts in a market. The
smallest market consists of 9 census tracts, and the largest market consists of 70 census
tracts. As this paper focuses on the midsized dialysis market, each market contains
three facilities on average.

3.3.2 Dialysis Facilities

The data on dialysis facility locations are obtained from the USRDS, which collects
information about ESRD patients, their treatments, and treatment provider. The
facility data include detailed information on each facility’s for-proﬁt status, whether the
facility is aﬃliated with a hospital, the date of certiﬁcation, etc. I use the facility-level
location information for 2015, when the number of dialysis facilities was maximized
in the available data periods. Dialysis facilities that closed before or opened after
2015 are not considered in the analysis. This paper focuses on the location decision of
freestanding and for-proﬁt dialysis facilities48, which have increased rapidly as shown
in Figure C.5.

For the minimum unit of location decision of dialysis facilities, this paper uses
United States census tracts because they are not overlapping and contain various de-
mographic characteristics available in the United States Census data. To match the
locations of dialysis facilities to census tracts, the precise location information of facil-
ities is necessary, although the USRDS data provide only zip code-level information.
To address these limitations on location information, I use the Dialysis Facility Com-
pare Dataset from the Centers for Medicare and Medicaid (CMS), which contains the
exact address of dialysis facilities. Using the address and the geocoding Stata module

47https://census.missouri.edu/geography/
48Not-for-proﬁt facilities are excluded as their goal of operation may not be the proﬁt maximization that
this paper is assuming. Hospital-based facilities are excluded as their location decision may depend on the
location of the aﬃliated hospitals.

65

- OPENCAGEGEO49, I derive the precise latitude-longitude coordinates of dialysis
facilities. The matched census tract for each dialysis facility is identiﬁed through the
ArcGIS program.

3.3.3 Local Demand for Dialysis Treatments

The number of ESRD patients in each census tract can be assumed as the local demand
for dialysis treatments because all ESRD patients need to receive dialysis immediately
and permanently for survival. Patients who received kidney transplants or died be-
fore 2015 are excluded from the analysis because they are not active ESRD patients.
Because USRDS patient data only include zip code-level residence information, the
number of ESRD patients in a census tract is calculated by weighting the percentage
of the total population of each zip code in each census tract50. Using ESRD patients as
the local demand for dialysis treatment is not suﬃcient because dialysis facilities could
determine their locations based on not only current demand but also the long-run ex-
pected local demand for dialysis treatments. As the alternative proxy for current and
future local demand, I also consider the census tract-level population age 65 and older,
which is the major group of ESRD patients (Figure C.2), and compare the estimates
with the results using census tract-level ESRD patients. According to the study of
Ward (2008), the incidence of ESRD could be aﬀected by the socioeconomic status
of the population, such as income and education51. These variables are available for
census tracts from the Census Bureau’s ACS data. As this paper analyzes the location
choice of dialysis facilities actively operating in 2015, the 2015 Census of Population
data are used for the estimation.

Table C.3 provides descriptive statistics of the variables used to estimate the
location choice model. As dialysis treatment is needed by patients with permanent
kidney failure, I use the census tract population diagnosed with ESRD or older than
65 years of age rather than the total tract population. I also use per capita income
and the share of people with low education (high school or below), which could be

49https://fmwww.bc.edu/repec/bocode/o/opencagegeo.pdf
502010 Zip Code Tabulation Area (ZCTA) relationship ﬁles from the United States Census Bureau were

51Ward (2008) found that the socioeconomic status of the population is highly associated with ESRD

used for the calculation.

caused by diabetes mellitus.

66

highly related to ESRD incidence. From the cost perspective, the property lease cost
might be important when each dialysis facility chooses the location. As the Census
Bureau does not provide information about commercial rent, I use the median gross
rent, which represents the housing cost including contract rent and utilities.

3.4 Model of Dialysis Facility Location Choice

3.4.1 Location Choice

The model in this paper assumes that all dialysis facilities choose their locations simul-
taneously. Additionally, this choice is structured as an incomplete information game,
which is similar to the framework of Seim (2006). That is, dialysis facilities have private
information about their proﬁt shocks speciﬁc to their own location that may not be
observed by other competitors. I deﬁne a series of M markets as explained in Section
3.3.1. The set of census tract-level locations is indexed by l = 0, 1, . . . , Lm in each
market m52. Let the set of potential dialysis facilities be f = 1, . . . , F . The facilities
simultaneously determine whether to enter each market m and where to locate their
facility in the market m.

This paper assumes that dialysis facility f’s payoﬀ at location l in market m is a
linear function of market and location characteristics and competition eﬀects in their
own location. Therefore, the payoﬀ function can be written as,

Πf lm = λm + Xlmβ + γNlm + εf lm

(16)

where λm is the market-level characteristics of market m, Xlm is the character-
istics of location l in market m, and Nlm is the number of dialysis facilities located
at location l in market m. εf lm is the facility-speciﬁc unobservable data for dialysis
facilities operating at location l in market m. I assume that each facility’s ε is pri-
vate information and independently and identically distributed (i.i.d) from the type-I
extreme value distribution. Because the idiosyncratic error of each ﬁrm, ε, is private
information, each facility will choose the optimal location that maximizes the expected
payoﬀ based on the expected location choices of other facilities and the distribution

52The decision of no entry is labeled as 0.

67

of private information, ε. To simplify the solution process, I assume that all dialysis
facilities are homogeneous as explained in Section 3.3.1. The expected payoﬀ of a ﬁrm
at location l in market m is

E(Πf lm) = λm + Xlmβ + γ{(ηm − 1)plm + 1} + εf lm

(17)
where (ηm − 1) is the total number of competitors that entered market m and
plm is the probability that competing facilities choose location l in market m, plm =
P r[E(Πlm) ≥ E(Πkm), ∀k (cid:54)= l].

Due to the assumption on the distribution of private information, ε, the condi-
tional probability of choosing location l given entry in market m can be simpliﬁed as
follows:

plm = P r(locate at l | Entry in m)

exp[λm + Xlmβ + γ{(ηm − 1)plm + 1}]
exp[λm + Xjmβ + γ{(ηm − 1)pjm + 1}]
exp{Xlmβ + γ + (ηm − 1)γplm}
exp{Xjmβ + γ + (ηm − 1)γplm}

=

=

(cid:80)
(cid:80)

j

j

(18)

In a free market assumption, dialysis facilities will enter the market until they
can earn nonnegative proﬁts by providing dialysis treatment. Hence, at equilibrium,
an additional entrant in the market will gain negative proﬁt. Based on this idea, I
assume that the outside payoﬀ of not entering market m is zero. Given the assumption
of private information, ε, the probability of entry in market m can be derived as the
combination of the average expected payoﬀ for each location in the market and the
outside payoﬀ.

exp(λm)[(cid:80)
1 + exp(λm)[(cid:80)

j

j

68

P r(Entry in m) =

exp{Xjmβ + γ + (ηm − 1)γpjm}]
exp{Xjmβ + γ + (ηm − 1)γpjm}]

(19)

Therefore, the expected number of entrants in market m can be derived by

calculating the following:

ηm = P r(Entry in m) × Fm

(20)

where Fm is the number of potential entrants in market m.

3.4.2

Identiﬁcation

A joint equilibrium that predicts the probability of location choice and market entry
can be derived by using Equations (18) and (20). The system of equations is highly
nonlinear and diﬃcult to solve because the market characteristics, λ, are unobserved.
To simplify the solution process, I follow the logic of Seim (2006), which assumes that
the expected number of entrants in each market is the same as the number of actual
entrants observed in the data by adjusting the market characteristics, λ. When we
solve equations (19) and (20), market characteristics λ can be derived as a function of
location characteristics.

λm = ln(ηm) − ln(Fm − ηm) − ln[

(cid:88)

j

exp{Xjβ + γ + (ηm − 1)γpjm)]

(21)

If we substitute the number of actual entrants in ηm of Equation (21), the mar-
ket characteristic λ equalizes the number of expected entrants as the number of actual
entrants. As λ is unobserved in the data, I assume that it is independently and iden-
tically distributed and drawn from the normal distribution with mean µ and variance
σ2.

The parameters to be estimated are θ = (β, γ, µ, σ) where β captures dialysis
facilities’ preference over location characteristics, γ shows the competitive eﬀects across
ﬁrms, and µ and σ determine the distribution of market characteristics. To estimate the
model, I nest the ﬁxed-point algorithm in Equation (18) into a maximum likelihood
routine. Given the parameters, the ﬁxed point solution, pm(X, β, γ, ηm; λm), can be
found which shows the structural probability vector of each location choice in market
m. When we solve this problem for M markets, the estimation problem maximizes the

69

following log-likelihood function:

M(cid:88)

Lm(cid:88)

lnL =

m=1

j=1

njmln(pjm) − M
2

[ln(2π) + ln(σ2)] − 1
2σ2

M(cid:88)

m=1

(λm − µ)2

(22)

where njm is the actual number of dialysis facilities at location j in market m.
The second part of the log-likelihood function shows the market-level characteristics
drawn from the normal distribution.

3.5 Results

Table C.4 reports the parameter estimates of the factors that aﬀect the location of
dialysis facilities. I obtain the parameter estimates by maximizing Equation (22) using
a pattern search algorithm. Because dialysis facilities might operate diﬀerently when
the demand is measured by the current ESRD patients than when the demand is
measured by the population age 65 and older, I estimate separate models for each local
demand measure. I assume that the number of potential entrants, Fm, is twice the
actual number of facilities in each market. As depicted in Equation (18), changing the
size of the potential entrants does not change the location choice decision of the entrants
in each market, and its eﬀect is absorbed by the estimates of market characteristics,
λm. The table additionally shows marginal eﬀect for each exogenous variable. For
each location, I calculate the change in the location-choice probability conditional on
the market entry when its exogenous variable increases by 10 percent. The reported
marginal eﬀects are derived by averaging the change in location-choice probabilities
across all census tracts.

As expected, the parameter estimates show that the attractiveness of a location
is aﬀected by two opposing forces; local demand and potential competition. Column (1)
shows the parameter estimates using the number of current ESRD patients as the local
demand. The number of ESRD patients positively aﬀect the dialysis facility’s proﬁt.
A 10 percent increase in the number of ESRD patients for a speciﬁc location makes
dialysis facilities 2.01 percent more likely to choose the location. On the other hand,
dialysis facilities are less likely to be located in areas with high property rental costs

70

because high rent would increase the cost of operating dialysis facilities. A 10 percent
increase in the gross rental cost for a location implies 1.17 percent lower probability of
the location choice.

The parameter for potentially competing facilities is large and negative. As
rivals entering in the same location will reduce proﬁts, dialysis facilities have a strong
incentive to avoid competition by choosing locations where the other facilities are
not located. When one additional dialysis facility enters a market, the likelihood of
choosing the location where it was most preferred decreases in all markets. On average,
the probability decreases by 1.61%. However, the change increases the likelihood of
choosing the location where it was least preferred by 1.18%, which means that more
expected competitors leads to a more even distributino of dialysis facilities among
locations.

Column (2) reports the parameter estimates using the population over 65 years
and socioeconomic status factors as the measure of the long-run expected local demand
of dialysis treatment. Dialysis facilities prefer locations with more at-risk patients who
are over 65 years of age and have a lower income per capita and a cheaper property
rental cost. When a location’s population with age 65 and above increases by 10
percent, dialysis facilities are 3.85 percent more likely to select this location. However,
income per capita is negatively related to the location-choice probability. For the same
level of change in income per capita, the likelihood of the location-choice decreases by
3.73 percent. With regard to education level, I ﬁnd that dialysis facilities are less likely
to be located in areas with a high share of poorly educated individuals. The negative
eﬀect of the gross rental cost is larger in Column (2). A 10 percent increase in the gross
rental cost of a location reduces the location-choice probability by 2.97 percent, which
is twice as high as the magnitude of the marginal eﬀect in Column (1). The eﬀect
of competition still negatively aﬀects the dialysis facility’s location choice in Column
(2). Although the size of the competition parameter, γ, is smaller in Column (2), the
impact of one additional entrant in a market is similar to that in Column (1). When
one additional facility enters a market, the probability of choosing the previously most
preferred location decreases by 1.2% and the probability of choosing the least preferred
location increases by 0.89%.

71

3.6 Robustness Check

This section presents a series of analyses to test the robustness of the main parameter
estimates. First, in Table C.5, I loosen the restrictions on the population size of the
largest city within 20 miles from each sample market to include more markets in the
analysis sample.
In the original sample, I excluded markets where the largest city
within a distance of 20 miles has a population greater than 25,000, and the parameter
estimates are shown in Columns (1) and (2). Columns (3) and (4) show parameter
estimates when I loosen the restriction of the population size to 40,000. With this
adjustment, 19 additional markets are included in the analysis sample. Finally, in
Columns (5) and (6), I increase the population cutoﬀ to 50,000, which is the minimum
population size of the sample market. Although more markets are added in the analysis
sample, the sign of most parameter estimates is the same as that of the main parameter
estimates of the base model. The magnitudes of the estimates slightly increase as the
number of sample markets increases, although the change is not that huge when we
consider the standard errors. With regard to the competition eﬀect, the magnitudes of
the estimates in Columns (5) and (6) were the largest for both of the dialysis demand
assumptions.

Second, I examine whether the main parameter estimates are aﬀected by the
size of potential entrants. As shown in Columns (1) and (2) of Table C.6, in the
base model, I assumed that the number of potential entrants is twice the number of
actual entrants in each dialysis market. In Section 3.4.2, the market characteristics,
λ, equalize the number of expected entrants as the number of actual entrants. Hence,
the location decision upon market entry should not be aﬀected by the change in the
number of potential entrants. For the test, I increased the number of potential entrants
by threefold and fourfold, and the estimates are reported in Columns (3) to (6). If a
smaller share of potential entrants enter the market, it would mean that the markets
are not attractive to potential entrants. This change would be indicated by a lower
estimate of the mean market characteristics, µ. This result is not found in the estimates
using the number of current ESRD patients as the demand factor. The estimates of
µ in Columns (3) and (5) are similar to that in Column (1). On the other hand, the
estimates using key factors related to ESRD incidence follow our expectations. The

72

estimate decreases from -2.0027 in Column (2) to -3.3038 in Column (6). Except for
the estimate of µ, the other estimates are similar in magnitude as expected.

3.7 Conclusions

In this paper, I estimate a simultaneous game for the entry and location choice decisions
of dialysis facilities. The model is set up as an incomplete information game among
potential entrants in the dialysis industry where facilities have private information on
their location-speciﬁc proﬁt shocks. The results show that dialysis facilities choose
their locations strategically and there is a tradeoﬀ between local demand and expected
competition. Firms prefer locations with more at-risk people, such as ESRD patients
or a high population of individuals with ages over 65, and lower per capita income.
From the cost perspective, these ﬁrms prefer locations with low property rental costs.
In terms of competitive interactions, all ﬁrms exert a negative impact on their potential
competitors in the same location.

There are several caveats to this paper and directions for future research. First,
I consider only the eﬀects of local demand and competitive interactions in the im-
mediate location. The related literature (Seim 2006; Orhun 2006; Zhu et al. 2009;
Gowrisankaran et al. 2011) incorporates distance band terms in models to observe how
the eﬀects change as distance from the targeted location increases. Because I assume
that dialysis facilities consider overall ESRD patients in a market as their demand,
this approach would lead to more reasonable parameter estimates. Second, this paper
only analyzes entry and location choice decisions of freestanding and for-proﬁt dialysis
facilities because the other types of facilities, such as hospital-based or not-for-proﬁt
facilities, may have objective functions other than proﬁt maximization. Although the
goal of these facilities is diﬀerent from that of the facilities studied here, the existence of
those facilities might exert negative impacts on expected proﬁts and result in a diﬀerent
site selection in a market. Third, the model in this paper might simplify the dialysis
industry too much and be not enough to analyze the spatial competition among dialysis
facilities. The key assumption of the model used in this paper is that dialysis facilities
are symmetric. However, the existence of a dialysis chain could weaken the assump-
tion. In 2012, approximately 76 percent of dialysis facilities are chain-aﬃliated, such

73

as Davita and Fresenius (Eliason 2017). Because chain-aﬃliated facilities could have
lower cost of operation, they might not be symmetric with the other dialysis facilities.
Additionally, this model does not consider the dynamics in the dialysis industry and
focuses on the distribution of dialysis facilities in 2015. Because the USRDS dataset
includes all the information on the entry and exit of dialysis facilities in the U.S. and
their characteristics, the estimation model that can analyze the longitudinal data will
provide valuable insights on the overall dialysis market.

74

APPENDICES

75

Appendix A Tables and Figures for Chapter 1

Table A.1 Descriptive statistics for liver transplant candidates

VARIABLES
Blood type

Gender

Age at transplant

Race

Education

A
B
O

Male

Age

White
Black
Asian

High school
Attend college
Bachelor
Grad school

Private insurance
Medicare
Medicaid

Payment source

Observations

(1)
(2)
aM ELD ≥ 35
SD
Mean

0.361
0.035
0.122

0.480
0.185
0.327

(3)

(4)
aM ELD < 35
Mean
SD

(5)
(6)
Status 1A
SD

Mean

0.378
0.036
0.122

0.485
0.187
0.327

0.338
0.043
0.136

0.473
0.202
0.343

0.628

0.483

0.648

0.478

0.387

0.487

52.36

11.06

55.02

10.31

43.70

15.03

0.381
0.325
0.198

0.488
0.414
0.354
0.239

0.499
0.399
0.410

0.824
0.120
0.041

0.392
0.220
0.146
0.061

0.532
0.198
0.214
5292

0.858
0.095
0.034

0.397
0.238
0.169
0.071

0.533
0.254
0.159
37,125

0.349
0.293
0.181

0.489
0.426
0.374
0.257

0.499
0.435
0.366

0.449
0.385
0.270

0.480
0.422
0.364
0.244

0.493
0.337
0.392

0.719
0.181
0.079

0.361
0.231
0.157
0.064

0.584
0.130
0.190
1,882

Notes: The table displays the means and standard deviation of transplant candidates categorized by health
status at the time of waitlist registration; aM ELD ≥ 35, aM ELD < 35, and Status 1A

76

Table A.2 Eﬀect of aM ELD ≥ 35 on patient outcomes, RD estimates

(1)

(2)

(3)

(4)

Transplant

Waitlist mortality

(6)

(5)
Overall mortality

(7)

90 d

180 d
Panel A. First stage and reduced form results
aM ELD ≥ 35

90 d

-0.059
(0.040)
0.186
1,524
1.852

-0.074*
(0.041)
0.210
1,538
2.043

1 yr

90 d

180 d

1 yr

-0.076*
(0.043)
0.222
1,589
2.606

-0.045

-0.026
-0.014
(0.042) (0.044) (0.055)
0.295
0.225
1,740
1,249
2.031
2.161

0.261
1,691
2.312

0.136***
(0.049)
0.704
1,399
1.681

Mean below 35
Observations
Bandwidth

Panel B. Fuzzy RD estimates
Pr (Transplant)

Observations
Bandwidth

-0.438** -0.554*** -0.651***
(0.202)
(0.204)
1,589
1,524
1.852
2.606

(0.192)
1,538
2.043

-0.351

-0.197
-0.114
(0.282) (0.281) (0.418)
1,249
1,740
2.161
2.031

1,691
2.312

Notes: The table shows the RD estimates for access to liver transplants and mortality rates. Each regression
includes the indicator for aM ELD ≥ 35 and a linear spline of the running variable, aMELD scores. Robust
standard errors are reported in parentheses.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

Table A.3 Eﬀect of the Share 35 policy on patient outcomes, DD estimates

(1)

(2)

(3)

(4)

(5)

(6)

(7)

Transplant

Waitlist mortality

Overall mortality

aM ELD ≥ 35

Mean
Observations

90 d
0.051*
(0.028)
0.633
6,724

90 d

180 d

1 yr

90 d

180 d

1 yr

-0.084*** -0.095*** -0.099*** -0.010*** -0.119*** -0.147***
(0.024)
(0.040)
0.409
0.299
6,724
5,018

(0.026)
0.302
6,152

(0.031)
0.381
6,152

(0.029)
0.306
5,018

(0.029)
0.362
6,724

aM ELD < 35 -0.051*
(0.026)
0.301
36,008

Mean
Observations

0.002
(0.018)
0.088
36,008

-0.018
(0.018)
0.135
33,044

-0.032
(0.022)
0.183
26,819

-7.13e-05
(0.020)
0.102
36,008

-0.021
(0.020)
0.162
33,044

-0.051*
(0.026)
0.233
26,819

Notes: The table shows DD estimates for access to liver tranplants and mortality rates. The estimation
includes waitlisted transplant center ﬁxed eﬀects, waitlisted year ﬁxed eﬀects, and covariates of transplant
candidates (blood type, gender, age at waitlist registration, race, education level, payment source). Standard
errors clustered at the waitlisted transplant center level are in parentheses.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

77

Table A.4 Eﬀect of the Share 35 policy on transplanted liver quality

(1)

(2)

(3)

(4)

(5)

(6)

Regional Log (Dist) Log (CIT) Donor age BMI Donation after
over 35 Cardiac Death
-0.004
(0.016)
0.090
9,432

share
0.359***
(0.037)
0.223
9,432

over 70
-0.001
(0.008)
0.015
9,432

0.001
(0.013)
0.026
9,432

aM ELD ≥ 35

Mean

Observations

0.828***
(0.123)
3.733
9,432

0.047***
(0.018)
1.952
9,432

aM ELD < 35

Mean

Observations

-0.031
(0.037)
0.177
25,343

-0.109
(0.136)
3.594
25,343

-0.015
(0.018)
1.927
25,343

0.003
(0.010)
0.038
25,343

0.018
(0.015)
0.121
25,343

0.033***
(0.012)
0.053
25,343

Notes: The table shows DD estimates for the transplanted liver quality. The estimation includes waitlisted
transplant center ﬁxed eﬀects, waitlisted year ﬁxed eﬀects, and covariates of transplant recipients (blood type,
gender, age at transplants, race, education level, payment source). Standard errors clustered at the waitlisted
transplant center level are in parentheses. “Dist” means the distance between the donor hospital and recipient
hospital. “CIT” means the cold ischemia time, which is the time between liver removal from the donor and
transplant. “BMI” means the body mass index.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

Table A.5 Eﬀect of the Share 35 policy on posttransplant survival

(1)

Ex-post
Survival

1 yr
0.039
(0.026)
0.827
7,874

-0.006
(0.019)
0.899
20,800

(2)

(3)
Ex-ante

(4)

(5)

- Log (DRI)

Predicted survival

-0.026***
(0.009)
-0.977
9,432

-0.014*
(0.008)
-1.005
25,343

1 yr
-0.008*
(0.004)
0.826
9,432

3 yr
-0.008
(0.005)
0.729
9,432

5 yr
-0.007
(0.005)
0.656
9,432

-0.011**
(0.004)
0.876
25,343

-0.010**
(0.004)
0.779
25,343

-0.009**
(0.004)
0.701
25,343

aM ELD ≥ 35

Mean
Observations

aM ELD < 35

Mean
Observations

Notes: The table shows DD estimates for the outcomes related to posttransplant survival rates. Columns
(1)-(2) include the waitlisted transplant center ﬁxed eﬀect, transplant year ﬁxed eﬀect, and covariates of liver
transplant recipients (blood type, gender, age at transplants, race, education level, payment source). As the
posttransplant survival prediction model uses speciﬁc recipient and donor covariates, Columns (3)-(5) use the
set of recipient covariates in Table A.13 along with the same set of ﬁxed eﬀects. Standard errors clustered at
the waitlisted transplant center level are in parentheses.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

78

Table A.6 Eﬀect of the Share 35 policy on liver oﬀer acceptance

aM ELD ≥ 35

Mean
Observations

(1)

(2)

(3)

(4)

(5)

-0.124*** -0.102***
(0.022)
(0.022)
0.560
0.560
21,020
21,020

aM ELD < 35

Mean
Observations
Donor covariates
Candidate covariates

-0.035
(0.022)
0.445
34,378

N
Y

-0.023
(0.022)
0.445
34,378

Y
Y

-0.010
(0.023)
0.442
11,942

Y
Y

0.008
(0.029)
0.455
4,896

Y
Y

Treatment group by aM ELD (M ) update frequency
25 ≤ M < 35 19 ≤ M < 25
(1 month)

15 ≤ M < 19
(3 months)

(7 days)
-0.038*
(0.022)
0.446
23,050

Y
Y

Notes: The table shows DD estimates for the liver oﬀer-acceptance rates. Column (1) includes waitlisted
transplant center ﬁxed eﬀects, waitlisted year ﬁxed eﬀects, and covariates of transplant candidates (blood
type, gender, age at waitlist registration, race, education level, payment source). Columns (2)-(5) addtionally
include donor characteristics (age, cause of death, indicator of liver sharing, distance between donor transplant
center and waitlisted transplant center, and BMI). Standard errors clustered at the waitlisted transplant center
level are in parentheses.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

Table A.7 [Placebo test] Eﬀect of aM ELD ≥ 35 on patient outcomes

(1)

Transplant

(3)

(2)
(4)
Waitlist mortality

aM ELD ≥ 35

Mean below 35
Observations
Bandwidth

90 d
-0.084
(0.069)
0.658
931
2.634

180 d
0.053

1 yr
90 d
0.071
-0.007
(0.068) (0.077) (0.084)
0.227
0.261
560
732
2.134
2.509

0.252
614
2.051

(6)

(5)
Overall mortality

(7)

180 d
0.038

1 yr
90 d
0.086
-0.004
(0.081) (0.097) (0.105)
0.300
0.399
392
577
1.692
1.847

0.341
441
1.513

Notes: The table shows the RD estimates for access to liver transplants and mortality rates. Each regression
includes the indicator for aM ELD ≥ 35 and a linear spline of the running variable, aMELD. Robust standard
errors are reported in parentheses.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

79

Table A.8 Diagnosis for exception MELD score

Diagnosis

Cholangiocarcinoma

Cystic Fibrosis

Familial Amyloid Polyneuropathy (FAP)

Hepatic Artery Thrombosis (HAT)

exception MELD

Growth

eMELD 22
eMELD 22
eMELD 22
eMELD 40

10% point increase every 3 months
10% point increase every 3 months
10% point increase every 3 months

Hepatocellular Carcinoma (HCC)

Hepatopulmonary Syndrome (HPS)

Portopulmonary Hypertension

Primary Hyperoxaluria

cMELD until 6 months
eMELD 28 after then

Increase by 34 every 3 months

eMELD 22
eMELD 22
eMELD 28

10% point increase every 3 months
10% point increase every 3 months
10% point increase every 3 months

Sources: OPTN Policies (OPTN 2017).
Notes: Exception PELD score is excluded in the table.

Table A.9 Balance of covariates

VARIABLES
aM ELD ≥ 35

Mean below cutoﬀ
Observations
Bandwidth

VARIABLES
aM ELD ≥ 35

Mean below cutoﬀ
Observations
Bandwidth

VARIABLES
aM ELD ≥ 35

Mean below cutoﬀ
Observations
Bandwidth

(1)
A

-0.002
(0.047)
0.375
2,013
2.452

White
0.056
(0.040)
0.832
1,561
1.765

(2)
B

0.037
(0.044)
0.139
1,185
1.444

Black
-0.030
(0.032)
0.109
1,754
2.023

(3)
O

-0.081
(0.067)
0.465
1,107
1.291

Asian
-0.009
(0.018)
0.032
1,234
1.491

Bachelor Graduate Private ins.

0.044
(0.042)
0.152
1,518
1.722

-0.012
(0.025)
0.064
2,197
2.522

0.014
(0.054)
0.527
1,686
1.944

(4)
Male
0.016
(0.046)
0.588
2,176
2.513

(5)
Age
0.525
(0.972)
53.26
2,334
2.738

High school

Attend college

-0.101
(0.063)
0.412
1,158
1.389

Medicaid
-0.013
(0.045)
0.204
1,584
1.797

0.007
(0.043)
0.225
1,795
2.098

Medicare

0.031
(0.051)
0.220
1,388
1.528

Notes: The table shows the estimated discontinuities of predetermined characteristics for transplant candi-
dates. In addition to the indicator for aM ELD ≥ 35, each regression includes a linear spline of the running
variable, aMELD. Robust standard errors are reported in parentheses.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

80

Table A.10 Eﬀect of aM ELD ≥ 35 on patient outcomes

(1)

Transplant

90 d

(2)

(3)

(4)

Waitlist mortality

90 d

180 d

1 yr

(5)

(6)

(7)

Overall mortality

90 d

180 d

1 yr

Panel A. Standard RD estimates
aM ELD ≥ 35

0.136***
(0.049)
1,399
1.681

-0.059
(0.040)
1,524
1.852

-0.074*
(0.041)
1,538
2.043

-0.076*
(0.043)
1,589
2.606

-0.026
(0.042)
1,740
2.161

-0.045
(0.044)
1,691
2.312

-0.014
(0.055)
1,249
2.031

Observations
Bandwidth

Panel B. Donut RD estimates
aM ELD ≥ 35

0.129**
(0.052)
1,182
1.681

-0.055
(0.043)
1,307
1.852

-0.077*
(0.043)
1,376
2.043

-0.076*
(0.044)
1,476
2.606

-0.027
(0.044)
1,523
2.161

-0.057
(0.047)
1.529
2.312

-0.015
(0.056)
1,177
2.031

Observations
Bandwidth

Notes: The table compares the main RD estimates (Panel A) with the donut RD estimates (Panel B) that
exclude heaped data at the aMELD scores with whole number units. Each regression includes the indicator
for aM ELD ≥ 35 and a linear spline of the running variable, aMELD. Robust standard errors are reported
in parentheses.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

81

Table A.11 Descriptive statistics for liver transplant recipients

VARIABLES
Blood type

Gender

Age at transplant

Race

Education

A
B
O

Male

Age

White
Black
Asian

High school
Attend college
Bachelor
Grad school

Private insurance
Medicare
Medicaid

Payment source

Observations

(1)
(2)
aM ELD ≥ 35
SD
Mean

(3)

(4)
aM ELD < 35
SD
Mean

(5)
(6)
Status 1A
SD

Mean

0.366
0.116
0.488

0.482
0.320
0.500

0.363
0.148
0.432

0.481
0.356
0.495

0.335
0.141
0.473

0.472
0.349
0.499

0.627

0.484

0.695

0.460

0.382

0.486

53.18

10.93

56.65

9.66

44.14

14.96

0.363
0.302
0.196

0.488
0.426
0.361
0.245

0.498
0.403
0.401

0.844
0.102
0.040

0.392
0.239
0.154
0.064

0.546
0.204
0.201
8,208

0.359
0.298
0.198

0.491
0.426
0.378
0.259

0.496
0.435
0.342

0.848
0.099
0.041

0.405
0.239
0.173
0.072

0.561
0.253
0.135
24,119

0.462
0.397
0.284

0.479
0.427
0.375
0.262

0.487
0.334
0.377

0.693
0.196
0.088

0.355
0.240
0.169
0.074

0.616
0.127
0.172
1,224

Notes: The table displays the means and standard deviations of transplant recipients categorized by health
status at the time of transplantation; aM ELD ≥ 35, aM ELD < 35, and Status 1A

82

Table A.12 Descriptive statistics for liver candidates in the match-run sample

VARIABLES
Blood type

Gender

Age at registration

Race

A
B
O

Male

Age

White
Black
Asian

Education

Payment

Observations

High school
Attend college
Bachelor
Grad school

Private insurance
Medicare
Medicaid

(2)

(1)
aM ELD ≥ 35
Mean

SD

(3)

(4)
aM ELD < 35
SD
Mean

(5)
(6)
Status 1A
SD

Mean

0.344
0.144
0.482

0.475
0.351
0.500

0.371
0.160
0.393

0.483
0.367
0.488

0.347
0.165
0.433

0.476
0.371
0.496

0.561

0.496

0.642

0.479

0.354

0.478

51.09

12.99

54.64

11.01

43.13

15.59

0.396
0.341
0.209

0.491
0.422
0.364
0.230

0.500
0.428
0.400

0.805
0.135
0.046

0.406
0.232
0.158
0.056

0.515
0.241
0.200
18,444

0.372
0.312
0.205

0.489
0.423
0.386
0.256

0.498
0.440
0.343

0.834
0.109
0.044

0.397
0.234
0.182
0.070

0.546
0.262
0.137
31,802

0.470
0.411
0.290

0.486
0.432
0.346
0.247

0.492
0.357
0.377

0.671
0.215
0.092

0.381
0.249
0.139
0.065

0.591
0.150
0.171
2,576

Notes: The table displays the means and standard deviations of transplant candidates categorized by health
status at the time of liver oﬀer; aM ELD ≥ 35, aM ELD < 35, and Status 1A

83

Table A.13 Selected variables by LASSO (40 variables)

Donor characteristics
Share = Regional
Age
Height
Cause of Death = Cerebrovascular accident
History of diabetes
Donation after Cardiac Death
Anti-Cytomegalovirus = Positive
Cold ischemia time (CIT)
Ethnicity = Latino
Weight
History of cocaine use
Death mechanism = Drug intoxication
[Square] CIT
History of other drug abuse, last 6 month
Tattoos
[Square] Height

Count Recipient characteristics

Count

Age
Race = Black
Race = Asian

Previous transplant
Previous abdominal surgery

5
5
5
5
5
5
5 Weight
5
5
5
5
5
5
5 Medical condition = ICU
5 Medical condition = Hospitalized not ICU 5
5
4
5
4
4
5
5
4
5
4
3
5
5
3
3
5
4
4
4
4
4
3
3
3

Hepatic encephalopathy
Primary diagnosis = Cholestatic cirrhosis
Primary diagnosis = Malignant neoplasms
Albumin
On ventilator
Any previous malignancy
Acute rejection episodes
[Square] Weight
History of Portal Vein Thrombosis
aMELD score
Primary diagnosis = Metabolic disease
[Square] Age
[Square] Albumin
Male
Ethnicity = Latino
[Square] Height

Notes: The table displays the variables selected by the LASSO algorithm to predict the 5-year posttransplant
survival rates of liver transplant recipients. Only variables selected at least 3 times among 5 estimations using
diﬀerent sample sets as the test sample are included.

84

Table A.14 Comparison of the predictive power

DRI
Variables of DRI
LASSO
LASSO w/ interaction
Observations

(1)
1st

0.2136
0.2130
0.2084
0.2093
8948

(2)
2nd
0.2079
0.2074
0.2011
0.2041
8979

(3)
3rd

0.2015
0.2010
0.1950
0.1990
8948

(4)
4th

0.2085
0.2080
0.2027
0.2070
8892

(5)
5th

0.2071
0.2062
0.2003
0.2059
8961

(6)

Average
0.2077
0.2071
0.2015
0.2050

Notes: The table displays the Brier scores, which calculate the mean squared error of the predicted probability,
for diﬀerent prediction models. As the prediction model was tested ﬁve times using one of 5 sample sets as
the test sample, each prediction model contains ﬁve Brier scores. Column (6) shows the average Brier score
for each prediction model.

Figure A.1 DSAs and Regions in U.S.

Figure A.2 Eﬀect of the Share 35 policy on the liver transplant market

85

Sources: OPTN Policies (OPTN 2017).
Notes: Allocation for candidates with aMELD scores less than 15 is excluded in the ﬁgure. After the match
in the ﬁgure, the donated liver is matched to candidates with aMELD scores of at least 15 and waitlisted in
the U.S. If the liver is not accepted, then candidates with aMELD scores of less than 15 are matched to the
liver in order of DSA, Region, and Nation.

Figure A.3 Deceased donor liver allocation process under the Share 35 policy

86

(a) Transplant

(b) [90d] Waitlist mort

(c) [180d] Waitlist mort

(d) [1yr] Waitlist mort

(e) [90 d] Overall mort

(f) [180d] Overall mort

(g) [1yr] Overall mort

Notes: Panels (a)-(g) plot the mean values of outcome variables along with linear ﬁtted lines (solid lines)
and the 95% conﬁdence intervals (shaded area) below and above the aMELD score 35 threshold. Each bin is
divided by the same width, and the size of each dot is scaled according to the number of observations in each
bin.

Figure A.4 Eﬀect of the Share 35 policy on patient outcomes

87

Notes: The ﬁgure plots the frequency of liver oﬀers, that were matched to top-ranked transplant candidates,
for each aMELD score at the time of oﬀer. As the number of donated livers is diﬀerent before and after
the Share 35 policy implementation, the adjusted number of liver oﬀers per 1000 donors is reported for each
aMELD score.

Figure A.5 Change in the access to liver oﬀers

88

(a) Transplant, lin

(b) Transplant, quad

(c) Waitlist mort, 90 days, lin

(d) Waitlist mort, 90 days, quad

(e) Waitlist mort, 180 days, lin

(f) Waitlist mort, 180 days, quad

(g) Waitlist mort, 1 year, lin

(h) Waitlist mort, 1 year, quad

Notes: I repeated the estimation for each dependent variable for a diﬀerent choice of bandwidth and polyno-
mial. I test the bandwidth range from 1 to 4 for every 0.25 units. The degrees of polynomials are degree 1
(linear) and degree 2 (quadratic).

Figure A.6 Sensitivity to bandwidth and polynomial

89

(a) Overall mort, 90 days, lin

(b) Overall mort, 90 days, quad

(c) Overall mort, 180 days, lin

(d) Overall mort, 180 days, quad

(e) Overall mort, 1 year, lin

(f) Overall mort, 1 year, quad

Notes: I repeated the estimation for each dependent variable for a diﬀerent choice of bandwidth and polyno-
mial. I test the bandwidth range from 1 to 4 for every 0.25 units. The degrees of polynomials are degree 1
(linear) and degree 2 (quadratic).

Figure A.7 Sensitivity to bandwidth and polynomial

90

(a) Transplant

(b) [90 d] Waitlist mort

(c) [180 d] Waitlist mort

(d) [1 yr] Waitlist mort

(e) [90 d] Overall mort

(f) [180 d] Overall mort

(g) [1 yr] Overall mort

Notes: Panels (a)-(g) plot the estimated coeﬃcients from the event study model for the access to liver trans-
plants and mortality rates for transplant candidates with aMELD scores greater than or equal to 35. The
dashed vertical line shows the year when the Share 35 policy was implemented, and the baseline year is one
year prior to the year of policy implementation. The estimation includes waitlisted transplant center ﬁxed
eﬀects, waitlisted year ﬁxed eﬀects, and covariates of transplant candidates (blood type, gender, age at wait-
list registration, race, education level, payment source). Standard errors clustered at the waitlisted transplant
center level are used for 95 percent conﬁdence intervals.

Figure A.8 Event study, transplant and mortality for aM ELD ≥ 35

91

(a) Transplant

(b) [90 d] Waitlist mort

(c) [180 d] Waitlist mort

(d) [1 yr] Waitlist mort

(e) [90 d] Overall mort

(f) [180 d] Overall mort

(g) [1 yr] Overall mort

Notes: Panels (a)-(g) plot the estimated coeﬃcients from the event study model for the access to liver trans-
plants and mortality rates for transplant candidates with aMELD scores greater than or equal to 35. The
dashed vertical line shows the year when the Share 35 policy was implemented, and the baseline year is one
year prior to the year of policy implementation. The estimation includes waitlisted transplant center ﬁxed
eﬀects, waitlisted year ﬁxed eﬀects, and covariates of transplant candidates (blood type, gender, age at wait-
list registration, race, education level, payment source). Standard errors clustered at the waitlisted transplant
center level are used for 95 percent conﬁdence intervals.

Figure A.9 Event study, transplant and mortality for aM ELD < 35

92

(a) Regional share

(b) Log (Distance)

(c) Log (CIT)

(d) Donor age, over 70

(e) BMI over 35

(f) Donation after cardiac death

(g) Survival, 1 year

(h) - Log (DRI)

(i) Predicted survival, 1 year

(j) Predicted survival, 3 year

(k) Predicted survival, 5 year

Notes: Panels (a)-(k) plot the estimated coeﬃcients from the event study model for transplanted liver quality
for transplant recipients with aMELD scores greater than or equal to 35. The dashed vertical line shows
the year when the Share 35 policy was implemented, and the baseline year is one year prior to the year of
policy implementation. The estimation includes waitlisted transplant center ﬁxed eﬀects, waitlisted year ﬁxed
eﬀects, and covariates of transplant recipients (blood type, gender, age at transplantation, race, education
level, payment source). As the posttransplant survival prediction model uses speciﬁc recipient and donor
covariates, panels (i)-(k) use the set of recipient covariates in Table A.13. Standard errors clustered at the
waitlisted transplant center level are used for 95 percent conﬁdence intervals.

Figure A.10 Event study, transplantation quality for aM ELD ≥ 35

93

(a) Regional share

(b) Log (Distance)

(c) Log (CIT)

(d) Donor age, over 70

(e) BMI over 35

(f) Donation after cardiac death

(g) Survival, 1 year

(h) - Log (DRI)

(i) Predicted survival, 1 year

(j) Predicted survival, 3 year

(k) Predicted survival, 5 year

Notes: Panels (a)-(k) plot the estimated coeﬃcients from the event study model for transplanted liver quality
for transplant recipients with aMELD scores below 35. The dashed vertical line shows the year when the
Share 35 policy was implemented, and the baseline year is one year prior to the year of policy implementation.
The estimation includes waitlisted transplant center ﬁxed eﬀects, waitlisted year ﬁxed eﬀects, and covariates
of transplant recipients (blood type, gender, age at transplantation, race, education level, payment source).
As the posttransplant survival prediction model uses speciﬁc recipient and donor covariates, panels (i)-(k) use
the set of recipient covariates in Table A.13. Standard errors clustered at the waitlisted transplant center level
are used for 95 percent conﬁdence intervals.

Figure A.11 Event study, transplantation quality for aM ELD < 35

94

(a) Accept, w/o donor cov.

(b) Accept

Notes: Panels (a)-(b) plot the estimated coeﬃcients from the event study model for liver oﬀer-acceptance
rates for transplant candidates with aMELD scores greater than or equal to 35. The dashed vertical line
shows the year when the Share 35 policy was implemented, and the baseline year is one year prior to the
year of policy implementation. Panel (a) includes waitlisted transplant center ﬁxed eﬀects, waitlisted year
ﬁxed eﬀects, and covariates of transplant candidates (blood type, gender, age at waitlist registration, race,
education level, payment source). Panel (b) additionally includes donor characteristics (age, cause of death,
indicator of liver sharing, distance between donor hospital and waitlisted transplant center). Standard errors
clustered at the waitlisted transplant center level are used for 95 percent conﬁdence intervals.
Figure A.12 Event study, liver oﬀer acceptance for aM ELD ≥ 35

95

(a) Accept, w/o donor cov.

(b) Accept

(c) 25 ≤ aM ELD < 35

(d) 19 ≤ aM ELD < 25

(e) 15 ≤ aM ELD < 19

Notes: Panels (a)-(e) plot the estimated coeﬃcients from the event study model for liver oﬀer-acceptance rates
for transplant candidates with aMELD scores below 35. The dashed vertical line shows the year when the Share
35 policy was implemented, and the baseline year is one year prior to the year of policy implementation. Panel
(a) includes waitlisted transplant center ﬁxed eﬀects, waitlisted year ﬁxed eﬀects, and covariates of transplant
candidates (blood type, gender, age at waitlist registration, race, education level, payment source). Panels (b)-
(e) additionally include donor characteristics (age, cause of death, indicator of liver sharing, distance between
donor hospital and waitlisted transplant center). Standard errors clustered at the waitlisted transplant center
level are used for 95 percent conﬁdence intervals.

Figure A.13 Event study, liver oﬀer acceptance for aM ELD < 35

96

(a) Mean frequency (0.4 binwidth)

(b) Histogram (0.01 binwidth)

(c) Histogram (using previous MELD)

(d) Histogram (using new MELD with
sodium)

Notes: Panel (a) plots the mean frequency along with the linear ﬁtted line and the 95% conﬁdence interval
above and below the aMELD threshold score of 35. Panel (b) plots the frequency of aMELD scores within the
bandwidth 4 units from an aMELD score of 34.5. Panels (c)-(d) plot the frequency of aMELD scores by the
applicability of the new aMELD score system, implemented in January 2016, which also considers the level of
serum sodium. Only the candidates in panel (d) are aﬀected by the new aMELD score system.

Figure A.14 aMELD distribution

97

Appendix B Tables and Figures for Chapter 2

Table B.1 Kidney allocation points

Candidates’ condition

Kidney points

Waiting time

1/365 points for each day

Aged 0-10 at time of match
Perfect tissue type match

Age 11-17 at time of match
Perfect tissue type match

A prior living donor

Sensitized

CP RA ≥ 80

⇓ [Dec 4, 2014]

Sliding scale

4 points

3 points

4 points

4 points

Table 2

Sources: OPTN, “OPTN Policies”, (2017), p.79.

Table B.2 Scale of sensitization points (From December 4, 2014)

0

CPRA Sensitization Point
0∼19
20∼29
30∼39
40∼49
50∼59
60∼69
70∼74
75∼79
80∼84

0.08
0.21
0.34
0.48
0.81
1.09
1.58
2.46

Sources: OPTN, “OPTN Policies”, (2017), p.79.

CPRA Sensitization Point
85∼89
90∼94

4.05
6.71
10.82
12.17
17.3
24.4
50.09
202.1

95
96
97
98
99
100

98

Table B.3 Summary statistics of outcomes

Transplant

Deceased donor
Living donor

Waitlist mortality
Overall mortality

Observations

(1)
All
0.23
0.15
0.08
0.18
0.20
49055

(2)

(3)

CP RA < 80 CP RA ≥ 80

0.23
0.14
0.09
0.18
0.20
37637

0.24
0.21
0.04
0.20
0.22
11418

Notes: The table shows the mean probability of certain key variables for kidney transplant candidates wait-
listed from October 1, 2009 to December 3, 2014. Candidates with zero CPRA are excluded.

Table B.4 Balance of covariates

VARIABLES
CP RA ≥ 80

mean below cutoﬀ

VARIABLES
CP RA ≥ 80

mean below cutoﬀ

VARIABLES
CP RA ≥ 80

mean below cutoﬀ

(1)
A

0.0113
(0.0182)
0.311

Male

-0.0548***
(0.0156)
0.546

(2)
B

0.00471
(0.0145)
0.160

Age

0.00856
(0.470)
52.346

Private ins.

Public ins.

-0.0114
(0.0190)
0.430

0.0171
(0.0191)
0.541

(3)
O

-0.0149
(0.0194)
0.492

< HS
0.00253
(0.0105)
0.070

BMI
0.0879
(0.221)
29.169

(4)

White
0.0134
(0.0194)
0.556

HS

0.0394**
(0.0192)
0.402

(5)
Black
-0.0144
(0.0187)
0.346

College
-0.0292
(0.0191)
0.409

(6)
Asian
0.00554
(0.0104)

0.075

Postgraduate

0.00543
(0.00898)

0.069

Diabetes On Dialysis
0.0312
(0.0193)
0.449

-0.00362
(0.0157)
0.795

Work
0.00476
(0.0172)

0.301

Notes: The table shows the estimated discontinuities of predetermined characteristics for kidney candidates.
In addition to the indicator for CP RA ≥ 80, each regression includes a linear spline of the running variables,
CPRA. Robust standard errors are reported in parentheses. Public insurance includes Medicare and Medicaid.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

99

Table B.5 The eﬀect of sensitization points on kidney source choice

Baseline

(1)

(2)

(3)

(4)

Panel A. Probability of Receiving a Deceased Donor Kidney (First stage)

CP RA ≥ 80

[0.139]

0.230***
(0.0174)

0.227***
(0.0172)

0.222***
(0.0167)

0.215***
(0.0162)

Panel B. Probability of Receiving a Living Donor Kidney (Reduced form)

CP RA ≥ 80

[0.092]

-0.0399***
(0.00882)

-0.0408***
(0.00861)

-0.0428***
(0.00857)

-0.0410***
(0.00853)

Panel C: Fuzzy RD estimates

Pr (Deceased)

-0.173***
(0.0385)

-0.179***
(0.0379)

-0.192***
(0.0380)

-0.191***
(0.0392)

Observations
Control variables
Year
Transplant Center

49,055

49,055

49,055

49,055

No
No
No

Yes
No
No

Yes
Yes
No

Yes
Yes
Yes

Notes: The table shows the estimated results of the eﬀect of receiving sensitization points on the probability
of receiving kidney transplants from each kidney source. In addition to the indicator for CP RA ≥ 80, each
regression includes a linear spline of the running variables, CPRA. Robust standard errors are reported in
parentheses. The mean probability of each outcome for candidates with CPRAs less than the threshold is
presented in the square brackets.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

100

Table B.6 The eﬀect of sensitization points on waitlist mortality

Panel A. Waitlist mortality rate (Reduced form)

Baseline

(1)

(2)

(3)

(4)

1 year CP RA ≥ 80

2 year CP RA ≥ 80

[0.026]
{39166}

-0.0113*
(0.00655)

-0.0109*
(0.00652)

-0.0109*
(0.00652)

-0.0115*
(0.00655)

[0.065]
{29181}

-0.0283**
(0.0115)

-0.0281**
(0.0115)

-0.0280**
(0.0115)

-0.0292**
(0.0114)

Panel B: Fuzzy RD estimates

1 year Pr (Deceased)

2 year Pr (Deceased)

Control variables
Year
Transplant Center

-0.0449*
(0.0260)

-0.102**
(0.0410)

-0.0442*
(0.0263)

-0.104**
(0.0416)

-0.0447*
(0.0264)

-0.0493*
(0.0279)

-0.103**
(0.0415)

-0.113***
(0.0435)

No
No
No

Yes
No
No

Yes
Yes
No

Yes
Yes
Yes

Notes: The table shows the estimated results for the eﬀect of receiving sensitization points on waitlist mortality
of kidney candidates. In addition to the indicator for CP RA ≥ 80, each regression includes a linear spline of
the running variables, CPRA. Robust standard errors are reported in parentheses. Kidney candidates whose
maximal waiting time, the diﬀerence between the registration date and December 3, 2014, is less than each
analysis period are excluded. The mean probability of each outcome for candidates with CPRAs less than the
threshold is presented in the square brackets. The number of observations for each analysis period is presented
in the curly brackets.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

101

Table B.7 The eﬀect of sensitization points on overall mortality

Panel A. Overall mortality rate (Reduced form)

Baseline

(1)

(2)

(3)

(4)

1 year CP RA ≥ 80

2 year CP RA ≥ 80

[0.029]
{39166}

-0.00779
(0.00725)

-0.00743
(0.00721)

-0.00750
(0.00721)

-0.00797
(0.00724)

[0.074]
{29181}

-0.0253**
(0.0125)

-0.0252**
(0.0123)

-0.0251**
(0.0123)

-0.0262**
(0.0123)

Panel B: Fuzzy RD estimates

1 year Pr (Deceased)

-0.0311
(0.0289)

-0.0302
(0.0292)

-0.0306
(0.0294)

-0.0342
(0.0309)

2 year Pr (Deceased)

-0.0913**
(0.0447)

-0.0931**
(0.0452)

-0.0925**
(0.0450)

-0.102**
(0.0472)

Control variables
Year
Transplant Center

No
No
No

Yes
No
No

Yes
Yes
No

Yes
Yes
Yes

Notes: The table shows the estimated results for the eﬀect of receiving sensitization points on overall mortality
of kidney candidates. In addition to the indicator for CP RA ≥ 80, each regression includes a linear spline of
the running variables, CPRA. Robust standard errors are reported in parentheses. Kidney candidates whose
maximal waiting time, the diﬀerence between the registration date and December 3, 2014, is less than each
analysis period are excluded. The mean probability of each outcome for candidates with CPRAs less than the
threshold is presented in the square brackets. The number of observations for each analysis period is presented
in the curly brackets.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

102

Table B.8 Heterogeneity of fuzzy RD results by candidates’ races

(1)

Living

(2)

(3)
Waitlist mortality
2 year
1 year

(4)

(5)
Overall mortality
2 year
1 year

White

{27008}

Black

{17368}

-0.255***
(0.0655)
[0.13]

-0.119***
(0.0408)
[0.04]

0.0166
(0.0427)
[0.03]

-0.123***
(0.0365)
[0.03]

-0.0885
(0.0611)
[0.07]

-0.109*
(0.0639)
[0.06]

0.0508
(0.0483)
[0.03]

-0.125***
(0.0395)
[0.03]

-0.0694
(0.0677)
[0.08]

-0.0993
(0.0678)
[0.07]

Diﬀerence by races

W - B

-0.136*
(0.077)

0.140**
(0.056)

0.021
(0.088)

0.176***
(0.062)

0.030
(0.096)

Observations

49,055

39,166

29,181

39,166

29,181

Notes: The table shows the heterogeneous estimation results for the eﬀect of increased access to deceased
donor kidneys on kidney candidates’ living donor kidney choices and mortality rates by kidney candidates’
races. The results for other races are excluded from the table. In addition to the indicator for CP RA ≥ 80,
each regression includes a linear spline of the running variables, CPRA. Robust standard errors are reported
in parentheses.
In the mortality analysis, kidney candidates whose maximal waiting time, the diﬀerence
between the registration date and December 3, 2014, is less than each analysis period are excluded. The mean
probability of each outcome for candidates with CPRAs less than the threshold is presented in the square
brackets. The number of observations for each analysis period is presented in the curly brackets.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

103

Table B.9 Heterogeneity of fuzzy RD results by candidates’ blood types

(1)

Living

(2)

(3)

Waitlist mortality
2 year
1 year

(4)

(5)
Overall mortality
2 year
1 year

A type

{15248}

B type

{7804}

O type

{24240}

-0.273***
(0.0614)
[0.12]

-0.282***
(0.103)
[0.08]

-0.0352
(0.0592)
[0.08]

0.0163
(0.0437)
[0.03]

-0.0529
(0.0609)
[0.03]

-0.0713*
(0.0394)
[0.03]

Diﬀerence by blood types

A - B

A - O

B - O

0.010
(0.120)

-0.238***
(0.085)

-0.247**
(0.119)

0.069
(0.075)

0.088
(0.059)

0.018
(0.073)

0.00367
(0.0644)
[0.07]

-0.219**
(0.104)
[0.06]

-0.126*
(0.0657)
[0.06]

0.222*
(0.122)

0.129
(0.092)

-0.093
(0.123)

0.0144
(0.0453)
[0.03]

-0.0839
(0.0641)
[0.03]

-0.0141
(0.0471)
[0.03]

0.098
(0.079)

0.029
(0.065)

-0.070
(0.080)

-0.0127
(0.0676)
[0.08]

-0.222*
(0.115)
[0.07]

-0.0863
(0.0724)
[0.07]

0.209
(0.133)

0.074
(0.099)

-0.136
(0.136)

Observations

49,055

39,166

29,181

39,166

29,181

Notes: The table shows the heterogeneous estimation results for the eﬀect of increased access to deceased donor
kidneys on kidney candidates’ living donor kidney choices and mortality rates by kidney candidates’ blood
types. The results for blood type AB candidates are excluded as the sample size (1764) is too relatively small.
In addition to the indicator for CP RA ≥ 80, each regression includes a linear spline of the running variables,
CPRA. Robust standard errors are reported in parentheses.
In the mortality analysis, kidney candidates
whose maximal waiting time, the diﬀerence between the registration date and December 3, 2014, is less than
each analysis period are excluded. The mean probability of each outcome for candidates with CPRAs less
than the threshold is presented in the square brackets. The number of observations for each analysis period
is presented in the curly brackets.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

104

Table B.10 Heterogeneity of fuzzy RD results by candidates’ dialysis status

(1)

Living

(2)

(3)
Waitlist mortality
2 year
1 year

(4)

(5)
Overall mortality
2 year
1 year

None

{9669}

Dialysis

{39386}

-0.304***
(0.0768)
[0.21]

-0.121***
(0.0416)
[0.06]

0.0256
(0.0424)
[0.02]

-0.0737**
(0.0328)
[0.03]

-0.0625
(0.0558)
[0.05]

-0.113**
(0.0519)
[0.07]

0.0298
(0.0446)
[0.02]

-0.0550
(0.0369)
[0.03]

-0.0522
(0.0614)
[0.06]

-0.100*
(0.0567)
[0.08]

Diﬀerence by dialysis status

None - Dial

-0.183**
(0.087)

0.099*
(0.054)

0.050
(0.076)

0.085
(0.058)

0.048
(0.084)

Observations

49,055

39,166

29,181

39,166

29,181

Notes: The table shows the heterogeneous estimation results for the eﬀect of an increased access to deceased
donor kidneys on kidney candidates’ living donor kidney choices and mortality rates by kidney candidates’
dialysis status. In addition to the indicator for CP RA ≥ 80, each regression includes a linear spline of the
running variables, CPRA. Robust standard errors are reported in parentheses.
In the mortality analysis,
kidney candidates whose maximal waiting time, the diﬀerence between the registration date and December
3, 2014, is less than each analysis period are excluded. The mean probability of each outcome for candidates
with CPRAs less than the threshold is presented in the square brackets. The number of observations for each
analysis period is presented in the curly brackets.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

105

Table B.11 Robustness to the exclusion of outermost observations

(1)

Living

(3)

(2)
Waitlist mortality
2 year
1 year

(4)
(5)
Overall mortality
2 year
1 year

All

Observations

Drop 1%

Observations

Drop 5%

Observations

Drop 10%

Observations

-0.173***
(0.0385)
49,055

-0.170***
(0.0383)
48,810

-0.162***
(0.0379)
46,733

-0.156***
(0.0375)
44,181

-0.0449*
(0.0260)
39,166

-0.0446*
(0.0258)
38,963

-0.0409
(0.0255)
37,324

-0.0374
(0.0251)
35,322

-0.102**
(0.0410)
29,181

-0.100**
(0.0408)
29,035

-0.0845**
(0.0404)
27,820

-0.0826**
(0.0396)
26,409

-0.0311
(0.0289)
39,166

-0.0305
(0.0287)
38,963

-0.0275
(0.0284)
37,324

-0.0236
(0.0280)
35,322

-0.0913**
(0.0447)
29,181

-0.0884**
(0.0445)
29,035

-0.0701
(0.0441)
27,820

-0.0726*
(0.0432)
26,409

Notes: The table shows the RD estimates for each outcome variable after dropping 1%, 5%, and 10% of kidney
candidates far from the CPRA 80 threshold. In addition to the indicator for CP RA ≥ 80, each regression
includes a linear spline of the running variables, CPRA. Robust standard errors are reported in parentheses. In
the mortality analysis, kidney candidates whose maximal waiting time, the diﬀerence between the registration
date and December 3, 2014, is less than each analysis period are excluded. The number of observations for
each analysis period is presented in the curly brackets.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

106

Table B.12 Diﬀerence-in-diﬀerences estimates

(1)

(2)

Living

(3)

(4)

(5)

(6)

Waitlist mortality
2 year
1 year

Overall mortality
2 year
1 year

-0.0474*
(0.0241)
51,584

-0.0166
(0.0168)
41,695

-0.0366
(0.0254)
31,710

-0.0169
(0.0179)
41,695

-0.0332
(0.0239)
31,710

VARIABLES Deceased
Panel A. DD estimates
CPRA80*Post 0.248***
(0.0344)
51,584

Observations

Panel B. RD estimates
CP RA ≥ 80

0.230*** -0.0399*** -0.0113* -0.0283** -0.00779 -0.0253**
(0.0125)
(0.0174)
49,055
29,181

(0.00655)
39,166

(0.00882)
49,055

(0.00725)
39,166

(0.0115)
29,181

Observations

Notes: Panel A shows the diﬀerence-in-diﬀerences estimates for each outcome. Each regression includes
covariates, waitlisted year ﬁxed eﬀects. Standard errors are clustered by kidney candidates’ waitlisted DSAs.
Kidney candidates who received sensitization points based on their (traditional) PRA are excluded from the
control group. Panel B shows the RD estimates for each outcome variable in the analysis period. (October
1, 2009 - December 3, 2014) In addition to the indicator for CP RA ≥ 80, each regression includes a linear
spline of the running variables, CPRA. Robust standard errors are reported in parentheses. In the mortality
analysis, kidney candidates whose maximal waiting time, the diﬀerence between the registration date and
December 3, 2014, is less than each analysis period are excluded.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

Table B.13 Polynomial model selection

(1)

(2)

(3)

(4)

(5)

(6)

Model 1 Model 2 Model 3 Model 4 Model 5 Model 6

Panel A. Without covariates
P-value of F-test

.0004764
39179.02

Panel B. With covariates
P-value of F-test

1.32e-11
38394.3

AIC

AIC

.973892
37971.27

.017061
38564.26

.999868
37866.82

.8735895
38065.05

.9985595
37883.46

.7847014
37195.03

6.55e-06
37777.64

.9983431
37088.96

.4452405

37285

.9862065
37105.46

Note: 1. Functional form of f (Xi) is same as below.
Model 1: f (Xi) = β1Xi
Model 2: f (Xi) = β1Xi + β2CP RA80i ∗ Xi
Model 3: f (Xi) = β1Xi + β2X 2
i
Model 4: f (Xi) = β1Xi + β2X 2
Model 5: f (Xi) = β1Xi + β2X 2
Model 6: f (Xi) = β1Xi + β2X 2
2. Included covariates are each candidate’s blood type, gender, race, age at waitlist registration, education
level, payment source, BMI, type of diabetes, dialysis, and work status.

i + β3CP RA80i ∗ Xi + β4CP RA80i ∗ X 2
i + β3X 3
i
i + β3X 3

i + β4CP RA80i ∗ Xi + β5CP RA80i ∗ X 2

i + β6CP RA80i ∗ X 3

i

i

107

Table B.14 The eﬀect of sensitization points on patient mortality

(1)
(2)
Waitlist mortality
2 year
1 year

(3)
(4)
Overall mortality
1 year

2 year

Panel A. Reduced form results
CP RA ≥ 80
{39,166}

-0.0113*
(0.00655)

-0.00779
(0.00725)

CP RA ≥ 80
{29,181}

-0.0135*
(0.00768)

-0.0283**
(0.0115)

-0.0118
(0.00825)

-0.0253**
(0.0125)

Panel B. Fuzzy RD estimates
Pr(deceased)

-0.0449*
(0.0260)

{39,166}

-0.0311
(0.0289)

Pr(deceased)

{29,181}

-0.0487*
(0.0276)

-0.102**
(0.0410)

-0.0427
(0.0297)

-0.0913**
(0.0447)

Notes: The table shows the estimated results of the eﬀect of receiving sensitization points on waitlist mortality
of kidney candidates with diﬀerent duration restrictions. For the precise comparison between 1 year and 2 years
mortality estimates, 1 year estimates which exclude candidates whose maximal waiting time, the diﬀerence
between the registration date and December 3, 2014, is less than 2 years are additionally reported in column
In addition to the indicator for CP RA ≥ 80, each regression includes a linear spline of the running
(1).
variables, CPRA. Robust standard errors are reported in parentheses. The number of observations for each
analysis period is presented in the curly bracket.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

108

Table B.15 Fuzzy RD results by candidates’ races

(1)
(2)
Waitlist mortality
1 year
2 year
0.0166
(0.0427)

(3)
(4)
Overall mortality
1 year
0.0508
(0.0483)

2 year

White Pr(deceased)

{21,564}

Pr(deceased)

{16,062}

0.00682
(0.0446)

-0.0885
(0.0611)

0.0333
(0.0494)

-0.0694
(0.0677)

Black Pr(deceased)

{13,979}

-0.123***
(0.0365)

-0.125***
(0.0395)

Pr(deceased)

{10,483}

-0.108***
(0.0386)

-0.109*
(0.0639)

-0.118***
(0.0394)

-0.0993
(0.0678)

Notes: The table shows the heterogeneous estimation results of an increased access to deceased donor kidneys
on kidney candidates’ mortality rates with diﬀerent duration restrictions by kidney candidates’ races. For the
precise comparison between 1 year and 2 years mortality estimates, 1 year estimates which exclude candidates
whose maximal waiting time, the diﬀerence between the registration date and December 3, 2014, is less than
2 years are additionally reported in column (1). In addition to the indicator for CP RA ≥ 80, each regression
includes a linear spline of the running variables, CPRA. Robust standard errors are reported in parentheses.
The number of observations for each analysis period is presented in the curly bracket.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

109

Table B.16 Fuzzy RD results by candidates’ blood types

(1)
(2)
Waitlist mortality
1 year
2 year
0.0163
(0.0437)

(3)
(4)
Overall mortality
1 year
2 year
0.0144
(0.0453)

A type Pr(deceased)

{12,226}

Pr(deceased)

{9,069}

-0.00867
(0.0428)

0.00367
(0.0644)

-0.0219
(0.0435)

-0.0127
(0.0676)

B type Pr(deceased)

{6,199}

-0.0529
(0.0609)

-0.0839
(0.0641)

Pr(deceased)

{4,587}

-0.0253
(0.0662)

-0.219**
(0.104)

-0.0370
(0.0682)

-0.222*
(0.115)

O type Pr(deceased)

{19,353}

-0.0713*
(0.0394)

-0.0141
(0.0471)

Pr(deceased)

{14,493}

-0.0648
(0.0444)

-0.126*
(0.0657)

-0.0267
(0.0500)

-0.0863
(0.0724)

Notes: The table shows the heterogeneous estimation results of an increased access to deceased donor kidneys
on kidney candidates’ mortality rates with diﬀerent duration restrictions by kidney candidates’ blood types.
The results of blood type AB candidates are excluded as the sample size (1764) is relatively too small. For the
precise comparison between 1 year and 2 years mortality estimates, 1 year estimates which exclude candidates
whose maximal waiting time, the diﬀerence between the registration date and December 3, 2014, is less than
2 years are additionally reported in column (1). In addition to the indicator for CP RA ≥ 80, each regression
includes a linear spline of the running variables, CPRA. Robust standard errors are reported in parentheses.
The number of observations for each analysis period is presented in the curly bracket.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

110

Table B.17 Fuzzy RD results by candidates’ dialysis status

(1)
(2)
Waitlist mortality
1 year
2 year
0.0256
(0.0424)

(4)
(3)
Overall mortality
1 year
2 year
0.0298
(0.0446)

None

Pr(deceased)

{7,488}

Pr(deceased)

{5,616}

0.00454
(0.0486)

-0.0625
(0.0558)

0.00328
(0.0489)

-0.0522
(0.0614)

Dialysis Pr(deceased)

{31,678}

-0.0737**
(0.0328)

-0.0550
(0.0369)

Pr(deceased)

{23,565}

-0.0660**
(0.0334)

-0.113**
(0.0519)

-0.0562
(0.0366)

-0.100*
(0.0567)

Notes: The table shows the heterogeneous estimation results of an increased access to deceased donor kidneys
on kidney candidates’ mortality rates with diﬀerent duration restrictions by kidney candidates’ dialysis status.
For the precise comparison between 1 year and 2 years mortality estimates, 1 year estimates which exclude
candidates whose maximal waiting time, the diﬀerence between the registration date and December 3, 2014,
is less than 2 years are additionally reported in column (1). In addition to the indicator for CP RA ≥ 80,
each regression includes a linear spline of the running variables, CPRA. Robust standard errors are reported
in parenthesis. The number of observations for each analysis period is presented in the curly bracket.
* signiﬁcant at 10%, ** signiﬁcant at 5%, *** signiﬁcant at 1%

111

Sources: OPTN database (https://optn.transplant.hrsa.gov/data)
Notes: The OPTN database reports the information on waitlist addition and removal from 1997. The number
of waitlisted candidates is calculated by adding the net increase (waitlist addition - removal) to the number
of candidates in the previous year. As candidates were already waitlisted before 1997, the real waitlist plot
needs to be scaled up. Candidates waitlisted at more than one transplant center or for multiple organs are
counted as only one candidate.

Figure B.1 Trends in the kidney transplant market

112

(a) Kidney source choice

(b) Kidney source choice with relaxed assumption

(c) Crowd-out of living donor kidneys

Notes: The net beneﬁt illustrates the relative beneﬁt of using a living donor kidney compared to waiting for
a deceased donor kidney at each waiting time (t). The net beneﬁt consists of the kidney quality gap (α) and
preference for a living donor kidney, which increases over waiting time. The net cost illustrates the emotional
cost (β) of living donor kidney receipients with a closely related donor. The oﬀer density plots the likelihood
of receiving a deceased donor kidney oﬀer at each waiting time (t). Panel (a) illustrates the kidney source
choice of kidney candidates who have a potential living donor at the initial time (t = 0). Panel (b) illustrates
the kidney source choice of kidney candidates who ﬁnd potential living donors at t0. Panel (c) shows the
crowd-out of living donor kidney choices when the likelihood of receiving a deceased donor kidney increases.

Figure B.2 Net costs and beneﬁts of a living kidney transplant

113

Figure B.3 Kidney sensitization measure and sensitization points

(a) Distribution of CPRA

(b) Distribution of CPRA within bandwidth 3

Notes: Panel (a) plots the frequency of CPRA at each 0.1 unit. Candidates with zero CPRA are excluded
from the plot. Panel (b) plots the frequency of CPRA at 0.01 units within the bandwidth 3 units from the
CPRA 80 threshold.

Figure B.4 CPRA distribution

Notes: The ﬁgure plots the mean frequency along with quadratic ﬁtted lines (solid lines) and the 95% conﬁ-
dence interval below and above the CPRA 80 threshold.

Figure B.5 Mean frequency test

114

(a) Pr(living tx)

(b) [1 year] Waitlist mortality

(c) [2 year] Waitlist mortality

(d) [1 year] Overall mortality

(e) [2 year] Overall mortality

Notes: Panels (a)-(e) plot the mean values of each predicted outcome variable derived from regressions with-
out using the indicator for CP RA ≥ 80 along with quadratic ﬁtted lines (solid lines) and the 95% conﬁdence
intervals below and above the CPRA 80 threshold. The covariates included in each regression are the candi-
date’s age at waitlist registration, blood type, gender, race, education level, payment source, diabetes status,
dialysis status, work status, and BMI.

Figure B.6 Discontinuities on predicted outcomes

115

(a) Pr (Deceased)

(b) Pr (Living)

Notes: Panels (a)-(b) plot the mean values of each outcome variable along with quadratic ﬁtted lines (solid
lines) and the 95% conﬁdence intervals below and above the CPRA 80 threshold.

Figure B.7 Crowd-out eﬀect on the demand of living donor kidneys

(a) [1 year] Waitlist mortality

(b) [2 year] Waitlist mortality

(c) [1 year] Overall mortality

(d) [2 year] Overall mortality

Notes: Panels (a)-(d) plot the mean values of each outcome variable along with quadratic ﬁtted lines (solid
lines) and the 95% conﬁdence intervals below and above the CPRA 80 threshold.

Figure B.8 The eﬀect on patient mortality

116

(a) Diﬀerence in the knowledge on the net beneﬁt

(b) Diﬀerence in the access to potential living donors

Notes: Net BW and BB illustrate the relative beneﬁt of using a living donor kidney compared to waiting for a
deceased donor kidney at each waiting time (t) for white and black candidates, respectively. Net C illustrates
the emotional cost to living donor kidney receipients with a closely related donor. The oﬀer density plots
the likelihood of receiving a deceased donor kidney oﬀer at each waiting time (t). An increase in the access
to deceased donor kidneys moves the oﬀer density graph to the left. Panel (a) illustrates the heterogeneity
in crowd-out eﬀects when the knowledge of the net beneﬁt diﬀers. Panel (b) illustrates the heterogeneity in
crowd-out eﬀects when the access to potential living donor kidneys diﬀers. Kidney candidates with limited
access to potential donors do not face the kidney source choice problem until they ﬁnd potential living donors
(t0).

Figure B.9 Heterogentiy of the crowd-out eﬀect by candidates’ races

117

(a) Heterogeneity by blood types

(b) Heterogeneity by dialysis status

Notes: Net B illustrates the relative beneﬁt of using a living donor kidney compared to waiting for a deceased
donor kidney at each waiting time (t) for white and black candidates, respectively. The net cost illustrates
the emotional cost of living donor kidney receipients with a closely related donor. The oﬀer density plots the
likelihood of receiving a deceased donor kidney oﬀer at each waiting time (t). An increase in access to deceased
donor kidneys moves oﬀer density graph to the left. Panel (a) illustrates the heterogeneity in crowd-out eﬀects
when the access to potential living donor kidneys diﬀers. Kidney candidates with limited access to potential
donors do not face a kidney source choice problem until they ﬁnd potential living donors (t0). Panel (b)
illustrates the heterogeneity in crowd-out eﬀects by dialysis status. Kidney candidates who are not receiving
dialysis treatment have a steeper Net B over the waiting time to avoid the initiation of dialysis due to longer
waiting.

Figure B.10 Heterogentiy of the crowd-out eﬀect

118

(a) Pr (Deceased)

(b) Pr (Living)

(c) [1 year] Waitlist mortality

(d) [2 year] Waitlist mortality

(e) [1 year] Overall mortality

(f) [2 year] Overall mortality

Notes: Panels (a)-(f) plot point estimates and 95% conﬁdence intervals from the quadratic regression excluding
data points around the CPRA 80 threshold; the excluded CPRAs range from +/- 0.25 to +/- 3.

Figure B.11 Donut RD estimation

Figure B.12 Sample of a diﬀerence-in-diﬀerence estimation

119

Appendix C Tables and Figures for Chapter 3

Table C.1 ESRD patient distance to dialysis facilities

Percentile

10
20
30
40
50
60
70
80
90

(1)
All

1.681
2.887
4.134
5.568
7.404
10.109
14.422
22.073
40.846

(2)

(3)

(4)

(5)

For-proﬁt

Not-for-proﬁt

Freestanding

Hospital

Freestanding

Hospital

1.761
2.928
4.120
5.489
7.236
9.744
13.708
20.658
37.280

1.386
3.091
4.439
6.044
7.951
10.650
15.231
23.769
46.869
17,759

1.806
2.956
4.227
5.788
7.636
10.227
14.628
21.826
39.932
172,754

0.786
2.500
4.157
5.949
8.269
12.150
18.610
31.272
62.723
353,384

Observations

2,183,149

1,639,252

Source: 2016 USRDS data
Notes: The distance between a residence of a patient and the patient’s registered dialysis facility is computed by
using the GEODIST stata command and coordinates of the two locations. Resident coordinates in ZCTA-level
come from United States Census Gazetteer ﬁles (https://www.census.gov/geographies/reference-ﬁles/time-
series/geo/gazetteer-ﬁles.html). Dialysis facility coordinates are found based on the facility address available
from CMS Dialysis Facility Compare Dataset.

Table C.2 Market characteristics (81 sample markets)

Market population
Largest market population within 20 miles
Number of census tracts
Number of for-proﬁt dialysis facilities

(1)
Mean

127,484.70
10,964.71

29.62
2.65

(2)

Std Dev
49,771.10
7,161.52

12.72
1.60

(3)
Min
56,548

-
9
1

(4)
Max

304,016
24,526

70
7

Sources: 2015 U.S. Census ACS, 2016 USRDS data
Notes: The largest market within 20 miles is relative to the market’s boundary census tracts. The distance
between locations is computed as the distance between the census tract’s population-weighted centroids.

120

Table C.3 Census tract-level characteristics

(1)
Mean

Population

Total
Diagnosed with ESRD
65 years and older
Per capita income ($)
Education with high school or under (%)
Median gross rent ($)

4,304.40

7.24
591.82

24,304.92

41.49
783.36

(2)

Std Dev

2,081
5.15
378

9,919.54

16.51
230.64

(3)
Min

0
0
0
0
0
0

(4)
Max

30,256

43

4,093
90,249
88.60
2,108

Sources: 2015 U.S. Census ACS, 2016 USRDS data
Notes: Median gross rent shows the monthly housing cost expenses for renters. This variable contains the
contract rent and the estimated cost of utilities paid by renters. The number of ESRD patients includes the
accumulated number of patients whose ESRD status was active in 2015.

121

Table C.4 Parameter estimates

(1)

(2)

Coeﬃcient Marginal
Eﬀect (%)

Coeﬃcient Marginal
Eﬀect (%)

(3)

(4)

ESRD patients

(units: 10 people)

Population over 65 years
(units: 1,000 people)

Education with high school

or under (units: 1%p)

Per capita income

(units: $100,000)

Median gross rent

(units: $100)

Competition eﬀect (γ)

Mean of market-level eﬀect
distribution (µ)

Standard error of market-level
eﬀect distribution (σ)

Log-likelihood

0.3265
(0.0977)

2.01

-1.17

-0.0193
(0.0278)

-1.8753
(0.9524)

-2.8078
(1.0166)

0.3905
(0.0291)

775.198

3.85

-2.70

-3.73

-2.97

0.6810
(0.0209)

-0.7484
(0.3709)

-1.7498
(0.3714)

-0.0434
(0.0164)

-0.6295
(0.0211)

-2.0027
(0.2842)

0.3768
(0.0279)

769.766

Notes: Standard errors are reported in parentheses. Parameter estimates are based on 2015 demographic and
dialysis facility location data. The marginal eﬀect shows the average change in the probability of location
choice conditional on entry for the response to a 10% increase in each demographics.

122

Table C.5 Robustness to the restrictions on the largest city within 20 miles

(1)
(2)
Pop < 25,000
(81 markets)

(3)
(4)
Pop < 40,000
(100 markets)

(5)
(6)
Pop < 50,000
(108 markets)

ESRD patients
(units: 10 people)

0.3265
(0.0977)

0.3813
(0.0742)

0.3801
(0.0702)

Population over 65 years
(units: 1,000 people)

Education with high school
or under (units: 1%p)

Per capita income
(units: $100,000)

Median gross rent
(units: $100)

0.6810
(0.0209)

-0.7484
(0.3709)

-1.7498
(0.3714)

0.7762
(0.1025)

-0.7873
(0.1694)

-2.1708
(0.1907)

0.7780
(0.0801)

-0.8190
(0.1087)

-2.5712
(0.1144)

-0.0193 -0.0434
(0.0278) (0.0164)

-0.0128 -0.0328
(0.0238) (0.0240)

-0.0100
(0.0090)

-0.0235
(0.0168)

Competition eﬀect (γ)

-1.8753 -0.6295
(0.9524) (0.0211)

-1.8353 -0.8490
(0.1366) (0.1909)

-2.1761
(0.1514)

-0.9450
(0.1143)

Mean of market-level eﬀect
distribution (µ)

-2.8078 -2.0027
(1.0166) (0.2842)

-1.5499 -1.7927
(0.2586) (0.2967)

-1.2147
(0.2260)

-1.6640
(0.1931)

Standard error of market-level
eﬀect distribution (σ)

0.3905
0.3768
(0.0291) (0.0279)

0.4020
0.3970
(0.0282) (0.0280)

0.4018
(0.0266)

0.3915
(0.0260)

Log-likelihood

775.198 769.766

903.732 896.320 1,025.564 1,015.205

Notes: The table shows the parameter estimates with diﬀerent restrictions on the population size of the
largest city within 20 miles from each sample market. Standard errors are reported in parentheses. Parameter
estimates are based on 2015 demographic and dialysis facility location data.

123

Table C.6 Robustness to the assumption on the size of potential entrants

(1)
(2)
2 × entrants

(3)
(4)
3 × entrants

(5)
(6)
5 × entrants

ESRD patients
(units: 10 people)

0.3265
(0.0977)

0.3205
(0.0969)

0.3817
(0.0968)

Population over 65 years
(units: 1,000 people)

Education with high school
or under (units: 1%p)

Per capita income
(units: $100,000)

Median gross rent
(units: $100)

0.6810
(0.0209)

-0.7484
(0.3709)

-1.7498
(0.3714)

0.6819
(0.1397)

-0.7495
(0.3858)

-1.7752
(0.8694)

0.6824
(0.1245)

-0.7504
(0.2553)

-1.7809
(0.3382)

-0.0193 -0.0434
(0.0278) (0.0164)

-0.0189 -0.0425
(0.0276) (0.0292)

-0.0191 -0.0426
(0.0276) (0.0275)

Competition eﬀect (γ)

-1.8753 -0.6295
(0.9524) (0.0211)

-1.6942 -0.6880
(0.9480) (0.8354)

-1.6927 -0.7092
(0.9461) (0.3403)

Mean of market-level eﬀect
distribution (µ)

-2.8078 -2.0027
(1.0166) (0.2842)

-2.3045 -2.6348
(1.0125) (1.0142)

-2.9962 -3.3038
(1.0109) (0.4542)

Standard error of market-level
eﬀect distribution (σ)

0.3905
0.3768
(0.0291) (0.0279)

0.3903
0.3768
(0.0291) (0.0283)

0.3902
0.3768
(0.0291) (0.0281)

Log-likelihood

775.198 769.766

775.171 769.764

775.171 769.764

Notes: The table shows parameter estimates with the diﬀerent assumptions on the number of potential
entrants in each market. Standard errors are reported in parentheses. Parameter estimates are based on 2015
demographic and dialysis facility location data.

124

Source: 2016 USRDS data
Notes: The number of ESRD incidences is computed by counting patients who received their ﬁrst ESRD
services in each year. I restrict the sample to ESRD patients who chose in-center hemodialysis as their ﬁrst
treatment modality (73 percent among total ESRD patients). Therefore, the real number of ESRD incidences
needs to be scaled up. To calculate the number of dialysis facilities, I count facilities that responded the CMS
ESRD Annual Facility Survey in each year.

Figure C.1 Trend of ESRD incidences and dialysis facilities

Source: 2016 USRDS data

Figure C.2 Trend of ESRD incidence by age

125

Source: 2016 USRDS data
Notes: Glomerulonephritis is diagnosed for patients with inﬂammation of the tiny ﬁlters in the kidneys.

Figure C.3 Trend of primary causes of ESRD

Source: 2016 USRDS data
Notes:
I restrict the sample to ESRD patients who chose in-center hemodialysis as their ﬁrst treatment
modality (73 percent among total ESRD patients). Approximately 6 percent of all ESRD patients receive
kidney transplant as their ﬁrst treatment. Transplant treatment choice in this plot is deﬁned as a broader
concept. It counts not only actual transplant, such as decesed or living donor kidney transplants, but also
waitlist registration for deceased donor kidneys.

Figure C.4 Treatment choice within 1 year of ESRD incidence

126

Source: 2016 USRDS data
Notes: Hospital-based facilities are either hospital units or hospital satellites, and freestanding facilities are
deﬁned as units not aﬃliated with a hospital.

Figure C.5 Trend of dialysis facilities

127

Appendix D Validity Check for RD estimation in Chapter 1

To identify a valid causal relationship by using an RD design, two assumptions are
required. First, the liver transplant candidates should be randomly distributed around
the 35 threshold. Second, the candidates are not able to perfectly manipulate their
aMELD scores to increase the likelihood of receiving liver transplants (Lee 2008; D. S.
Lee et al. 2010).

For the ﬁrst assumption, I test whether the predetermined characteristics of
candidates are similar around the 35 threshold. Table A.9 presents the results of
the RD estimation for the predetermined characteristics. Using an RD design with
a linear polynomial and a triangular kernel, I examine whether the RD estimates of
the predetermined characteristics are signiﬁcantly diﬀerent from zero. None of the
estimates for the predetermined characteristics are signiﬁcantly discontinuous around
the aMELD 35 threshold, which implies that candidates in the analysis sample are as
good as randomly distributed around the threshold.

To check the second assumption, I examine whether there is any evidence of
aMELD score manipulation near the 35 threshold. Panel (a) of Figure A.14 shows
the aMELD score frequency with local linear ﬁtted lines. Each circle shows a mean
frequency with 0.4 aMELD score bins within bandwidth 4. Solid lines show local linear
regression graphs regressed separately below and above the 35 threshold. The ﬁgure
shows a smooth mean frequency across the threshold. Panel (b) presents a histogram
of the aMELD score with 0.01 aMELD score bins and a bandwidth of 4. I ﬁnd some
large heaps of aMELD scores with whole numbers that could be caused by the new
cMELD score system described in Section 1.2.153. Other than those heaps of aMELD
scores, I do not observe any irregular heaps around the 35 threshold, which is consistent
with patients being unable to perfectly manage their blood factors, namely, creatinine,
bilirubin, INR, and sodium.

53There would be several other hypotheses for the heaps at whole number units. (1) Rounding in reporting
cannot be the reason because the aMELD scores in panel (a) of Figure A.1 are recovered by using blood factors
and the MELD equation rather than reported scores. (2) The eMELD score is assigned by whole number units,
which would have some eﬀect. However, only 6 candidates have eMELD scores among the 3,557 candidates
within bandwidth 4. Furthermore, among the 6 candidates, only 2 have eMELD scores greater than their
cMELD score. Hence, the eﬀect of the eMELD score on the observed heaps is almost zero.

128

Candidates who registered after January 11, 2016, are aﬀected by the new
cMELD score system including serum sodium, if their initial cMELD score, which is cal-
culated using the original cMELD score equation, is 11 or higher. The observed heaps
are generated as the new cMELD score equation uses the rounded original cMELD
score, and the amount of serum sodium is reported as whole numbers. Panels (c) and
(d) show the diﬀerence in the distribution of aMELD scores between candidates whose
aMELD scores do and do not contain serum sodium. Unlike panel (d) which shows no
heap for aMELD scores with whole numbers, I ﬁnd heaps in panel (c) similar to those
in the overall sample, panel (b).

If the observed heaps of aMELD scores with whole numbers are irregular, the
RD estimates of the liver transplant outcomes may not be valid (Barreca et al. 2016).
Hence, I examine whether the RD estimates in Section 1.5.1 are sensitive to heaps
of aMELD scores with whole numbers. I compare the RD estimates with donut RD
estimates excluding the heaped data in the RD estimation, as proposed by Barreca et
al. (2016). If the outcomes at the heaps are outliers and they drive the RD estimates to
a large degree, the magnitude of the donut RD estimates would show a large diﬀerence
from that of the standard RD estimates. Table A.10 shows the standard RD estimates
and donut RD estimates regarding the eﬀect of the Share 35 policy on patient outcomes.
Overall, the donut RD estimates in Panel B are similar to the standard RD estimates
in Panel A in magnitude and signiﬁcance, suggesting that the heaps with the whole
numbers do not drive the RD estimates.

129

Appendix E Variable Choice for Survival Prediction in Chapter 1

To derive the data-driven liver match quality measure that predicts posttransplant
survival, I use the LASSO algorithm. This algorithm selects highly predictive variables
by adding a penalization term λ to the OLS objective function (Belloni et al. 2014).

k(cid:88)

k(cid:88)

ˆβ(λ) = argmin

β∈Rk

(yi − x(cid:48)β)2 + λ

|βj|

(23)

i=1

j=1

When predicting a certain outcome using related variables, avoiding over-ﬁtting is
important; speciﬁcally, a well-ﬁtted model in the sample used for designing the model
may not have high prediction power out of the sample. To avoid this concern, I
randomly divide the sample into the model sample (80%) and test sample (20%). After
selecting highly predictive variables using the LASSO algorithm and the model sample,
the predictive power of the model is tested using the test sample. One concern about
this approach is that the test sample is not exploited in the prediction model design. If
there are outliers in one of the two samples, the model may not show good prediction
performance. To address this concern, I randomly split the overall sample into ﬁve
sets and apply the LASSO algorithm ﬁve times using one of the sample sets as the
test sample. Among the ﬁve diﬀerent sets of selected variables, I ﬁnally select variables
chosen at least three times as the predictor of the model. The LASSO algorithm selects
40 variables, and the variables are shown in Table A.13.

When highly predictive variables are selected, I predict the posttransplant sur-
vival rates using the logit estimation as the outcome with the binary variable, which is
one if the transplant recipient is surviving. In the logit estimation, however, the stan-
dard R-squared value cannot be used to check the predictive power of the estimation
model. Hence, I use the Brier score, which calculates the mean squared error of the
predicted probability, for the predictive power evaluation.

Brier score =

1
n

(yi − ˆyi)2 =

1
n

(1 − ˆyi)2 +

(ˆyi)2]

(24)

(cid:88)

(cid:88)

[
yi=1

(cid:88)

yi=0

where yi is the actual posttransplant survival outcome and ˆyi is the probability that
is predicted in the model. n presents the number of observations used for the predic-

130

tion. If the prediction model explains the outcome better, the value of the Brier score
becomes smaller.

Table A.14 displays the Brier scores of four diﬀerent prediction models. The ﬁrst
prediction model is DRI which focuses on the liver donor characteristics. The second
model expands the approach of the ﬁrst model by allowing coeﬃcients of DRI factors
to be ﬂexible; speciﬁcally, I predict the posttransplant survival using the variables of
DRI. The third model predicts survival rates with LASSO-selected variables, and the
fourth model allows interaction of LASSO-selected variables. To avoid the over-ﬁtting
problem, the Brier scores are calculated by comparing the predicted survival rates and
the actual survival outcome in the test sample. As I repeat 5 diﬀerent predictions using
one of the ﬁve sample sets as the test sample, each prediction model has ﬁve diﬀerent
estimates in Columns (1) - (5). Among the four prediction models, the third model,
which uses only the LASSO-selected variables without the interaction terms, shows the
smallest Brier scores for all 5 results.

131

Appendix F Selection of Functional Form in Chapter 2

I select the functional form using the F-test approach and the Akaike information
criterion (AIC) (Akaike 1974) of model selection. First, the F-test approach (D. S. Lee
et al. 2010) tests whether the polynomial model ﬁts well with the unrestricted graph.
For the test, I add the set of bin dummies and test whether the bin dummies are jointly
signiﬁcant.5455 If a polynomial model shows insigniﬁcant results on the F-test, then
it indicates that the model adequately explains the relationship between the outcome
variable and the running variable, CPRA. Row 1 of Table B.13 panel (A) shows the
p-values of the F-tests for each polynomial model. The results of models 1 and 3
show that the bin dummies are jointly signiﬁcant at a 5 percent signiﬁcance level and
imply that the model has the poor goodness of ﬁt. The other prediction models show
insigniﬁcant results. Second, the AIC shows the trade-oﬀ between the bias and the
precision. The value of the AIC is derived by using the equation below.

AIC = N ln((cid:98)σ2) + 2p

where (cid:98)σ2 is the mean squared error and p is the number of parameters in the

(25)

regression. A smaller AIC means a better model in explaining the real data. In row 2,
the AIC value of model 4 is the smallest. Panel (B) shows the F-test results and AIC
values derived with baseline covariates. Models 1 and 3 still show signiﬁcant results
on the F-test. Among the models left, model 4 has the smallest AIC value, similar
to the result of the panel (A). Based on the test results above, I choose model 4 with
quadratic polynomials and interactions for the identiﬁcation of the eﬀect on crowd-out
and mortality risks.

54To avoid the collinearity with the constant and the treatment dummy, CPRA80, I excluded two dummies

which is just left and right from the CPRA 80 threshold.

55F statistic =

(R2
(1−R2

squared of the regression without bin dummies and R2
dummies (Jacob et al. 2012). In this study, I grouped candidates into 19 bins (K).

r )/K

u−R2
u)/(n−K−1) , n is the number of observations, K is the number of bins, R2

r is the R
u is the R squared of the regression with K-2 bin

132

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