The Effect of Paid Leave of Absence Legislation on
Living Kidney Donation in the United States
Fırat Bilgel∗
Abstract
This article investigates the causal impact of paid leave of absence legislation to serve as an organ
donor on living related and unrelated kidney donation rates in the U.S. We create a synthetic control
group that mimics the pre-legislation living kidney donation rates of the states that enacted paid leave
of absence legislation. We then compare the living kidney donation rates of the synthetic states with
no legislation to the paid leave-enacted states for the period 1988-2010. Of the 16 states analyzed that
passed the legislation, the paid leave was found to be effective only in California; the passage of paid leave
of absence legislation increased living unrelated kidney donation rates by about 2 percent in California
relative to a comparable synthetic California in the absence of legislation. However, our analysis was
unable to identify a causal effect on living related kidney donation rates in any of the states that passed
the legislation.
JEL Classification: I18; K32; C15
Keywords: Living kidney donation, paid leave of absence, synthetic control, comparative case study
*Department of Economics, Okan University Tuzla Campus Akfırat 34959 Istanbul Turkey. Email: firat.bilgel@okan.edu.tr
1
1 INTRODUCTION
Rising prevalence of diabetes and hypertension together with the advances in transplant technology led to
an ever-growing demand for transplantable organs. As of November 2013, there are about 99,000 patients
waiting for a kidney transplant in the US. However during 2013, about 11,000 kidneys are recovered of which
only about 3,700 were from living donors. Despite the efforts, the yearly additional number of patients
registered for a transplant far outstrips the yearly number of removals from the waiting list, resulting in an
increasing shortage of transplantable organs in the U.S. In an effort to alleviate organ shortages and increase
living donation rates, several states in the U.S. passed paid leave of absence and tax incentive legislations to
compensate living donors.
This study contributes to the empirical literature by investigating the causal impact of paid leave of
absence legislation for public employees in the U.S states for the period of 1988-2010 using a novel and
superior methodology compared to the difference-in-differences (DiD) estimator employed in the literature.
In the context of potential outcomes framework for causal inference, we ask the following research question:
how the living kidney donation rates would have evolved in a particular paid leave-enacted state if the
legislation had not been enacted. To answer this question, we invoke the synthetic control method developed
by Abadie and Gardeazabal (2003) and extended by Abadie et al. (2010). We create a synthetic control
group that mimics the pre-legislation living kidney donation rates of the states that enacted paid leave of
absence legislation by using the convex combination of other states that have not enacted any legislation.
Causal inference is carried out by comparing the living kidney donation rate of the synthetic states (absence
of legislation) against that of the paid leave-enacted states in the post-legislation period. We find that the
passage of paid leave of absence legislation increased living unrelated kidney donation rates by about 2 percent
in California relative to a comparable synthetic California without paid leave of absence legislation. However,
our analysis was unable to identify a causal effect on living related kidney donation rates in any of the states
that passed the legislation. This suggests that the legislation may help removing barriers to living kidney
donation for unrelated persons but only in California. On the other hand, paid leave legislation is found to
be ineffective in Colorado, New York and Kansas and unidentifiable in the remaining twelve states in which
the legislation is in effect. Potential explanations of the latter finding are that the scale of the legislation
may be too narrow to detect the causal effect; some states may have extremely high/low donation rates
leading to the failure to satisfy the convex-hull criteria; and the donor pool may not consist of states with
similar observable characteristics to that of the treated state��s in order to yield a good approximation due to
the fact that a very large number of states have passed such legislations and greatly reduced the number of
comparable control states.
Section 2 discusses the background on state legislation, section 3 discusses the synthetic control method
and its advantages over the traditional panel regression analysis, sections 3.2 and 3.3 respectively present the
results and the placebo studies, section 3.4 performs a robustness check and section 4 discusses the findings
of the analysis and its policy implications.
2 BACKGROUND ON STATE LEGISLATION
It is known that individuals willing to become living donors are exposed to serious financial and medical risks
and that these risks may generate disincentives or barriers to donation. In the face of insurmountable shortage
and widely acknowledged repugnance for explicit monetary incentives for donation, an increasing number of
proposals emphasizes the urgent need to introduce reimbursement for living donors for non-medical costs
2
incurred throughout the process of donation (Delmonico et al., 2002; Gaston et al., 2006; Klarenbach et al.,
2006a; Matas, 2007; Abouna, 2008). The idea is to provide some monetary compensation that is ethically
and politically acceptable while retaining the giftlike features of the exchange (Healy, 2006). Avoiding the
language of the market also allows both the transplant community and the public to regard reimbursement or
compensation as a slight modification of the current system without resorting to drastic changes (Mahoney,
2009). Reimbursement schemes of this kind include compensation for the costs of travel, lodging, forgone
earnings, social security in the form of life insurance or long-term health insurance. A survey by the Gallup
(2005) showed that 52 percent of Americans strongly supports compensation of living donors for the costs of
travel, child care and forgone earnings and 73 percent stresses that living donors should not be denied health
or life insurance after donation.
A second line of proposals discusses tax deduction schemes to exhort individuals to serve as an organ or
bone marrow donor (Calandrillo, 2004; Milot, 2008). Tax deduction that may be claimed for organ donation
is subtracted from the gross income at the time of filing tax returns. As a result this lowers the overall taxable
income and the amount of tax paid. Tax deductions are peculiarly regressive because they depend on the tax
bracket (Calandrillo, 2004). A tax credit might correct this inequity problem because it is independent of
tax bracket and it reduces the tax owed rather than reducing taxable income. Milot (2008) stresses that tax
deduction, albeit it prima facie appears to be a sound legislative approach, turns an otherwise non-tax event
into a tax item that increases complexity of the tax system and provides differential tax returns to those who
become living organ donors because it depends on the tax bracket. At the national level, a study by Boulware
et al. (2006) reveals that of those 845 participants surveyed, 91 percent were in favor of reimbursement of
medical costs, 84 percent were in favor of paid leave but only 35 percent were in favor of tax deduction/credit.
Within the last two decades, several states in the U.S. enacted legislation that allows individuals to
take paid leave of absence or to receive tax deduction should they decide to become living donors. In 1998,
Colorado became the first state that allows paid leave of absence for prospective donors followed by Wisconsin
and Maryland in 20001. A number of states further enacted legislation that allows a $10,000 tax deduction or
to receive tax credit to serve as an organ or bone marrow donor which may be claimed for lost wages, travel,
lodging and medical expenses. Tax deduction was first introduced in the states of Wisconsin and Georgia
in 2004 followed by Arkansas in 2005. Since 1998, 35 states in the U.S enacted some type of compensation
legislation for living donors. Figure 1 shows the yearly number of states by enactment year of paid leave of
absence and tax incentive legislations.
The first study that investigates the impact of state legislation and federal policies on living kidney
donation rates in the U.S. was carried out by Boulware et al. (2008). The findings show that the state
legislation and the federal policies were not associated with sustained improvements in the larger number
of living related donations and therefore overall living donation rates. On the other hand, state and federal
policies were positively associated with living unrelated kidney donations. This indicates that legislation
related to compensation of living donors may selectively decrease barriers to living kidney donation from
unrelated persons and does not provide additional incentives for related donors. Boulware et al. (2008)
emphasize that most of the states that enacted legislation to compensate living donors allow compensation of
public employees only for becoming an organ donor and/or address only employed persons with sufficiently
high levels of income to benefit from a $10,000 tax deduction or credit, indicating that those who could
1See Boulware et al. (2008) and Lacetera et al. (2012) for a detailed description of state legislation and federal initiatives for
the compensation of living organ donors in the US. A concise and updated version of state legislation can be found in table 2.
For a detailed description of international legislation on reimbursement of living donors consult Pattinson (2003) and Klarenbach
et al. (2006b).
3
potentially benefit from the legislation may be a very small group. Wellington and Sayre (2011) examines
the association between financial incentives that either allow for tax deduction or 30 days of paid leave of
absence and organ donations in the U.S. The results, in line with the findings of Boulware et al. (2008), show
that state legislation is not associated with overall living donations. A recent study by Lacetera et al. (2012)
employs a DiD methodology to assess the impact of paid leave of absence legislation on organ and bone
marrow donation and concludes that the legislation had no overall effect on the number of organ donations
but exerts a positive effect on bone marrow donation.
Albeit the existing strand of empirical research reaches a consensus, they share two common method-
ological shortfalls. First, they are unable, by design, to assess the individual heterogenous causal effects. By
employing the synthetic control method, this paper accounts for unobservable and time-varying state-level
heterogeneity, reduces other potential biases that might persist in a traditional regression analysis, and most
importantly identifies the state-specific causal effect of paid leave of absence legislation. As we show in the
following sections, in a treatment sample of sixteen states that passed the legislation, the paid leave of absence
legislation has a causal effect on living unrelated kidney donation rates only in California. By employing a
DiD methodology, one is likely to find no effect of the legislation due to pooling of states and the fact that
a very small causal effect in a treatment unit may be clouded by zero causal effects in other treated units
and that the average treatment effect on the treated is too small to detect. This problem sheds light on the
importance of identifying heterogenous causal effects in assessing the impact of the legislation when only very
few states are causally affected by the legislation.
A second potential problem is that the introduction of paid leave of absence legislation may not be
exogenous to kidney donations for the changes may be more likely related to lobbying in organ transplantation.
When state policies respond, given enough constituents care about organ donation, we might expect benefits
for organ donors to arise in years after a large number of living donors have made donations. Mean reversion
would push the estimates of the effects of the legislation down as the states that have the policies had
unusually high-donation rates in the pre-legislation period. As a result, a positive increase in donation could
look insignificant if these effects are at play. The synthetic control method is robust to this type of endogeneity
if the identifying assumptions are met. In the following section, we seek to answer, along the lines of Abadie
et al. (2010), how the living kidney donation rates at the state level would have evolved in the absence of
paid leave of absence legislation.
3 SYNTHETIC CONTROL METHOD
The synthetic control method, developed by Abadie and Gardeazabal (2003) and extended by Abadie et al.
(2010) and Abadie et al. (2012), has a number of advantages over the traditional panel data regression
framework. In traditional regression analysis, the choice of the comparison units is left at the discretion of
the researcher, based on the degree of similarity between the control and the treated units. In the synthetic
control method, the choice of the appropriate counterfactual is selected from a pool of unaffected units (the
donor pool) to compare to the treated state. The appropriate comparison unit is based on observable and
quantifiable characteristics which reduce subjectivity and allows for better causal inference (Abadie et al.,
2010).
Unlike traditional regression analysis which relies on extrapolation outside the support of the data, the
synthetic control method constructs a linear combination of states that have not enacted paid leave of absence
legislation with positive weights that sum to one. The traditional regression also, but rather in an implicit
4
way, computes these weights which can be positive or negative but not necessarily sum to one. This may
lead to severe extrapolation biases. In synthetic control method, the weights are assigned to states in the
donor pool in such a way that the pre-legislation living kidney donation rates and the covariates that are
thought to influence living kidney donation rates are comparable to those of the treated state before the
passage of legislation2. This comparability is determined by the minimization of root mean square prediction
error (hence RMSPE) in the pre-legislation period, which measures the lack of fit between the trajectory of
the outcome variable and its synthetic counterpart (Abadie et al., 2012)3.
The synthetic control method allows the effect of unobservable state heterogeneity to vary over time. In
the fixed effects (FE) model and the DiD estimator, the effect of unobservable heterogeneity is assumed to
be fixed over time. Hence, the synthetic control method provides an improvement over FE and DiD methods
and deals better with endogeneity caused by the presence of time-varying unobservable confounders, all of
which are presumed to have been accounted in the traditional regression framework. Throughout our analysis
we maintain the Stable Unit Treatment Value Assumption (SUTVA) such that the potential outcome for
any state do not vary with the legislation enacted in other states. Specifically, the paid leave of absence
legislation should not have an effect on states that did not pass the legislation (absence of geographical
spillover). Hypothetically speaking, if the legislation in California had positive spillover effects on kidney
donations in the weight-assigned control states, for example Nevada and Arizona (i.e. states that did not pass
such legislation), then the synthetic control states would underestimate the counterfactual kidney donation
rate trajectory of the treated state in the absence of legislation and the synthetic control estimates would be
biased downward. On the other hand, spillover effects on states not included in the synthetic control do not
affect synthetic control estimates (Abadie et al., 2012).
3.1 Data and Sample
We use state-level panel data for the period 1988-2010. Until 2010, 31 states in the U.S enacted paid leave of
absence legislation for state employees and 15 states did not enact any type of legislations. Of the 31 states
that enacted paid leave of absence, one state (Idaho) was discarded due to lack of data on the number of living
kidney donors and 14 states (Arkansas, Georgia, Iowa, Mississippi, Utah, Illinois, Pennsylvania, Minnesota,
New Mexico, Connecticut, Maine, South Carolina, Wisconsin, North Dakota) were discarded because they
have further enacted tax deduction/credit or paid leave for private employees on the same or near period of
the passage of paid of leave of absence legislation (i.e. one cannot isolate the effect of paid leave and the
effect of tax incentive legislation). This leaves 16 states or treated units to be used in the synthetic control.
On the other hand, of the 15 states that enacted none of the above laws, 2 states (Montana, Wyoming) were
discarded due to lack of data on the number of living kidney donors. This leaves a total of 13 states to be
considered in the donor pool for each of the 16 treated states. Table 1 displays the assignment of treated and
donor states.
The set of characteristics we consider to synthetize our outcome variables, the living related and unrelated
kidney donation rates per million adult population (pmap) for 16 states that enacted paid leave of absence are
2For technical details, consult section C of the appendix and Abadie et al. (2010) p:494-496.
3The
pre-legislation
RMSPE
is
(
1
T0
T0
��
t=1
(
Y1t − ��P +1
j=2 w*
j Yjt
)2
)1/2
and
the
post-legislation
RMSPE
is
(
1
T1
T1
��
t=T0+1
(
Y1t − ��P +1
j=2 w*
j Yjt
)2
)1/2
where T0 and T1 are the pre-legislation and post-legislation number of periods
respectively, w*
j Yjt is the synthetic living kidney donation rates using the jth state, absent legislation, with weight w* and Y1t
is the actual living kidney donation rate of the paid leave-enacted state.
5
the living related and unrelated kidney donation rates of the control states without any such legislation for
every year in the pre-legislation period, kidney waiting list additions per million population (pmp), deceased
kidney donations pmap, the number of transplant centers pmap, the prevalence of end-stage renal disease
(ESRD) pmp, traffic fatalities pmp, cerebrovascular deaths pmp and real GDP per capita for the period 1988-
2010. The living related and unrelated kidney donation rates were available for each year under consideration,
hence used for every year in the pre-legislation period. The remaining covariates are used when available at
least for one year in the pre-legislation period.
Our pre-legislation period ranges from 10 to 17 years depending on the year in which a particular state
enacted the paid leave of absence legislation4. With a large number of pre-legislation periods, matching on
pre-legislation outcomes allows to control for heterogenous responses to multiple unobserved factors. The
intuition is that only states that are alike in both observed and unobserved determinants as well as in the effect
of those determinants on kidney donation rates should produce similar trajectories of the kidney donation
rates over extended periods of time (Abadie et al., 2012).
State data on the number of living related and unrelated living adult kidney donors, the number of
deceased kidney donations, kidney waiting list additions (candidates) and the number of transplant centers
are retrieved from the Organ Procurement and Transplantation Network (OPTN)5. Total state population
and the population over the age of 18 are obtained from the US Census Bureau6. The number of living related
and unrelated kidney donors, the number of deceased kidney donations and the number of transplant centers
are divided by the respective adult population and multiplied by million to obtain the per million adult
population (pmap) rates. Kidney waiting list additions are divided by the respective total state population
and multiplied by million to obtain the per million population (pmp) rates. The prevalence of ESRD pmp is
retrieved from the US Renal Data System (USRDS) 2010 Annual Report7. The real GDP per capita (in 2005
US dollars) is obtained from the US Department of Commerce, Bureau of Economic Analysis8. The number
of traffic fatalities is retrieved from the National Highway Traffic Safety Administration, Fatality Analysis
Reporting System (FARS)9. The number of cerebrovascular deaths is retrieved from CDC-WONDER10. Both
variables are expressed in pmp rates. The state legislation is collected from the National Kidney Foundation11,
TransplantLiving12, National Conference of State Legislatures13, Boulware et al. (2008) and Lacetera et al.
(2012).
In the final specification for which we report our results, we dropped all the covariates except the living
kidney donation rates of the unexposed control states for every year in the pre-legislation period because
4The earliest year of passage of legislation is 1998 and the latest is 2005.
5In the U.S., most of the kidney transplants from living donors are associated with kidneys donated by relatives, spouses or
partners, known as living related donation. In our sample, related donation is composed of donations by blood related child,
full sibling, half sibling, identical twin, other relative, parent, spouse and life partner. In order to increase the number of living
donor organ transplants, individuals are further allowed to direct their donation to a specific but unrelated (sometimes unknown)
individual, known as living unrelated donation. This type of living donors are those who do not have any biological, romantic
or legal ties with the organ recipient. In our sample, unrelated donation is composed of non-biological anonymous donations
and other unrelated directed donations only. Pairwise kidney exchanges (PKEs) have been excluded from unrelated donations
although they are coded as such by OPTN. The reason for excluding PKEs is that the decision to donate by a relative to
a biologically unrelated person under pairwise kidney exchange is conditioned upon his/her recipient receiving a kidney from
another biologically unrelated person. Thus the motivation under pairwise exchanges is not based upon the same reasons to
donate under typical unrelated donations. See http://optn.transplant.hrsa.gov/.
6http://www.census.gov/popest/states.html
7http://www.usrds.org/reference.htm
8http://www.bea.gov/regional/gsp/
9www.-fars.nhtsa.dot.gov/States/StatesFatalitiesFatalityRates.aspx.
10http://wonder.cdc.gov/controller/datarequest/D72;jsessionid=2D458CFDCFCF17D2F52A54B2A78D71FF
11http://www.kidney.org/transplantation/LivingDonors/pdf/LDTaxDed_Leave.pdf
12http://www.transplantliving.org/livingdonation/financialaspects/legislation.aspx
13http://www.ncsl.org/default.aspx?tabid=13383
6
neither did other covariates improve the pre-legislation fit of the trajectory of the living kidney donation rates
nor yield accurate donation rate trajectories when all the covariates except the living kidney donation rates
of the unexposed control states were used. This implies that the pre-legislation actual donation trajectory is
best reproduced by some linear combination of the donation rates of the unexposed states.
3.2 Results
With two types of outcome variables (related and unrelated donation rates) for 16 treated states, we obtain
32 distinct synthetic controls, 32 placebo runs and 32 placebo distributions for a total of 96 figures. For
space concerns, we omit the results of the synthetic controls and the results of the subsequent placebo studies
for all states for which the synthetic control method was unable to reproduce the pre-legislation donation
rate trajectory. As a result, the synthetic control method was unable to reproduce the pre-legislation living
related kidney donation rate trajectory for any of the states that passed the legislation. For living unrelated
donation rates, of the 16 states which enacted paid leave of absence legislation, the synthetic control method
was able to reproduce the pre-legislation unrelated donation rate trajectory only for four states (California,
Colorado, New York and Kansas)14. We therefore report here and in the following sections the results of
the analysis for these four states�� unrelated donation rates only. The entire analysis for the remaining twelve
treated states is available from the author upon request.
Figure 2 plots the trends in living unrelated kidney donation rates for California, Colorado, New York and
Kansas and their synthetic counterparts over the period 1988-201015. The synthetic living unrelated kidney
donation rate trajectory is constructed by using the convex combination of states in the donor pool that
closely resembled the treated state before the passage of paid leave of absence16. In California, the synthetic
unrelated donation rate trajectory almost perfectly reproduces the actual unrelated donation rate trajectory
in the pre-legislation period. In the next four years following the passage of paid leave, the synthetic unrelated
donation rate keeps rising while the actual unrelated donation rate in California rises until 2004 and begins
to fall which lasts until 2006, and then rises again.
The estimate of the impact of paid leave of absence legislation for a treatment state is given by the
difference between the actual and the synthetic unrelated kidney donation rates in the post-legislation pe-
riod. Our findings suggest that in the post-legislation period, the living unrelated kidney donation rates in
California increased on average by 2 percent relative to synthetic California in the absence of legislation17.
The paid leave of absence legislation increased living unrelated kidney donation rates by about 37 percent
in Colorado but decreased by 1.74 percent in New York and 43.2 percent in Kansas relative to synthetic
Colorado, synthetic New York and synthetic Kansas respectively.
14When the synthetic control method fails to reproduce the actual outcome trajectory for a number of states in the pre-
legislation period, an alternative and potentially promising strategy is to aggregate the living kidney donation rates and the
predictors that are thought to influence living kidney donation rates of the paid-leave-enacted states by the enactment year.
State aggregation could result in an increase in the power of the synthetic control but poses problems in the discussion of the
results with respect to policy implications since the treated units are no longer states but a collection of states. We avoid state
aggregation because the correct unit of observation at which the laws and the policy decisions are made is the state level.
15The actual and the synthetic trends for New York end in 2005 because New York further passed tax deduction legislation
in 2006.
16We use the synth command in STATA, which can be found at http://www.mit.edu/~jhainm/synthpage.html
17This causal effect is calculated by taking the ratio of the difference between the average unrelated donation rate of California
and the average unrelated donation rate of the synthetic California to the average unrelated donation rate of the synthetic
California in the post-legislation period.
7
3.3 Inference about the impact of state legislation
In order to ensure that a particular synthetic control estimate reflects the impact of the legislation (i.e.
the synthetic controls provide good predictors of the trajectory of living kidney donation rate in the pre-
legislation periods), we perform a series of falsification tests known as in-space placebo test, in which we
artificially reassign the legislation period to each of the 13 states which did not enact paid leave of absence
legislation and shift the treated state into the donor pool. If a particular state enacted the legislation and
other states did not, our expectation is that the control states that are subject to the synthetic control method
should not be affected by the legislation, thus should not yield a diverging actual and synthetic living kidney
donation rate akin to that of the treated state in the post-legislation period. Therefore, our confidence that a
sizeable synthetic control estimate reflects the effect of legislation would be severely undermined if similar or
larger estimated kidney donation rate gaps are obtained when the legislation is artificially assigned to states
that did not enact such legislation (Abadie et al., 2010)18.
Figures 3 and 4 report the results of the placebo experiments for living unrelated kidney donation rates in
California, Colorado, New York and Kansas. The black line represents the estimated living unrelated kidney
donation rate gap and the gray lines represent the estimated living unrelated kidney donation rate gap for
states that did not enact the legislation. In order to infer that the paid leave of absence legislation imposes a
significant positive effect on kidney donation rate, the estimated gap (synthetic - actual) of the treated state
should be very close to zero in the pre-legislation period (i.e. should yield a good fit) but should also stand
out in the post-legislation period (i.e. the gap should be as negative as possible) relative to the estimated
gaps for the states in the donor pool. Otherwise, we would either infer that the post-legislation donation
gap is artificially created by a lack of fit (Abadie et al., 2010), or the legislation does not have any sizeable
impact on donation rates of the treated state. The former may happen when the pre-legislation fit is poor
and the latter may happen when the synthetic living kidney donation rate closely tracks the actual over the
entire sample period. In addition to the placebo results for all 13 control states, we report two sets of the
placebo results for a restricted number of placebo runs based on the mean square prediction error (MSPE)
cut-off level.
The left panel in figures 3 and 4 shows the living unrelated kidney donation rate gaps in treatment states
and placebo gaps in all 13 control states. In the mid panel of figures 3 and 4, we discard all the states with
a MSPE five times higher than that of treated state��s. At this cutoff level, 8, 1, 4 and 4 states are discarded
from the donor pool for California, Colorado, New York and Kansas respectively. In the right panel of figure
3 and 4, we discard all the states with a MSPE two times higher than that of the treated state��s. At this
cut-off level, a total of 13, 5, 7 and 8 states are discarded for California, Colorado, New York and Kansas
respectively. In figure 3, the synthetic living unrelated kidney donation rate yields a good fit for California
in the pre-legislation period. In the post-legislation period, the estimated gap widens (in absolute value) and
clearly stands out. As shown below, not only the post-legislation living unrelated kidney donation rate gap in
California is among the largest of all placebo gaps but also the effect of the paid leave of absence legislation
on living unrelated kidney donation rates in California is causal rather than a random effect.
In order to assess whether the estimated effect is causal, we apply the synthetic control method to estimate
in-space placebo kidney donation gaps for every potential control state in order to create a distribution of
placebo effects. This distribution enables us to identify the exact significance level of the estimated effect of
the legislation. Our confidence that a sizeable synthetic control estimate reflects the effect of the legislation
18A second array of falsification tests is known as in-time placebo tests, in which the passage of paid leave of absence legislation
is artificially reassigned to dates earlier than the actual date. We did not perform in-time placebos because our sample period
is not sufficiently long to assign an artificial date of passage of legislation.
8
would be severely undermined if the estimated gap fell well inside the distribution of placebo gaps (Abadie
et al., 2012). This would imply that our results are driven by randomness rather than causality. In other
words, a significant causal effect of the legislation in the treated state requires that the estimated effect should
be unusually large relative to the distribution of placebo effects. The estimated effect of the legislation for the
treated state is evaluated by calculating the ratio of post-legislation RMSPE to pre-legislation RMSPE that
are equal to or greater than the one for the treated state. This ratio is the p-value that can be interpreted
as the probability of obtaining a post/pre-legislation RMSPE that is at least as large as the one obtained for
the treated state when the legislation is artificially and randomly reassigned to a state that did not enact
such legislation (Abadie et al., 2012).
Figure 5 plots the distribution of placebo effects for California, Colorado, New York and Kansas and for
every 13 states in the donor pool for unrelated donations. The estimated living unrelated kidney donation
rate gap fell well outside the distribution of placebo gaps only for California. This means that, if a state would
have been randomly selected from the sample, the probability of obtaining a post/pre-legislation RMSPE
ratio as high as that of California would be 2/14 = 0.1429. Only one control state in the sample (South
Dakota) achieves a ratio higher than that of California��s. On the other hand, the estimated unrelated kidney
donation rate gaps fell inside the distribution of placebo gaps for Colorado, New York and Kansas, indicating
that the estimated effect is not causal and therefore the paid leave of absence legislation in these three states
is not effective in raising donation rates.
3.4 Robustness Test
In this section, we perform a robustness check to test the sensitivity of our results to the changes in the
synthetic control state weights induced by the exclusion of any particular state from the sample. From table
3, the synthetic California is constructed by the weighted average of six states, namely Alabama, Florida,
Michigan, North Carolina, Nevada and South Dakota. We iteratively re-estimate our model to construct a
synthetic California omitting in each iteration one of the states that was assigned a weight in table 3. Our
aim is to assess the extent to which our results are driven by any particular state (Abadie et al., 2012).
Figure 6 displays the results in which the black solid line is the actual living unrelated donation rate, the
black dashed line is the synthetic living unrelated donation rate of California with all six weight-assigned
states and the gray lines are the leave-one-out estimates.
The average of all six leave-one-out estimates of the synthetic control (gray lines) are on average 0.94
percent higher than the actual living unrelated donation rate in California (black solid line) in the pre-
legislation period and 1.8 percent higher than the original synthetic California (black dashed line) in the
pre-legislation period. In the post-legislation period, the average of all six leave-one-out estimates of the
synthetic control are on average 4 percent higher than the original synthetic California. The leave-one-out
estimate of the synthetic control is sensitive to the exclusion of Nevada and Alabama. This is shown by the
upper two gray lines in the post-legislation period in figure 6.
The pre-legislation RMSPE of the leave-Alabama-out estimate of the synthetic California is 23 percent
higher than the RMSPE of the original synthetic California whereas the pre-legislation RMSPE of the leave-
Nevada-out estimate is more than twice the RMSPE of the original synthetic California. The leave-one-out
distribution of synthetic California is not robust to the exclusion of Nevada and Alabama but the pre-
legislation fit leave-Alabama-out and leave-Nevada-out estimates are also poor. This implies that if Nevada
or Alabama was excluded from the donor pool, the post-legislation living unrelated kidney donation rate gap
would be artificially created by a lack of fit and would show a lower-than-otherwise estimated effect of the
9
legislation.
4 DISCUSSION
We used state-level panel data for the period 1988-2010 in order to reveal the causal impact of paid leave
of absence legislation on living kidney donation rates in the U.S states. We employed the synthetic control
method which is based on estimating the counterfactual: how the state living related and unrelated kidney
donation rates would have evolved in the absence of legislation. Extended over a period of 8 years (from
2002 to 2010), we find an average gap of about 2 percent between the actual living unrelated kidney donation
rates in California and the living unrelated kidney donation rates in a comparable synthetic California in
the absence of legislation. Albeit very small, this positive effect is attributed to the passage of paid leave
of absence legislation. However our results are sensitive to the exclusion of two control states; Nevada and
Alabama, indicating that these states are vital comparison units for California in order to yield a good linear
approximation. On the other hand, our analysis was unable to identify a causal effect on living related kidney
donation rates in any of the states that passed the legislation.
It is important to discuss why a similar causal effect cannot be identified for the remaining fifteen paid-
leave-enacted states�� unrelated donation rates. First, the scale of the legislation may be too narrow to identify
the causal effect of the legislation. The intervention has to be significant in the sense that it has the potential
to exert a large-scale impact and should sustain for a period of time. The legislation for which we attempt
to identify this effect affects only public employees. If the share of public employees in the state employment
is too low, that is those who could potentially benefit from the legislation are a very small group, then the
synthetic control may not be able to pick up any effect of the legislation in that state. To assess whether
there are significant differences in the share of public employees between California and other treated states,
we collected data on the share of public employees in the total state employment for the period of 2001-2010
for our 16 treated states, which we use as a proxy for the scale of legislation19. Our aim is to discuss whether
the failure to identify a causal effect of the legislation in all states but California could be attributed to
the variations in the scale of the legislation. Although a mere inspection of this distribution cannot identify
whether this is true, it gives us hints about the validity of the argument. Figure 7 shows the distribution
of the scale of the legislation. The average share of public employees in the total state employment ranges
from 12.8 percent in Massachusetts to 20.8 percent in Oklahoma with an average share of 16.94 percent for
all 16 treated states as shown by the vertical red line. Among our four treated states for which we were
able to obtain good pre-legislation fits, the share of public employees for California and Colorado is below
the average whereas this share is above the average of all 16 treated states for New York and Kansas. If the
variations in the scale of the state legislation is what determines or causes whether the legislation is effective
or not, then we would either expect to observe an unusually large share of public employees in California
relative to other treated states or would have failed to identify a causal effect of the legislation in California
on the grounds that the scale of the legislation is too small to identify this effect. Neither of these cases
prevails in our analysis. Further, the share of public employees in total employment for any of the sixteen
states is fairly large indicating that the failure to meet the requirement of minimum efficient scale in order for
the legislation to function as intended may not be so severe. Other arguments may be more likely to explain
our findings.
19Bureau
of
Labor
Statistics,
Quarterly
Census
of
Employment
and
Wages
(QCEW):
http://data.bls.gov/pdq/querytool.jsp?survey=en
10
Second, the method constructs a synthetic version of the paid leave-enacted (treated) state by using
some linear weighted combination of states that did not enact the legislation (convex-hull criteria). This
means that the synthetic control would not yield accurate trajectories of the states with extreme values of
the variable of interest and other observable characteristics. The synthetic control method would fail to
reproduce the pre-legislation living kidney donation rates of the most ��egotistic�� and the most ��altruistic��
treated state in the sample because the linear weighted combination of the living kidney donation rates of the
donor states cannot yield a synthetic donation rate as low as the donation rates of the most ��egotistic�� and
as high as the donation rates of the most ��altruistic�� treated state. This may explain the failure to reproduce
the pre-legislation outcome trajectory for states like Hawaii, West Virginia and Delaware where the living
kidney donation rates are extremely low and for states like Maryland where the living kidney donation rates
are extremely high (results not reported).
Third, for other states, a potential explanation of this failure is that the donor pool may not consist of
states with similar observable characteristics in order to yield a good approximation. Until 2010, 70 percent
of all U.S states have passed some sort of compensation legislation, leaving the remaining 30 percent to be
used as control units. Even though the synthetic control method does not require a large number of control
units and in fact may yield good approximations even with a number of control units as few as six, the control
states in our analysis may not be good comparison units for those twelve paid-leave-enacted states for which
the pre-legislation fit was poor, and we were unable to identify the causal effect of the legislation in those
states.
Finally, most of the states that enacted paid leave of absence legislation only allow compensation of public
employees for becoming an organ donor. Failure to allow compensation for the unemployed, uninsured or
low-income individuals who are a major proportion of the population and who are more likely to experience
financial hardship as a result of donation hinders the effectiveness of the legislation. If the aim is to lower the
barriers to living donation by offering modest monetary incentives that are ethically and politically acceptable
it is suggestsed that the current legislation should be amended in order to cover a broader group of beneciaries
of the legislation to ensure that the barriers to living donation are lowered and that the provisions of the
amendment should be independent of whether beneciaries of the legislation are employed or not. However
this might be a difficult task considering the indistinct line between offering modest rewards and outright
payments prohibited by the National Organ Transplant Act of 1984.
11
A Tables
Table 1: Synthetic Control States
Treated States
Donor States
California
Maryland
Alabama
New Hampshire
Colorado
New York
Arizona
New Jersey
Delaware
Ohio
Florida
Nevada
Hawaii
Oklahoma
Kentucky
South Dakota
Indiana
Texas
Michigan
Tennessee
Kansas
Virginia
North Carolina
Vermont
Massachusetts West Virginia
Nebraska
Missouri
Washington
12
Table 2: State Legislation for Kidney Donors
State
Paid leave of absence (up to 30 days)
Tax deduction
Tax credit
Public employees
Private employess
($10,000)
($10,000)
Alaska
2008 (HB.252)
Arkansas
2003 (HB.1289)
2005
2005 (HB.1393)
2005
(ACA ��11-3-205)
(Act No.2235)
California
2002 (AB.1825)
Colorado
1998
(CRS 24-50-104)
Connecticut
2007 (SB.1447)
2004 (SB.327)
Delaware
2001 (SB.45)
Georgia
2002 (HB.1049)
2004 (HB.1410)
Hawaii
2005
(HRS ��78-23.6)
Idaho
2006 (SB.1373)
2006 (SB.1373)
Illinois
2002 (HB.0411)
2005 (HB.324)
Indiana
2002 (HB.1030)
Iowa
2003 (HB.381)
2005 (HF.801)
Kansas
2001
(Exec. Order 2001-02)
Lousiana
2005 (SB.26)
Maine
2002
2002
(26 MRSA ��843)
(26 MRSA ��843)
Maryland
2000 (SB.17)
Massachusetts
2005 (149:33E)
Minnesota
2006
2005 (HF.785)
(MN Stat ��181.9456)
Mississippi
2004 (SB.2639)
2004 (SB.2639)
2006 (HB.1512)
Missouri
2001 (HB.679)
New Mexico
2007
2005 (HB.105)
(NM Stat ��24-28-3)
New York
2001 (AB.4138)
2006 (AB.372)
North Dakota
2005 (SB.2298)
2005 (HB.1474)
Ohio
2001 (HB.326)
2007 (HB.119)
Oklahoma
2002 (SB.1628)
2007 (SB.806)
Oregon
1991
Pennsylvania
2006
2006
(35 PS ��6120.3)
(35 PS ��6120.3)
Rhode Island
2009 (SB.76)
South Carolina
2002 (SB.830)
2006
(SC Code ��8-11-65)
Texas
2003 (HB.89)
Utah
2002 (SB.125)
2005 (SB.164)
Virginia
2001 (HB.1642)
2005
(VA Code ��58.1-322)
Washington
2002
(Exec. Order 02-01)
West Virginia
2005 (SB.240)
Wisconsin
2000 (AB.545)
2004 (AB.477)
Note: The following fifteen states passed none of the above laws: Alabama, Arizona, Florida, Kentucky, Michigan, Montana,
North Carolina, Nebraska, New Hampshire, New Jersey, Nevada, South Dakota, Tennessee, Vermont, Wyoming.
Source: National Kidney Foundation, TransplantLiving, National Conference of State Legislatures, Boulware et al. (2008)
and Lacetera et al. (2012). See text.
13
Table 3: Synthetic Control State Weights, Living Unrelated Kidney Donation
Selected Treated States
CA
CO
NY
KS
Donor
States
AL
0.074
0.121 0.150
AZ
0.153 0.062
FL
0.08
KY
0.049 0.216
MI 0.431
NC
0.065 0.668 0.211
NE
0.076 0.066
NH
0.082
NJ
0.412
NV
0.297 0.049
0.22
0.100
SD
0.052 0.049
TN
0.23
VT
0.032 0.056
Source: Author��s own calculations.
14
B Figures
Figure 1: Number of U.S states by enactment year, 1998-2009
15
Figure 2: Trends in living unrelated kidney donation rates: treated vs. synthetic states
Notes: The actual and synthetic trends for New York end in 2005 because New York further passed tax deduction legislation in
2006.
16
Figure
3:
In-space
placeb
o
exp
erimen
ts,
living
unrelated
kidney
donation
(P
anel
I)
17
Figure
4:
In-space
placeb
o
exp
erimen
ts,
living
unrelated
kidney
donation
(P
anel
II)
18
Figure 5: In-space placebo distributions, living unrelated kidney donation
Notes: The pre-legislation RMSPE for two conrol states in the in-space placebo distributions for Colorado were zero, therefore
we were unable to calculate the post/pre-legislation RMSPE for these two control states and excluded them.
19
Figure 6: Leave-one-out distribution of the synthetic control, living unrelated kidney donation
20
Figure 7: Distribution of the scale of legislation
Source: Bureau of Labor Statistics, Quarterly Census of Employment and Wages (QCEW)
21
C Technical Details
The synthetic control method is developed by Abadie and Gardeazabal (2003) and expanded by Abadie et al.
(2010) and Abadie et al. (2012). In this section, we overview the technical details of the methodology and
discuss its advantages over the traditional regression framework.
Suppose there are P +1 states in the sample, indexed by i = 1, 2,...,P +1 over T periods, t = 1, 2,...,T.
Only state i = 1 enacted the legislation and the remaining P states are the potential control states not enacted
the legislation, called the donor pool. There are T0 number of pre-legislation periods and T1 number of post-
legislation periods so that T0 + T1 = T. The effect of paid leave of absence for unit i at time t is given by
��it = Y I
it − Y N
it where Y I
it is the living kidney donation rate of unit i if enacted the legislation in T0 + 1 to
T and Y N
it is the living kidney donation rate in the absence of legislation. Since only unit i = 1 enacted the
legislation, we need to estimate (��1T0+1,...,��1T ). We first estimate Y N
it by the following factor model:
Y N
it = ��t + ��tZi + ��tµi + ��it
(1)
where ��t is an unknown common factor invariant across units, Zi is the covariate vector not affected
by the legislation, ��t is a vector of unknown time-specific parameters, ��t is a vector of unknown common
factors, µi is the state-specific unobservable and the error term ��it are the zero-mean transitory shocks. The
presence of anticipatory effects are irrelevant in our case, implying that all the elements in Zi that belong to
pre-legislation period are unaffected by the law.
Equation (1) allows the effect of unobservable state heterogeneity to vary over time. In the fixed effects
(FE) model and the difference-in-differences (DiD) estimator, the effect of unobservable heterogeneity, ��t,
is assumed to be fixed over time. Hence, the synthetic control method provides an improvement over FE
and DiD methods and deals better with endogeneity caused by the presence of time-varying unobservable
confounders, all of which were presumed to have been accounted in the traditional regression framework.
The method aims to construct the missing counterfactual, Y N
it , from states not enacted the legislation.
Let W = (w2,...,wP +1) be (P �� 1) vector of weights such that 0 �� wj �� 1 for j = 2, 3,...,P + 1 and
��P +1
j=2 wj = 1. Define the linear combination of pre-legislation values of kidney donation rate as ¯Yk
j
=
��T0
m=1 kmYjm. Abadie et al. (2010) show that if the following conditions hold, then the estimate of the effect
of paid leave of absence legislation for the affected/exposed unit, ˆ��1t = Y1t − ��P +1
j=2 w∗
j Yjt, is an unbiased
estimator of ��1t:
��P +1
j=2 w∗
j Zj = Z1
�� ��P +1
j=2 w∗
j¯Yk
j = ¯Yk
1
(2)
where w∗
j is the weight assigned to the jth unexposed state.
Equation (2) can hold exactly only if (¯Yk
1 ,Z1) belongs to the convex hull of [(¯Yk
2 ,Z2) ,..., (¯Yk
P +1,ZP +1)].
This means that the living kidney donation rate of some of the states that passed the legislation may not be
synthetized accurately using the pre-legislation characteristics of the states that did not pass any legislation.
The vector W∗ is chosen to minimize the distance between the vector of pre-legislation characteristics
for the exposed state (X1) and the weighted matrix that contains the pre-legislation characteristics of un-
exposed states (X0):
X1 − X0W =
��
(X1 − X0W) V (X1 − X0W) where V is a symmetric and positive
semidefinite matrix. This minimization procedure is subject to the constraints that the weight assigned to
each unexposed state should lie between zero and one and that the sum of the weights is bounded by one.
22
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24