Uterus at a Price: Disability Insurance and Hysterectomy

Elliott Fan
Department of Economics, National Taiwan University; elliottfan@ntu.edu.tw

Hsienming Lien
Department of Public Finance, National Chengchi University; hmlien@nccu.edu.tw

Ching-to Albert MaΤ

Department of Economics, Boston University; ma@bu.edu

July 2017

Abstract
Taiwanese Labor, Government Employee, and Farmer Insurance programs provide 5-6 months of salary toenrollees who undergo hysterectomy or oophorectomy before their 45th birthday. These programs result in
more and earlier treatments, referred as, respectively, inducement and timing effects. Difference-indifference and nonparametric methods are used to estimate these effects on surgery hazards between 1997
and 2011. For Government Employee and Labor Insurance, inducement is 11-12% of all hysterectomies,
and timing 20% of inducement. For oophorectomy, both effects are insignificant. Induced hysterectomies
increase benefit payments and surgical costs, at about the cost of a mammogram and 5 pap smears perenrollee.

JEL: I00, I10, I12, I18
Keywords: disability insurance, moral hazard, hysterectomy, oophorectomy

We thank Stacey Chen, Minchung Hsu, Tor Iversen, Kevin Lang, Tzu-Ting Yang and seminar participants at Boston
University, Brandeis University, Institute of Economics at Academic Sinica, Queen’s University, University of
Bologna, and University of Oslo for their valuable comments and suggestions. We thank Johannes Schmieder for
generously providing us with codes that assisted us in the nonparametric estimation, and the Taiwanese National
Health Research Institute for providing National Health Insurance Data. Support from National Science Council(MOST 105-2410-H-004-004 to Hsienming Lien) is greatly appreciated. The paper represents the authors’ views anddoes not reflect those of the Bureau of National Health Insurance or the National Science Council.

1.

Introduction
In this paper, we study the effect of disability insurance on the moral hazard of health care use.

Disability insurance compensates enrollees for accidental or inherited loss of physical and mental
capacities that adversely affect labor market potentials (Staubli, 2011; Maestas, Mullen and Strand, 2013;
French, and Song, 2014). Taiwan adopts a set of mandatory, employment-based comprehensive disability
programs. The incentive effects of disability insurance are well known. However, the Taiwanese programs
have an uncommon component: they include coverage for women’s infertility due to i) hysterectomy(surgical removal of the uterus), ii) oophorectomy (surgical removal of both ovaries), and iii) radio-chemo
therapy. Enrollees are entitled to a cash benefit, equal to about 5 to 6 months of salary when they undergo
these treatments, but the coverage ends when enrollees become 45 years old.
Organ dismemberment insurance policies are not uncommon. However, we are unaware of evidence
that these policies have “caused” enrollees to lose a thumb, a toe, an eye, or get an eardrum perforated.
Normally, compensations are insufficient to cause excessive claims because the loss disutility is too high.
However, the Taiwanese programs afford us the rare opportunity to examine cases in which some enrollees
react to coverage by electing to have organ-removal surgeries.
We study disability insurance’s effect on the incidence of hysterectomy and oophorectomy, both ofwhich involve the removal of major organs. We are unaware of the same infertility coverage or age limit inany other social insurance program.1 Although it may sound sinister to suggest that enrollees undergo
serious organ-removal surgeries to qualify for disability benefits, the economic perspective is that thecoverage, perhaps unintentionally, has created such an incentive. Furthermore, there is an incentive toundergo surgeries before the benefit expires at the 45th birthday. Clearly, hysterectomy and oophorectomy
must be performed based on illness indications, but they may still be performed when the indicatedseverity may not fully justify surgery. Does disability insurance lead to excessive treatments that would not

1 In Japan, benefits due to infertility suffered at work are covered, but the Taiwan programs are universal, not limited
to injury at work.

1

have been performed in the absence of the insurance: an inducement effect? Does disability insurance leadto treatments being expedited to before the 45th birthday: a timing effect?
Only hysterectomy exhibits significant inducement and timing effects; oophorectomy does not. These
are striking results. First, we can interpret this particular infertility coverage as a natural experiment thatoffers the same benefit on infertility due to two different medical interventions. Although both
hysterectomy and oophorectomy will lead to infertility (qualifying enrollees for benefit), oophorectomy
has far more serious adverse health consequences than hysterectomy (more thorough discussions in
Subsection 2.1). In the scenario that an enrollee has chosen to undergo one of the two procedures solely forthe disability benefit, the preferred procedure would be hysterectomy due to lower disutility. The likely
scenario is that a medical intervention is indicated due to an illness. Our results indicate that the monetarydisability benefits would have no effect on oophorectomy, but lead to more hysterectomy, again, likely
because hysterectomy is associated with a lower disutility. This natural experiment yields behaviors thatare consistent with optimizing behavior---even when the decision involves a surgery to remove a majororgan.
Second, our results indicate that the way the disability insurance is implemented may lead to serious
deadweight loss. About 11-12% of hysterectomies in our sample are unnecessary. The deadweight loss isthe cost of this surgical procedure, precisely because the qualification requires it. Linking a disability to asurgical procedure creates double moral hazard, one in the claim of disability, and another in health careuse. Although the infertility coverage in Taiwan is unique, our results serve as a warning against using a
medical treatment as a qualification for disability insurance benefits.
Third, our results shed some light on monetary incentives and organ donation. In almost all countries,
direct financial compensations to donors of transplant organs or tissues do not exist. However, our naturalexperiment does involve financial compensations for someone whose organ is removed---although uterus
or ovaries are not used for transplants. Furthermore, the disability insurance programs are sanctioned andproperly run by the Taiwanese government.

2

Our evidence suggests that individuals make consistent choices. The lack of inducement and timing
effects in oophorectomy perhaps is the strongest indication that the usual benefit-cost analysis commonly
practiced in economic activities is in force. In fact, the evidence suggests that a well-organized or regulated
market may work as expected even for a human organ. For a given price of an organ, if the disutility of its
removal is sufficiently high, individuals reject the offer, as in the case of oophorectomy; however, if thedisutility is sufficiently low, individuals accept it, as in the case of hysterectomy. In fact, we have foundthat, in the income-stratified samples, induced-hysterectomy rates are increasing in the benefit level. To
avoid the exploitation of the poor in organ donation, our finding supports a donation compensation schemethat is positively related to a donor’s income.
We estimate the inducement and timing effects by a difference-in-difference method and by anonparametric method. Our difference-in-difference design is based on the comparison of enrollees inthree disability insurance programs and those uninsured for the period between 1997 and 2011 in Taiwan.
The three programs are Labor Insurance, Government Employee Insurance, and Farmer Insurance. The
control consists of those who have not belonged to these programs, mostly those inactive in the labor force.
Our data are from Taiwan’s National Health Insurance, and indicate the type of disability insurance foreach individual, and if and when hysterectomy, oophorectomy, or both surgeries have taken place. In
addition, the data are merged with variables obtained from the Survey of Family Income and Expenditure(SFIE) to help control for socio-demographic and economic factors.
We follow female enrollees in the three insurance programs and in the control group between their
39th and 50th birthdays. In the main analysis, we include only enrollees who have not changed theirinsurance programs in the sample years. We then group enrollees by their birth cohorts and insurance
programs, and calculate the corresponding hysterectomy and oophorectomy hazards. Our main variable isthe quarterly surgery hazard in the number of quarters (a 91-day period) from the 45th birthday. Because
we follow enrollees for 11 years, there are 24 such benefit quarters before the 45th birthday, and 20 quarters
after. For each birth cohort, we also use the average numbers of children and sons, marital status, andhousehold income as covariates.

3

Our difference-in-difference design is unconventional because there is not a before-and-after policy
regime change. However, the insured lose the infertility insurance benefit at age 45. Obviously, that benefit
expiration is irrelevant to the uninsured. Our hypothesis is that when there is a lot of time before the benefit
expires, the insured’s behaviors are unaffected by the deadline. However, at some later point, the deadline
becomes pressing. To operationalize our empirical strategy, we let the deadline become relevant whenenrollees turn 40 years old. In other words, we treat the benefit expiration at the 45th birthday as a policy
intervention on disability-program enrollees at their 40th birthday. Our approach is conservative: quarters
just after the 40th birthday need not exhibit differences. If the relevance of the deadline only appears at
some time after the 40th birthday, our difference estimates would simply vanish.
Using the hazards before age 40 as the benchmark, we examine the dynamic, quarter-by-quarter
hazard differences between the insured and uninsured, for the 5 years before and 5 years after the 45thbirthday (20 quarters before and after the benefit expires). How do the hazards differ when enrollees areapproaching their 45th birthday? How do they differ thereafter? Indeed, for hysterectomy, Labor Insuranceand Government Employee Insurance enrollees’ hazards begin to rise rapidly 8 quarters before expiration,
but drop rapidly for 2 quarters after. Enrollees in Farmer Insurance show similar but less pronounced
hazard changes. For oophorectomy, these rapid changes are absent in all insurance programs.
From the estimates we calculate inducement and timing effects. The inducement effect is the total
number of insured enrollees’ extra surgeries between their 40th and 50th birthdays compared to the control.
The timing effect consists of the total number of surgeries that the insured would have undergone after the
45th birthday compared to the control group. In our sample, Labor Insurance enrollees have a total of
43,845 hysterectomies, and the inducement effect is 5,076 hysterectomies, or about 11.6%. For
Government Employee Insurance, the total is 7,262, and the inducement effect is 789, or 10.9%. For
Farmer Insurance, the total is 9,100, and the inducement effect is 347, or 3.8%. (Later, we will provide all
the details of these three insurance programs, which partially account for some of the magnitudedifferences.) No inducement or timing effects have been found for oophorectomy.

4Besides the difference-in-difference estimation, we also use a nonparametric method. Here, we use thebunching method (e.g. Saez, 2010; Chetty et al., 2011) and assume that hazards follow a smooth time path
if the disability benefit would never expire. Conceptually, we maintain the counterfactual assumption thatsurgeries do not happen abruptly over time. Operationally, we use hazards in benefit quarters far from the45th birthday in order to fit a polynomial. Then we use the fitted polynomial to predict the hazards in
benefit quarters near the 45th birthday. Any discrepancy between the predicted and actual hazards is
attributed to benefit expiration. These discrepancies are used to define the inducement and timing effects asin the difference-in-difference approach. In any case, the nonparametric estimates of the inducement andtiming effects for hysterectomy and oophorectomy are similar to those in the difference-in-difference
method.
As a check, we estimate inducement and timing effects of two other surgeries: partial oophorectomy(the removal of one ovary), and myomectomy (the removal of the inner lining of the uterus). These
procedures are used to alleviate problems in the female reproductive system, but do not qualify for theinfertility insurance benefit. We have found no inducement or timing effects for these procedures.
We also consider a number of robustness issues and policy implications. Our primary sample consistsof female enrollees who have not switched between insurance programs. We relax this restriction by
including those who have switched between programs. This makes the sample larger. Furthermore, ourdata include medical records of women aged between 39 and 49 years old during the period 1997 to 2011.
Therefore, the panel is unbalanced: early cohorts are subject to left censoring while late cohorts are subject
to right censoring. Later we restrict our sample to those with uncensored medical records in the sample
period. Our results are robust to various compositions of samples.
We estimate the social costs of the disability insurance programs. The costs are the additional benefit
payments and hysterectomy expenditures due to inducement over enrollees’ lifetime. Benefit payments aretransfer, which may be inefficient or unintended, whereas induced hysterectomies are unnecessary
treatments, a deadweight loss. We estimate that for the three programs on average, the increase in benefit
payment is about NT$1,410 per enrollee, and the hysterectomy cost is about NT$400 per enrollee. For

5comparison, the reimbursement rate for mammogram and pap smear are, respectively, NT$1,245 andNT$80. Hence, the inducement cost is more than enough to pay for 1 mammogram and 5 pap smears foreach enrollee during her lifetime.
The plan of the paper is as follows. In the next subsection, we review the literature. We present the
study background in Section 2. Section 3 describes the data for the study, and the construction of oursample of enrollees who have not changed insurance status throughout the entire sample period. We alsopresent sample statistics. In Section 4, we present the two econometric methods. Subsection 4.1 is on the
difference-in-difference method, and Subsection 4.2 is on the nonparametric method. In each case, we set
up the regression equations, and define the inducement and timing effects in terms of the parameters to be
estimated. The two subsections in Section 5 contain the estimation results of the two econometric methods.
In Section 6, we consider a number of robustness checks and policy implications. We consider a bigger
sample that includes individuals who may have switched insurance programs. We also consider a smaller
sample in which individuals are never censored. Then we perform various robustness checks based onthese expanded and restricted samples. Next, we stratify the sample of Labor Insurance enrollees according
to five benefit levels, and examine the size of inducement with respect to benefit levels. Finally, we present
estimates of social costs due to inducement. We draw some conclusions in Section 7.
1.1.

Literature review
Insurance benefits that are based on age and time are quite common. Medicare in the United States

provides health insurance to individuals over 65 years old. In most countries, unemployment benefits
expire after a period of time. The incentives of insurance benefits that are based on time and enrollees’ age
influence enrollees’ behaviors. For instance, research has shown that patients delay treatment or surgeries
until they become eligible for Medicare (McWilliams et al., 2003; McWilliams et al., 2007; Card, Dobkin
and Maestas, 2008; Card, Dobkin and Maestas, 2009). Research also has shown that recipients of
unemployment insurance delay job search until benefits are about to expire; this delay leads to a spike ofthe unemployment duration distribution around the expiration point (Caliendo, Tatsiramos, andUhlendorff, 2013; Farber and Valletta, 2015; Schmieder, Wachter, and Bender, 2016). In our study setting,6

similar incentives exist: the infertility benefits of the Taiwanese disability program expire at age 45.
However, our setting has one major difference: benefit qualification requires hysterectomy oroophorectomy, and Taiwan’s National Health Insurance covers these surgeries. In other words, anenrollee’s incentive to qualify for the benefit implies a second incentive for a surgery.
Our empirical strategy uses a modified form of difference-in-difference regression, and a
nonparametric method. Difference-in-difference regression is the standard method for program evaluations
and policy assessments (for a review see Imbens and Wooldridge, 2009). However, the standard method
considers only the average policy effect. Here, we go beyond the average effect to study policy effects overtime, particularly the periods right before and after benefit expiration. As in Chandra, Gruber, andMcKnight (2010), we use quarter-by-quarter estimates for the policy effect over time. Autor, Kerr andKugler (2007) use a similar year-by-year difference-in-difference model to understand how mandated
employment protections reduce productive efficiency. Hoynes, Miller and Simon (2015) also use the same
method to study how earned income tax credit influences infant health outcomes.
Our nonparametric method is similar to the bunching method for assessing discontinuity effects
created by policies. For example, taxes can be discontinuously related to reported incomes (Saez, 2010;
Chetty et al., 2011; Kleven and Waseem, 2013), tax reliefs may be available to couples only if marriages orchild births happen before a certain date (Persson, 2015), or students’ test scores bump up over key grade
cutoffs in nationwide math tests, and teachers use discretion in their grading to achieve the discrete jumps(Diamond and Persson, 2016). The standard assumption is that, absent the policy, the variable of interest
should change smoothly, so any bunching is due to the policy. We use the same basic methodology.
However, our method is more closely related to Diamond and Persson (2016) in that we adopt an
optimality criterion---minimum mean-squared errors---to determine the manipulated regions and thenestimate the counterfactual polynomial of surgeries.

2.

Background

2.1.

Hysterectomy and oophorectomy

7

Hysterectomy is the surgical removal of a woman’s uterus, the organ that holds the fetus. This is thesecond most common elective surgery among women, after cesarean section for childbirth. Hysterectomies
are performed mainly for uterine fibroids and malignant tumors in a woman’s reproductive system.2
Common indications are menstrual irregularities, such as heavy bleeding, and serious pain (Department of
Health and Human Services, 2011). Alternative treatments for some of these indications are available.
Myomectomy---the surgical removal of some uterine lining---may be a remedy for uterine fibroids.
Endometrial ablation---surgical removal of endometrium---may be suitable for excessive bleeding. Pain
medication, synthetic steroid hormones, and pelvic floor exercises are other alternatives.
Usually performed by a gynecologist or an obstetrician, hysterectomy can be either complete (removalof the uterus and cervix) or partial (without the removal of the cervix). There are three variants of thesurgical procedure: abdominal, vaginal, and laparoscopic. Hysterectomy carries a minimal morbidity risk,
at a mortality rate below 0.05%. Complications, such as bleeding and dysfunctional uterine parity, are alsorare (McPherson et al., 2004). The length of hospital stay for the procedure ranges from 3 to 5 days.
The incidence of hysterectomy exhibits an age pattern over a woman’s lifetime: the rate rises steadily
from ages 30 to 39, reaches a peak between 45 and 49, and then declines steeply (McPherson, Gon and
Scott, 2013). Despite an obvious age pattern, incidence rates vary substantially across different countries.
According to OECD Statistics, in 2012, the average hysterectomy incidence rate was 179 per 100,000
women. However, in the same year, the hysterectomy incidence rate in Germany was 318 per 100,000,
whereas it was only 49 per 100,000 in Denmark (McPherson, Gon and Scott, 2013).
For Asian countries, the incidence rate (per 100,000 women) for South Korea was 198 in 2012
(OECD Health Data, 2016). In Taiwan, with a population of 23 million, an average of 23,000
hysterectomies are performed each year. From 1996 to 2005, the hysterectomy incidence rates per 100,000
in Taiwan varied between 268 and 303 (Wu et al, 2010). According to National Health Insurance Data,
when Taiwanese women become 50 years old, more than 20% of them would have had hysterectomies.

2

In a random sample of 658 Taiwanese women, the most common indication for hysterectomy was uterine fibroids(at 46.2%), followed by malignancy and pre-malignancy (at 22.2%) (Wu et al., 2005).

8

Oophorectomy is the surgical removal of a woman’s ovaries, the organs that hold her eggs. The
primary indication for oophorectomy is ovarian cancer. The common technique to perform oophorectomy
is abdominal laparoscopy. Oophorectomies and hysterectomies are sometimes performed in the same
operation, mainly for preventing cancer. A partial oophorectomy, the removal of only one ovary, iscommonly performed for medical indications such as endometriosis, benign tumor, inflammation, etc., so
may not be combined with a hysterectomy.
The removal of ovaries causes hormonal changes and the spontaneous onset of menopause. Most
patients are advised to start hormonal replacement post operation. The health risks associated with totaloophorectomy are more serious---women who have had oophorectomies before 45 years old carry amortality risk 170% higher than women who have retained their ovaries (Parker et al., 2005). The
incidence of complete oophorectomy is relatively low. Between 1997 and 2011, for instance, less than
2,300 completed oophorectomies among women aged between 40 and 49 were performed in Taiwan eachyear. By contrast, more than 10,000 hysterectomies were performed in the same age group each year
during the same time period.
2.2 Disability insurance
In Taiwan, three mandatory social insurance programs provide disability insurance to the working
population. Enrollment is only for the individual; there is no family coverage. Labor Insurance is thelargest program, covering nearly 9 million workers in the private sector in 2012. When it was firstestablished in 1956, it provided only health insurance, but by 1978 insured enrollees had coverage fordisability, maternity, occupational injuries, unemployment, pension, and death. After 1995, Taiwan’s
National Health Insurance replaced health insurance in Labor Insurance.
The second largest social insurance program is Farmer Insurance. In 2012, this program covered 1.5
million farmers. Government Employee Insurance, the third program, is for public employees and teachers
in both public and private schools and colleges. In 2012, Government Employee Insurance covered about90.6 million lives. Similar to Labor Insurance, Farmer Insurance and Government Employee Insurance
provide a portfolio of benefits, which include disability insurance.3
With few exceptions, disability insurance benefit is paid as a lump sum;4 the benefit amount varies
according to the type and severity of disabilities. In this research, we focus on the disability benefit for afemale enrollee’s loss of her reproductive function. A woman is eligible for this disability benefit if, due toillnesses, she undergoes any of three medical procedures before turning 45 years old: hysterectomy,complete oophorectomy, and radio-chemo therapy on ovaries. The disability insurance benefit is not meant
to compensate for medical expenses because Taiwan’s National Health Insurance covers most in-patient
medical expenses.5
Recipients of insurance benefits are mostly patients who have undergone hysterectomy. In contrast,
complete oophorectomy and radiation and chemotherapy are less common. Our hypothesis is that the cash
benefit from disability insurance may cause excessive treatments. The effect of disability insurance on
hysterectomy is plausible because the adverse consequences of hysterectomy are relatively mild. On theother hand, radio-chemo therapies have very serious consequences and side effects, so the insurance
benefit is unlikely to have any effect on such decisions. Oophorectomy also carries adverse consequences,
but we will study the effect of insurance on this treatment. As a check, we will study partial oophorectomy
and myomectomy, which do not qualify for insurance benefit.
The disability benefits are calculated according to an enrollee’s “insurance salary”, to be defined next;
they are 6 months of insurance salary in Government Employee Insurance, and 5.3 months in both Labor
Insurance and Farmer Insurance. For Farmer Insurance, the insurance salary is fixed at NT$10,200 per
month, so the reproductive disability benefit is fixed at NT$54,060 (= 10200*5.3). (In 2015, the exchange
rate was about NT$30 to US$1.) For Labor Insurance, in 2013, the insurance salary is defined to be the3

Government Employee Insurance does not provide unemployment insurance. Farmer Insurance does not offer
unemployment insurance or pension scheme.
4
Disability insurance does provide long-term benefits for those who contract chronic illnesses or have accidents that
impair their capacity to work.
5
The co-insurance rate of inpatient services for Taiwan’s National Health Insurance is 10%, with spending caps. In
2011, the caps per admission and per year were NT28,000 and NT47,000 respectively (In 2015, the exchange rate
was about NT$30 to US$1).

10lower of an enrollee’s actual monthly salary and NT$43,900. In other words, the benefit is 5.3 months ofsalary for those with monthly pay below NT$43,900, but will correspond to a smaller number of months ofsalary for those with higher pay. For Government Employee Insurance, the insurance salary is the lower ofan enrollee’s base monthly salary and NT$53,900. However, the base salary does not include various
stipends (e.g. research stipends for teachers), and an enrollee in Government Employee Insurance typicallyhas actual monthly earnings higher than the base salary.6 For those with base pay below NT$53,900, thebenefit is lower than six months of actual earnings. For those with higher base pay, the benefit willcorrespond to an even smaller portion of monthly salary.

3.

Data and samples

3.1.

Data
Our sample period spans the 15 years between 1997 and 2011. The subjects in our study are females

born between 1948 and 1972, and we study their experiences in the time between their 39th and 50thbirthdays during the sample period. We use three data sets. The first is the set of hospital claims of Taiwan
National Health Insurance between 1997 and 2011. The claims data include all inpatient admissions in
Taiwan because National Health Insurance covers the entire population. Each claim includes a patient’s
demographics (gender and date of birth), admission date, disease diagnoses, medical reimbursement, andany surgery performed during the admission. Each claim also has scrambled unique identifiers for a patient,doctors and hospitals. We use the surgical-procedure information to identify those who have undergone
hysterectomy, oophorectomy, myomectomy, and partial oophorectomy. We use a patient’s date of birthand admission date to check whether hysterectomy and oophorectomy have been performed before the 45thbirthday, the disability insurance benefit qualification criterion.7

6

For instance, the base salary and the research stipend for an assistant professor in 2012 was approximately the same,at NT$41,755 and NT$39,555, respectively.
7 The infertility benefit is paid once even if both hysterectomy and oophorectomy have been performed.

11

Our second data set is the National Health Insurance enrollment file. The file contains the last entry ofeach enrollee’s insurance program and disability insurance salary at the end of a calendar year.8 We firstuse an enrollee’s insurance type to infer the disability insurance status. National Health Insurance started in
1994 by merging many private and public insurance programs, and its enrollment file has continued to
track enrollees’ other social insurance modules. Therefore, from the enrollment file, we classify subjects’
disability insurance status into four groups: Government Employee Insurance, Labor Insurance, Farmer
Insurance, and otherwise uninsured. However, the current-year insurance program status may beinappropriate if some enrollees change insurance status and programs after undertaking a hysterectomy.
Later we use an enrollee’s disability insurance status in the previous year as a robustness check.
Next, we obtain enrollees’ disability benefit information in the National Health Insurance enrollment
file. Recall that the disability benefit is determined by an enrollee’s salary up to a maximum (forGovernment Employee Insurance and Labor Insurance) or by a fixed amount (for Farmer Insurance).
National Health Insurance charges a premium equal to a percent of an enrollee’s monthly salary up to
NT$188,000, which is much higher than the salary caps for disability insurance benefits. Therefore, fromthe National Health Insurance premium, we can infer an enrollee’s salary, and, in turn, the benefits. This
inference is exact for enrollees in Labor Insurance. Government Employee Insurance uses the base salary,a fraction of the total salary, for benefit calculation, so the enrollee’s salary in the National Health
Insurance enrollment file will over-estimate the benefit. (For this reason, our analysis in Subsection 6.2
will be based on Labor Insurance enrollees.) The disability benefit in Farmer Insurance is fixed, so we do
not need to use salary information from National Health Insurance.
Our third data set is from the Survey of Family Income and Expenditure, conducted by Taiwan’s
Directorate General of Budget, Accounting and Statistics. Each year the survey randomly samples 13,00016,000 households (or about 52,000–68,000 individuals) and collects information on socio-demographic

8

Up until 2002, the National Health Insurance enrollment file contains full disability insurance enrollment records.
From 2003 onward, the enrollment file only contains enrollees’ last disability insurance record in a calendar year; it
no longer tracks an enrollee’s disability insurance program changes during the year. For consistency, we use the last
disability insurance record even for years before 2003.

12

characteristics of each member of the sampled households. For our sample period 1997-2011, we obtainthe following information about female respondents who are in the corresponding age group (39-49 yearsold): highest education level attained, marital status, number of children by gender, monthly household
earnings, and disability insurance type. We then use the insurance information to merge with theenrollment files to control for demographics of enrolled populations.
3.2. Samples
We define our sample in the following way. First, our research is on the effect of disability insurance
benefit. This is only available to female enrollees undergoing hysterectomy and oophorectomy before theyturn 45 years old. To investigate the insurance program effects, we follow enrollees’ decisions for six years
before, and for five years after the expiration of the benefit.
Next, we impose a number of restrictions. We remove those in Labor Insurance whose enrollments
were through trade union memberships, because their reported incomes might be unreliable.9 These
enrollees are able to manipulate their benefit levels, so their decisions may be different from others inLabor Insurance. We also delete a small number of enrollees who were in military or welfare programs,
because their access to health services might be different.
Furthermore, enrollees may change social insurance programs through employment changes. Whereas
most will not change jobs in order to switch from Labor Insurance to Government Employee Insurance
principally because of the small difference in disability-insurance benefits, the possibility cannot be
excluded for all. The strategic switch between disability insurance programs creates a selection problem.
To control for this selection, for the main analysis we use a sample of enrollees who have never changed
their insurance status within the sample period. We call this the nonswitching sample. The general sample
refers to all female enrollees regardless of any change in insurance programs during the sample period.

9

Labor law in Taiwan requires private companies with five or more employees to purchase Labor Insurance for all
employees. Self-employed workers or those who work in firms with fewer than 5 employees are not required toparticipate, or they can participate through trade unions. Salaries of these workers are often unstable or underreported. For the comparison between insured salary and earned salary in various insurance groups, see Lien (2011).

13

Table 1 illustrates the extent of strategic insurance program switches. (All tables are at the end of themanuscript.) We consider all enrollees who have had hysterectomies during the sample period, and haveincluded those in Labor Insurance who are covered by trade union memberships. There are almost 180,000
hysterectomies. For each enrollee, we note her insurance program in the year in which hysterectomy isundertaken, and her insurance program the year before. Consider the row under Labor Insurance in Table 1.
The number 91.94% is the fraction of all Labor Insurance enrollees who have undergone hysterectomies
under the same program. Only 0.03% of Labor Insurance enrollees have changed to Government
Employee Insurance when they have had hysterectomies the following year; 0.18% of Labor Insurance
enrollees have changed to Farmer Insurance, etc.
Table 1 shows that insured enrollees overwhelmingly have had the same insurance program as theyear before when they undergo hysterectomy. More than 90% of those in Labor Insurance have notchanged the program from the year before hysterectomies; the corresponding numbers for Government
Employee Insurance and Farmer Insurance are even higher, at 98 and 97%. The lower corresponding
percentage of just below 87% for the uninsured likely indicates some strategic changes. Almost 6% of theuninsured have become insured under Labor Insurance when they have hysterectomies, and almost 7%
have become insured through trade union memberships. We use the nonswitching sample for the main
analysis, and the general sample for robustness check and social cost calculations.
Our data period is between 1997 and 2011, a total of 15 years. Female enrollees born between 1948
and 1972 were included for their experiences between their 39 and 49 birthdays, as long as theseexperiences happen between 1997 and 2011. Table 2 presents the birth cohorts and their corresponding
ages in 1997 and 2011. The oldest cohort, those born in 1948, would be 49 years old in 1997, so would
only stay in the sample for one year. They would also have experienced the deadline prior to the data
period. The youngest cohort, those born in 1972, would be 39 years old in 2011. Likewise, they would
only stay in the data period for one year, and they would experience the deadline after the data period. In
other words, enrollees’ experiences can be left censored or right censored. However, for those enrollees

14

born between 1958 and 1962, they would spend all their 11 years between their 39th and 49th birthdays
within the data period between 1997 and 2011. These enrollees constitute a balanced sample.
In total we use three samples. The nonswitching sample is used throughout. We use the general andbalanced samples for robustness checks. We use the balanced sample for social cost calculation. Censoring
happens in both nonswitching and general samples, but they have a lot more enrollees. Censoring does not
happen in the balanced sample, but it is much smaller.
3.3 Summary statistics
The first half of Table 3 presents the summary statistics of the nonswitching sample in the years 2000,
2005 and 2010. The number of subjects in the nonswitching sample ranges from 0.93 to 1.23 million in theyears 2000, 2005, and 2010. Because each subject is selected to be in the sample only when she is between
39 and 49 years old in that sample year, there is a significant change in the distribution of birth cohorts
across the years. In 2000, for instance, subjects born between 1960 and 1964 account for 17.9% of thesubjects in that year, but those born between 1950 and 1954 account for 38%, and those born between
1955 and 1959 account for the rest. In 2005, the birth-year distribution shifts forward: none were born
between 1950 and 1954, but 33.0% were born between 1955 and 1959, with the largest group (45.7%)
being born between 1960 and 1964. For the year 2010, the subjects’ birth-year distribution follows thesame forward-shift pattern.
Table 3 also shows the distributions of the enrollees’ insurance programs in the nonswitching sample.
The percentages of enrollees having Government Employee Insurance seem to be quite stable in the three
years, ranging from 9.6% to 10.2% in the sample. Labor Insurance has the largest share of enrollment,
about 50%, in each of the three years. However, the share of Farmer Insurance enrollments gradually
declines over time. This is likely due to the diminishing and aging farmer population. Finally, the shares of
the uninsured females seem to exhibit a slightly downward trend, declining from 31.0% in 2000 to 27.5%
in 2010.
The second half of Table 3 shows the corresponding figures of the general sample. In contrast with thenonswitching sample, the general sample has a higher percentage of enrollees in Labor Insurance and15uninsured groups. Enrollees in Government Employee Insurance and Farmer Insurance are less likely tochange programs, so their shares become smaller when this restriction is lifted. Likewise, a higher
percentage of older cohorts can be observed because those enrollees are more likely to switch between
insurance groups (e.g. from being employed to being unemployed and hence uninsured).
The lowest part of Table 3 displays the incidence rates of four reproductive-organ related surgeries in
the nonswitching sample. Whereas the incidence rates of hysterectomy fall from 1,128 (per 100,000) in
2000 to 695 in 2010, myomectomy incidence rates almost double between 2000 and 2010. This likely
indicates that myomectomy has become a more effective treatment for those suffering from uterine fibroids.
Myomectomy may also become a more popular substitute for hysterectomy. For oophorectomy, theincidence rates of complete oophorectomy decline over time, but the opposite is true for partial
oophorectomy. Better diagnosis and more conservative treatments may have been behind this trend.
Similar trends can be also found in the general sample.

4.

Econometric methods
Our hypothesis is that an enrollee’s decision to undergo hysterectomy or oophorectomy issignificantly affected by the disability insurance, a hypothesis that is based on cost and benefit.
Nonetheless, our data do not allow us to test this directly at the individual level because we do not haveinformation of individual or household income, marital status, or number of children. However, from SIFE
we obtain these variables for birth cohorts. Therefore, we aggregate medical records in order to constructcohort hazards. In any case, each enrollee in a disability insurance program faces the same incentives. If
individual surgery decisions respond to incentives, enrollees as a group also respond similarly. Our data
allow us to test our hypothesis at the cohort level reliably.
We group enrollees into cohorts by two discrete time scales: i) a natural time scale and ii) the amountof time from the 45th birthday. The natural time scale is represented by the vector 𝑐 ≡ (𝑦, 𝑠) where 𝑦 is ayear and 𝑠 is a season, or a three-month period of the year. An enrollee’s birthday fits her into a birthcohort 𝑐 ≡ (𝑦, 𝑠). Our sample consists of female enrollees born between 1948 and 1972, so we have 10016(= 25 years × 4 seasons) birth cohorts, with y taking values of 1948, 1949,…, and 1972, and s taking
values of 1, 2, 3, and 4.
The second time scale measures how much time an enrollee has available before, or elapsed after, theexpiration of the disability insurance benefit. We call the second time scale an enrollee’s benefit quarter,and denote it by the variable q. The 91-day period that begins with the 45th birthday is called quarter 0; thenext 91 days is quarter 1; the 91 days before quarter 0 is quarter -1, and so on. Enrollees in our sample are
between 39 and 49 years old, so the benefit-quarter variable q takes values -24, -23,…, -1, 0, 1,…,19. Bymaking distinctions between year, season, and benefit quarters we allow for more decision variations.
Clearly, the choice of a 91-day length for a time unit, both for chronological and benefit dimensions,is for convenience and practicality. A shorter time length may imply sharper differences between adjacentcohorts because treatment incidences occur less frequently, whereas a longer time length reduces thenumber of groups. (We have also defined the cohort length to six months, and have verified that results are
similar.)For each birth cohort in a given benefit quarter, the hysterectomy hazard is defined to be the ratio of
the total number of enrollees undergoing hysterectomy within this benefit quarter to the total number ofenrollees who have not undergone hysterectomy at the beginning of the benefit quarter. We define
analogously the hazards of total oophorectomy, partial oophorectomy, and myomectomy. All the hazards
are calibrated separately for the three insured groups and the uninsured group. In Figure 1, we present four
panels. Each panel is for a surgery, and plots the hazards of the three insured groups and the control group.
The grey curve plots the hazards of the uninsured; the red curve is hazards of enrollees in Labor Insurance,
whereas the blue and green curves are for those in Government Employee Insurance and Farmer Insurance,
respectively. Recall that hysterectomy and oophorectomy qualify for disability insurance benefit if they are
performed by the 45th birthday, but partial oophorectomy and myomectomy do not qualify.

17

300
200
100
0

Hazard (of 10^6)400

Figure 1(A) Hysterectomy hazards

-24

-20

-10
0
10
Quarters from the 45th birthday
Government Employee
Farmer

20

Labor
Uninsured

60
40
20
0
-20

Hazard (of 10^6)80 100(B) Total oophorectomy hazards

-24

-20

-10
0
10
Quarters from the 45th birthday
Government Employee
Farmer18

Labor
Uninsured

20

60
40
20
-20

0

Hazard (of 10^6)80(C) Partial oophorectomy hazards

-24

-20

-10
0
10
Quarters from the 45th birthday
Government Employee
Farmer

20

Labor
Uninsured

20 40 60 80 100 120-20 0

Hazard (of 10^6)(D) Myomectomy hazards

-24

-20

-10
0
10
Quarters from the 45th birthday
Government Employee
Farmer

19

Labor
Uninsured

20

The four panels show some striking patterns. First, in Panel A, enrollees’ hysterectomy hazards inLabor Insurance and Government Employee Insurance exhibit a sharp increase just before the 45th birthday,
but drop significantly right after; a similar but less pronounced pattern can also be observed for those inFarmer Insurance. After a few quarters past the 45th birthday, hazards of all insured return to the samesmooth trend. However, hazards of uninsured enrollees follow a smooth pattern throughout the entire time.
In Panel B, total oophorectomy hazards follow an increasing trend. However, it is unclear whether
Government Employee Insurance and Labor Insurance enrollees’ hazards show an accelerated increase justbefore the 45th birthday. In Panels C and D, myomectomy and partial oophorectomy hazards do not exhibit
any abrupt changes, either for the insured groups or uninsured group.
There is no medical literature to support the pattern of hysterectomy among female enrollees in
Government Employee, Labor, and Farmer Insurances. Adverse uterine conditions cannot be especiallyserious in the few quarters before the 45th birthday, but the opposite will happen the few quarters after. Our
hypothesis is that such a pattern is caused by the disability-insurance benefit expiration when enrollees turn45 years old.
The hypothesis is consistent with the lack of any abrupt changes in myomectomy and partial
oophorectomy hazards. Total oophorectomy indeed qualifies for the disability benefit when it is performedby the 45th birthday. However, the removal of both ovaries carries much higher short-term and long-term
health risks than the removal of the uterus. In other words, because the same benefit is paid to both
hysterectomy and oophorectomy, we should expect different responses because these two treatments carrydifferent explicit and implicit health costs.
For hysterectomy, the plots in Panel A suggest a timing manipulation effect. It appears that some
hysterectomies might have been moved earlier to qualify for disability benefits, a timing effect. There is,however, a more serious possibility. Some hysterectomies might not have been performed if the insurance
benefits were absent, an inducement effect. We estimate these effects by two methods. The first is based on
the difference-in-difference method: enrollees in the three insurance programs are the treatment groups,
and uninsured females are the control group. Our method allows the treatment group to experience20different effects in each benefit quarter, so we estimate dynamic, quarter-by-quarter differences between
the insured and the uninsured. The implementation is different from the conventional method, and will be
explained in the next subsection. The second is a nonparametric method based on a smoothness hypothesis:
there should not be any abrupt changes in enrollees’ probability of undergoing hysterectomy at the 45thbirthday if there were no disability benefit. The nonparametric method estimates a counterfactual hazard
distribution for the insured as if the disability benefits were absent. Kleven and Waseem (2013) introduce
this “bunching” method to estimate labor supply elasticity using discontinuity points in income distribution
caused by piecewise linear progressive tax rates. Again, we have to adapt that methodology for our sample
and the variable of interest, and will explain details later.
4.1 Difference-in-difference by benefit quarters
Obviously, we need to estimate the difference of surgery experiences between the insured and theuninsured, the first difference. However, the disability insurance programs have been in place for the entire
sample period, so there are no before-and-after regimes. Our innovation is to exploit the benefit expiration
at enrollees’ 45th birthday to create a second difference. Clearly, no point in time has special significance tothe uninsured’s surgery decisions. Our identification assumption is this: at a point in time far before the45th birthday, the benefit expiration also has no significance to the insured’s surgery decision. Notice that
we do not claim that the benefit availability has no impact on surgery decisions; we only claim that when
the deadline is far into the future, the deadline has no impact on a current decision.
To implement this empirical strategy, we assume that the benefit expiration deadline becomes relevant
when enrollees turn 40 years old. It is as if the benefit expiration at the 45th birthday is a policy
intervention imposed on insured enrollees starting from their 40th birthday, a pseudo-intervention date, so
we have chosen the 4 quarters between the 39th and 40th birthdays as the omitted benefit quarters. This is aconservative way to implement the estimation strategy. From Panels A and B in Figure 1, the hysterectomy
and oophorectomy hazard time trends are similar around enrollees’ 40th birthday (benefit quarter -20). To
guard against an improperly imposed pseudo-intervention date, we actually examine the quarter-by-quarter
differences between the insured and the uninsured. If the insured actually thought that the deadline was21

relevant at a later time, say the 41st birthday, the quarter-by-quarter differences would vanish in the four
quarters between the 40th and 41st birthdays in our difference-in-difference setting.
The three treatment groups (Government Employee Insurance, Labor Insurance, and Farmer Insurance)
have different disability benefits, and a separate regression is estimated for each group. For brevity, we
present the regression equation for hysterectomy; the regression equations for the other three procedures
are set up analogously. The regression equation is:1919

i =−20i =−20H c ,q = α + β × Insured + ∑ γ i × 1[i = q ] + ∑ ρi × 1[i = q ] × Insured
2011+ Χc ,q η + ∑ k j × 1[ j = T (c)] + ε c ,qj =1998(1)c ≡ ( y, s ) with y = 1948, 1949,....,1972, and s = 1, 2, 3, 4, andq = −24, -23, -22,...., 1, 0, 1, 2,...., 19
In equation (1), 𝐻!,! , either for the insured group or the control group, is the hysterectomy hazard of birthcohort c at benefit quarter q, a birth cohort c being defined by birth year y and birth quarter s. The variable
𝐼𝑛𝑠𝑢𝑟𝑒𝑑 is the dummy variable for an insured group (Government Employee Insurance, Labor Insurance,or Farmer Insurance). It is set to 1 if the hazard belongs to the insured, and 0 otherwise. The function 1[i =q] is an indicator, and set at 1 if the condition inside the square brackets is satisfied; it is set at 0, otherwise.
The covariates 𝐗 !,! are cohort-cell means of variables of the total number of children, the number of sons,marital status, and log household incomes. The function 𝑇(𝑐) ≡ Int[𝑦 + 45 + 𝑠/4] is the smallest
integer bigger than (y + 45 + s/4), so its range is simply the years between 1997 and 2011; this function isused for the data-year fixed effects. Finally, 𝜀!,! is the error term. To mitigate the concern of serial
correlation in the error term, we allow for clustered standard errors.10
In equation (1), parameter 𝛾! is the mean hysterectomy hazard difference between quarter q and thebenchmark, which we have taken to be quarters 𝑞 = −24 to 𝑞 = −21, the four quarters in age 39. (Ourresults change only slightly when the benchmark age quarters are extended to those quarters corresponding
10 For details as to why the standard errors of the coefficient estimates of interest tend to be underestimated in the
difference-in-difference model, see Bertrand, Duflo, and Mullainathan (2004) and Donald and Lang (2007).

22

to ages from 35 to 39). For 𝑞 = −20,..,19, the parameter 𝜌! measures the incremental difference between
the insured and the uninsured, our chief focus. If disability insurance does not affect enrollees’
hysterectomy decisions, all estimates of 𝜌! should be zero. However, if these estimates are nonzero, we
can estimate how disability insurance impacts hysterectomies under the deadline.
In the specification in equation (1), we are able to differentiate the inducement effect and the timing
effect. The inducement effect is the total increment of hysterectomies of the insured over the uninsured in
the period between the 40th and 50th birthdays. Let ρ̂ q denote the estimate of 𝜌! . Let 𝑛! denote the numberof enrollees who have not undergone hysterectomy at the beginning of quarter q. The inducement effect on
hysterectomy due to disability insurance is∑19
q =−20ρ̂ q ⋅ nq . If this measure is zero, we conclude that thedisability benefit has not increased the total number of hysterectomy among enrollees over their lifetime.
Next, the timing effect is the total number of hysterectomies that the insured would have undergone
after the 45th birthday in the absence of the benefit. In other words, disability insurance may have
incentivized enrollees to have hysterectomies earlier. As a result, there will be fewer of them after the 45thbirthday among insured enrollees. The timing effect on hysterectomy due to disability insurance is

∑

19
q =0

ρ̂ q ⋅ nq . If disability insurance has not favored earlier hysterectomies, then this measure will be zero.

Finally, our analysis is at the birth cohort level, and the dependent variable is hysterectomy hazard ofenrollees born at a certain time. We thus use the number of enrollees at every birth cohort as weights in theestimation. Given that all the covariates within a birth cohort are constant for each enrollee, estimatesobtained from the individual-level regression would be identical to those from the cohort-level regression(Lee and Card, 2008; Lemieux and Milligan, 2008).
4.2

Nonparametric counterfactual estimation
The method above assumes that the hysterectomy hazards of insured groups before the 40th birthday

share a common time trend, which is supported by the plots of hazards before age 40 in Figure 1. As analternative, we use a nonparametric method that is free of any time-trend assumption. Instead, the23nonparametric method is based on a “smoothness” assumption: without the expiration of disability benefits,
there should not be any abrupt hysterectomy-hazard changes at age 45. We estimate a counterfactual
hysterectomy hazard distribution for each insured group, and compare it to the actual hazard distribution.
Figure 2: An illustrative example of nonparametric hazard method

For the nonparametric estimation we have extended the data periods to 40 quarters before and after
the 45th birthday, so these hazards are for ages between 35 and 55. We use Figure 2 to illustrate thismethod. There, the blue curve plots the empirical distribution of hysterectomy hazard of an insured group.
It shows the sudden hazard changes around the 45th birthday. To construct a counterfactual distribution, we
imagine that the abrupt changes had not existed. We choose a lower quarter threshold and an upper quarter
threshold, which are denoted, respectively, by 𝑞! and 𝑞! , with 𝑞! < 0 < 𝑞! . We then use hazard data
outside of quarters between 𝑞! and 𝑞! to fit an Nth-order polynomial. The fitted curve is then used to
predict the hazards between quarters 𝑞! and 𝑞! . This is the red curve in Figure 2. The interpretation is thatquarter 𝑞! marks the beginning of disability insurance impact on hysterectomy before the 45th birthday,
whereas quarter 𝑞! marks the end of the impact after the 45th birthday.

24

We use more observations outside the 𝑞! and 𝑞! thresholds than the difference-in-difference method
for a better fit of the polynomial. We use a 20-year window of quarter ages, double the time window for
the difference-in-difference estimation. We augment the sample in the difference-in-difference analysis
with enrollment and surgery records between 35 and 39 years old, and between 50 and 54 years old. Noticethat these new data are used even if some enrollees have changed insurance programs between 35 and 39
years old, or between 50 and 54 years old. This is to maintain the same set of enrollees in the
nonparametric method as those in the difference-in-difference estimation.
The regression for estimating the counterfactual hysterectomy hazard is this:
N

qU

n =0

j = qLH c ,q = ∑ α n × q n + ∑ ρ j ×1[ j = q] + ε c ,q(2)c ≡ ( y, s ) with y = 1948, 1949,....,1972, and s = 1, 2, 3, 4, andq = −40, -39, -38,...., -1, 0, 1, 2,...., 39,
where 𝐻!,! is the hysterectomy hazard of birth cohort c at benefit quarter q; 𝑞 ! is quarter q raised to thepower n ; 𝑞! and 𝑞! , again, are the lower and upper bounds; and 𝜀!,! is the error term. Notice that the birthcohorts still range between 1948 and 1972, the same cohorts in difference-in-difference estimation, but thequarter number now is from -40 to 39 because we incorporate more data points. Notice also that our data
period spans 15 years, but we attempt to track enrollees’ experiences for 20 years, so a balanced sample
would be impossible to construct.
Following Kleven and Waseem (2013), we use a fifth-order polynomial in the main specification (N =5). For each quarter between 𝑞! and 𝑞! we use a coefficient 𝜌! to capture the difference between theempirical and the counterfactual hazards at quarter q. If disability insurance has no effects on enrollees’
hysterectomy decisions, all estimates of 𝜌! should be zero.
For each insured group, we use a grid search over the ranges of 𝑞! ∈ −18, −9 and 𝑞! ∈ 2,12 toselect a pair of bounds that minimize the root mean squared error (RMSE) of the regression, a common
optimality criterion in econometric models (Ichimura and Todd, 2007; Lee and Lemieux, 2010; Imbens

25and Kalyanaraman, 2012).11 Because each insured group sets its own lower and upper thresholds, thenumber of estimated coefficients in each insured group is different.
As in the difference-in-difference estimation, we are able to obtain inducement and timing effects.
The inducement effect is the impact of disability insurance on enrollees’ lifetime hysterectomy, and ismeasured by (∑qU
q = qLρ̂q ⋅ nq ), where 𝜌! is the estimate of 𝜌! in equation (2), and 𝑛! is the number ofenrollees who have not had hysterectomy at the beginning of quarter q. Likewise, the timing effect is theimpact of disability insurance on the timing of hysterectomy, and is measured by

∑

qU
q =0

ρ̂ q ⋅ nq . This is thedifference in hysterectomy hazard between the counterfactual and the empirical hazard distributions after
the 45th birthday but before 𝑞! . More importantly, if our nonparametric estimation approach is valid, theestimates of 𝜌! should all be zero for the uninsured group, and this could serve as the validity check in theanalysis.

5.

Estimation results

5.1.

Difference-in-difference estimation
Table 4 presents some of the regression estimates of the difference-in-difference terms 𝜌! in equation(1). We estimate the regression separately for each treatment group, so the three columns in Table 4 show
results of Labor Insurance, Government Employee Insurance, and Farmer Insurance groups, respectively.
In each column, the number of observation is 5,280, smaller than one would expect from a complete
sample of balanced data (which would have 25 years * 4 seasons * 44 birth quarters * 2 insurance status or
8,800 observations). This is because that quite a number of enrollees only appear in a few years in the data;
censoring reduces the number of observations.
Our focus in Table 4 is the set of interaction terms for the quarterly hazard differences between thetreatment group and the uninsured. These are the quarterly parameters 𝜌! , q between -20 and 19. For
11 RMSE is a common measure for comparing the performance of different econometric models or parameterselections. For example, Ichimura (1993) proposes a semiparametric model and compares its RMSE to those of othermodels such as the truncated Tobit, binary choice, and duration models. RMSE is also the optimality criterion for
selecting the smoothing parameter in nonparametric methods (Ichimura and Todd, 2007); for selecting the bandwidth
for regression discontinuity designs (Imbens and Kalyanaraman, 2012); and for selecting the polynomial order of theregression function of regression discontinuity designs (Lee and Lemieux, 2010).

26

brevity, Table 4 presents only estimates of 𝜌! for q between -10 and 7; these benefit quarters are aroundthe 45th birthday, at which time the disability benefit expires. In fact, for quarters before -10 and after 7,
most estimates of 𝜌! are insignificant. However, for an effective illustration, Figure 3 plots the entire set of
𝜌! , 𝑞 = −20 through 𝑞 = 19. The red plots are for enrollees in Labor Insurance, the blue plots and thegreen plots are for enrollees in Government Employee Insurance and Farmer Insurance, respectively. In
addition, significant estimates are plotted with solid dots, whereas insignificant estimates are plotted withhollow dots.
In Figure 3, for Labor Insurance enrollees 𝜌! starts at almost zero at 𝑞 = −20, gradually increases,
and becomes significantly different from zero (solid dots) at 𝑞 = −14. Then 𝜌! continues to increase asenrollee’s age approaches 45, peaks at 𝑞 = −1 (the difference between the two groups being 193.8 cases
per 100,000 at 𝑞 = −1) and then sharply declines at 𝑞 = 0. Except for 𝑞 = 0, most estimates after 𝑞 = 0
are small and insignificant. Likewise, the plot of Government Employee Insurance group follows a similar
pattern. The plots of Farmer Insurance group also peak at one quarter before age 45, though the magnitude
is only half of the other two insurance groups.
In equation (1) the parameter 𝛽 measures the average difference between the treatment and control
groups. The treatment group dummy estimate is also presented in Table 4. The hysterectomy hazard foreach treatment group is significantly different from the control group. For both Labor Insurance andFarmer Insurance enrollees, their hysterectomy hazard is higher than the insured, and this is stronger for
Farmer Insurance enrollees than Labor Insurance enrollees. For Government Employee Insurance enrollees,
this difference turns out to be negative. The identification power is not diminished by the sign differencesin 𝛽 because the treatment and control groups share the same time trend. This can be seen from theinsignificant coefficients in the first few quarters in Figure 3.
Finally, equation (1) includes a number of controls. In all three equations, enrollees with higher
household income are less likely to undertake hysterectomy. This is consistent with wealthier households
being less responsive towards financial incentives. Enrollees with more children tend to have a smaller27

hysterectomy hazard, though this effect is insignificant for Government Employee Insurance enrollees.12
Conditional on the total number of children, the number of sons does not seem to matter. Finally, being
married is associated with a higher hazard, but the estimate is only significant for the Labor Insurance
enrollees. By and large, estimated coefficients from controls are consistent with common models of healthcare services.

-100

-50

0

50

100

Hazard (of 10^6) relative to uninsured women

150

200

Figure 3: Difference-in-difference estimates of 𝝆𝒒 for hysterectomy

-20

-16

-12

-8

-4
0
4
Quarters from the 45th birthday

8

12

16

Labor Insurance

Significant at 5%

Insignificant at 5%

Government Employee Insurance

Significant at 5%

Insignificant at 5%

Farmer Insurance

Significant at 5%

Insignificant at 5%20

We now turn to the inducement and the timing effects. Recall that the inducement effect on
hysterectomy is∑19
q =−20ρ̂ q ⋅ nq , where nq is the number of female enrollees who have not had ahysterectomy at the beginning of quarter q. The inducement effect for enrollees in Labor Insurance ismeasured at 5,076 hysterectomies. This is about 11.6% of the total 43,845 hysterectomy surgeries
12

Studies have shown that the number of pregnancies (or living children) is negatively related to the prevalence ofuterine fibroids, one of the major causes for hysterectomy (Ross, et al, 1986; Chen et al, 2001).

28

undertaken by Labor Insurance enrollees between 40 and 49 years old in the sample period. Recall that thetiming effect is measured as

∑

19
q =0

ρ̂ q ⋅ nq . Generally, hysterectomies have been expedited, so the timing

effect will turn out to be negative. For ease of exposition, we omit the negative sign when we present
timing effects. For Labor Insurance enrollees, the timing effect is measured at 1,008 hysterectomies, or atabout 20% of the inducement effect. However, the value of 𝜌! at q = 0 is significantly negative for the
Labor Insurance enrollees. Although the overall timing effect is not large, we are confident that some
hysterectomies have been shifted earlier due to the disability benefit.
In fact, we can visualize both inducement and timing effects from Figure 3. The inducement effect isthe weighted sum of the areas under each plot, with weights nq, for q between -20 and 19. Now the numberof enrollees who have not had a hysterectomy must be decreasing over time, so nq is a decreasing sequence.
In other words, the inducement effect is area under each plot weighted by this decreasing sequence. Given
that the number of hysterectomies is small relative to the total number of survivors, the inducement effectwould be slightly smaller than the area between the hazard curve and the x-axis. It is quite obvious that the
total weighted area for q before 0 is much bigger than after. The timing effect can be visualized
analogously. This is simply the weighted sum of the area for positive quarters q. It is also obvious that thisnumber is negative, although much smaller than the inducement effect.
Columns (2) and (3) in Table 4 present the estimates of 𝜌! for Government Employee Insurance andFarmer Insurance enrollees. These two columns exhibit the same pattern as Column (1): a large increase inhazard just before quarter 0, and then vanishing. In Government Employee Insurance, the inducement
effect is measured at 789 hysterectomies, or about 11% of the total hysterectomy cases among Government
Employee Insurance enrollees between 40 and 49 years old in the sample period while the timing effect is
142 cases. For Farmer Insurance enrollees, the inducement effect is smaller, at 347 cases, or about 3.8% of
all hysterectomy surgeries among Farmer Insurance enrollees between 40 and 49 years old in the sample
period. The timing effect for Farmer Insurance is measured at 283 cases.

29

Regression results on hysterectomy hazards are strong evidence that enrollees respond to incentives
created by the disability insurance program. The differences in inducement and timing effects in the threetreatment groups are consistent with the differences in the three disability insurance programs. Benefits ofLabor and Government Employee Insurance are higher than Farmer Insurance.
We now turn to regression results of the other three surgeries: total oophorectomy, partial
oophorectomy, and myomectomy. Almost all estimates of regression results for equation (1) for these threesurgeries are insignificant. For completeness, we present these in online Tables A1, A2, and A3 at

http://goo.gl/sA3994 (again, only estimates of 𝜌! for q between -10 and 7). In Figures 4, 5, and 6 we plot
the entire set of estimates of 𝜌! for q between -20 and 19, and we use the same color convention for thethree treatment groups. From these estimate plots, it is clear that the disability insurance program has notcaused behavioral change.
For partial oophorectomy and myomectomy, these insignificant results are to be expected. These
surgeries are not eligible for benefits. The insignificant result for total oophorectomy is actually an
important finding. Total oophorectomy and hysterectomy carry the same benefits and qualification.
However, the health risks and long-term morbidity and harmful consequences of total oophorectomy aremuch more severe than hysterectomy. Our results indicate that the benefits are not enough to change
enrollees’ behavior. Indeed, ours can be regarded as evidence that enrollees have taken seriously the costand benefit of each surgery.

30

15
5
-5
-15
-25

Hazard (of 10^6) relative to uninsured women25

Figure 4: Difference-in-difference estimates of 𝝆𝒒 for oophorectomy

-20

-16

-12

-8

-4
0
4
Quarters from the 45th birthday

8

12

Labor Insurance
Government Employee Insurance

Significant at 5%
Significant at 5%

Insignificant at 5%
Insignificant at 5%

Farmer Insurance

Significant at 5%

Insignificant at 5%

16

20

15
5
-5
-15
-25

Hazard (of 10^6) relative to uninsured women25

Figure 5: Difference-in-difference estimates of 𝝆𝒒 for partial oophorectomy

-20

-16

-12

-8

-4
0
4
Quarters from the 45th birthday

8

12

Labor Insurance
Government Employee Insurance

Significant at 5%
Significant at 5%

Insignificant at 5%
Insignificant at 5%

Farmer Insurance

Significant at 5%

Insignificant at 5%

31

16

20

-25

-15

-5

5

15

Hazard (of 10^6) relative to uninsured women25

Figure 6: Difference-in-difference estimates of 𝝆𝒒 for myomectomy

-20

5.2

-16

-12

-8

-4
0
4
Quarters from the 45th birthday

8

12

Labor Insurance
Government Employee Insurance

Significant at 5%
Significant at 5%

Insignificant at 5%
Insignificant at 5%

Farmer Insurance

Significant at 5%

Insignificant at 5%

1620

Nonparametric estimation
Table 5 presents the estimates 𝜌! of equation (2). Because the nonparametric approach does not relyon the existence of a control, we do estimation for all three insured groups and the uninsured. The numberof observation is 4,498 for the Labor sample, and 4,474 and 4,481 for the Government Employee andFarmer samples, respectively. These are smaller than those in from a complete and balanced sample(which would have 25 years * 4 seasons * 80 birth quarters, or 8,000 observations) in part because of
censoring, and also because of more missing observations when the data are extended to 20 years. As wehave mentioned earlier, we apply a grid search over wide ranges of 𝑞! and 𝑞! to select a pair of bounds
that minimize the root mean squared error (RMSE) of the regression. In Table 5, the four columns list theestimates of 𝜌! for the uninsured, and enrollees in Labor Insurance, Government Employee Insurance, andFarmer Insurance, respectively, with the optimal bounds presented at the bottom of each column. Given
that each insurance group has its own lower and upper bounds, the number of estimated coefficients varyacross different insurance groups. As in the previous subsection, we plot the four sets of 𝜌! estimates, andthey are in Figure 7. The gray plots refer to those of the uninsured. The red, blue, and green plots refer to32those estimates of enrollees of Labor Insurance, Government Employee Insurance, and Farmer Insurance,
respectively.
From Figure 7 the gray line fluctuates minimally along the horizontal axis line; this indicates that the
fifth-order polynomial fits the uninsureds’ hazard rates quite well. In fact, in Table 5 almost all estimatesof 𝜌! of the uninsured are insignificant, and we cannot reject the hypothesis that estimates of 𝜌! are jointly
zero (F statistics = 1.01). This serves to validate our nonparametric approach. We now turn to the three
insured groups.13

-50

0

50

100

150

Hazard (of 10^6) relative to uninsured women200

Figure 7: Nonparametric estimates of 𝝆𝒒 for Hysterectomy

-18

-14

-10

-6
Quarters from the 45th birthday-2

2

Labor Insurance

Significant at 5%

Insignificant at 5%

Government Employee Insurance

Significant at 5%

Insignificant at 5%

Farmer Insurance

Significant at 5%

Insignificant at 5%

UninsuredSignificant at 5%

Insignificant at 5%6

For enrollees in Labor Insurance, most estimates from q = -11 to -1 are significantly positive,
followed by significantly negative estimates from q = 0 to q = 4; see Table 5. The red plots in Figure 7
show the dramatic spike just before the 45th birthday, and then the sharp drop. The pattern is similar to thecorresponding difference-in-difference estimates. The estimated number of induced hysterectomies, based

13

We also present the hazard distributions for three insurance groups (respectively, in parts B to D of Figure A1) inonline Appendix A at http://goo.gl/1Am7Yd. Each graph shows the counterfactual hazard distribution (dark graycurve) and the actual hazard distribution (curve in corresponding colors).

33

on

∑

qU
q = qLρ̂q ⋅ nq , is 4,842, which accounts for 11 percent of total hysterectomies (43,845) undertaken by

Labor Insurance enrollees between 40 and 49 years old. Compared with the corresponding figures in the
difference-in-difference method, the percentage is slightly smaller than the percentage (11.6%) estimatedby the difference-in-difference method. The timing effect, measured by

∑

qU
q =0

ρ̂ q ⋅ nq , is 722

hysterectomies, about 14.9% of the total inducement effect; it is somewhat lower than the corresponding
percentage in the difference-in-difference estimates. Nevertheless, the nonparametric method confirms thetiming effect for Labor Insurance enrollees.
From Table 5, estimates of 𝜌! for Government Employee Insurance enrollees are significantly
positive for q between -7 and -1, but significantly negative at q = 0 and q = 1. The pattern can be seen in
the blue plots in Figure 7, which also allows a visualization of the inducement and timing effects. We
obtain the estimated inducement and timing effects at 756 and 87 hysterectomies, respectively. Theseestimates are relatively near to the corresponding difference-in-difference estimates (789 and 143 cases).
Finally, in Table 5, for enrollees in Labor Insurance, 𝜌! is significantly positive at 𝑞 = −1 andsignificantly negative at 𝑞 = 0. In Figure 7, the green curve plots those estimates 𝜌! for Farmer Insurance
enrollees. Compared to Table 4, the estimates for Farmer Insurance group (the last column of Table 5)have fewer coefficients significantly different from zero before age 45. The estimated inducement effect is
280 hysterectomies, which is near the difference-in-difference value. However, the estimated timing effectis only 60 hysterectomies, much smaller than the difference-in-difference estimate (283).
So far the results of the nonparametric estimation for hysterectomy are by and large similar to those of
the difference-in-difference estimation. Results from both methods suggest that inducement and timing
effects have larger impacts for Labor Insurances and the Government Employee Insurance enrollees, butless so for Farmer Insurance enrollees. However, compared to results of the difference-in-difference
method, estimates of nonparametric method indicate a smaller timing effect in the three insurance groups.
We now report results of nonparametric estimation for the other three surgeries: total oophorectomy,
partial oophorectomy, and myomectomy. For each surgery, we continue to use the uninsured group to34

select the polynomial order. For partial oophorectomy and myomectomy, the fifth-order polynomial
achieves a good fit, as most 𝜌! are insignificant and the corresponding F-test (all coefficients) is
insignificant for the uninsured group. For total oophorectomy, however, the fifth-order polynomial fails the
F test (F statistics = 11.22) and the sixth-order polynomial fits the function better and passes the F test (Fstatistics = 0.92). Hence, we present the results from estimating the sixth-order polynomial function. Again,
for completeness, we present the estimates of 𝜌! for q from optimal 𝑞! to 𝑞! in Tables A4, A5, and A6(available online at http://goo.gl/WV6opa) and plot the entire set of estimates in Figures 8, 9, and 10.
From these three figures, it is obvious that the two estimation methods yield very similar findings.
First, for total oophorectomy, which qualifies for insurance benefits, Figure 8 shows that very few 𝜌! aresignificantly different from zero in all insurance groups. Again, hysterectomy and total oophorectomy
entitle the enrollee to the same benefit, but total oophorectomy typically has worse health consequences
than hysterectomy. The evidence is consistent with benefit-cost analysis. Second, almost all the plots in
Figures 9 and 10 (for partial oophorectomy and myomectomy, respectively) are insignificant for every
insurance group. In addition, the total inducement effect and the timing effect are minimal.

15
5
-5
-15
-25

Hazard (of 10^6) relative to uninsured women25

Figure 8: Nonparametric estimates of 𝝆𝒒 for total oophorectomy

-10

-8

-6

-4

-2

0
2
Quarters from the 45th birthday

4

6

8

Labor Insurance

Significant at 5%

Insignificant at 5%

Government Employee Insurance
Farmer Insurance

Significant at 5%
Significant at 5%

Insignificant at 5%
Insignificant at 5%

UninsuredSignificant at 5%

Insignificant at 5%

35

10

12

-25

-15

-5

5

15

Hazard (of 10^6) relative to uninsured women25

Figure 9: Nonparametric estimates of 𝝆𝒒 for partial oophorectomy

-24

-22

-20

-18

-16

-14

-12
-10
-8
-6
Quarters from the 45th birthday

-4

-2

0

2

Labor Insurance

Significant at 5%

Insignificant at 5%

Government Employee Insurance
Farmer Insurance

Significant at 5%
Significant at 5%

Insignificant at 5%
Insignificant at 5%

UninsuredSignificant at 5%

Insignificant at 5%

4

6

-25

-15

-5

5

15

Hazard (of 10^6) relative to uninsured women25

Figure 10: Nonparametric estimates of 𝝆𝒒 for myomectomy

-22

6.

-20

-18

-16

-14

-12

-10
-8
-6
-4
Quarters from the 45th birthday

-2

0

2

Labor Insurance

Significant at 5%

Insignificant at 5%

Government Employee Insurance
Farmer Insurance

Significant at 5%
Significant at 5%

Insignificant at 5%
Insignificant at 5%

UninsuredSignificant at 5%

Insignificant at 5%

4

6

8

Robustness checks, benefit effects, and social costs
In this section, we further investigate inducement and timing effects in samples that have been chosen

by more or less restrictive criteria, and in subsamples determined by different insurance benefit levels.
Then in the last subsection, we assess the social costs due to the disability programs.
6.1.

Sample without nonswitching restriction and sample without censoring36

In this subsection, we examine the robustness of our results by employing two different samples. First,
we use a bigger, “general sample” consisting of all enrollees between the ages of 39 and 49, not only those
who have not switched insurance programs. The general sample allows us to detect bias associated withthe choice of insurance groups. Our data only allow us to identify an enrollee’s insurance status at the endof a calendar year. We do not know the exact time or quarter of an insurance-status change. Therefore, foreach individual, for each quarter within a calendar year, we use the end-of-year insurance status for allquarters in the year. Within each calendar year, insurance status of each enrollee remains constant byconstruction. Then, we calculate the hazard rates for the enrollees in each insurance group for each quarterin the year.
Second, we use a smaller, “balanced sample” consisting of all enrollees born between 1958 and 1962(see Table 2). The balanced sample consists of those who had complete medical records between 39 and 49
in our sample of 1997-2011. These individuals were born between 1958 and 1962, and we also require
their disability insurance status to be the same in the sample period. By construction, data censoring does
not happen.
To illustrate the differences among various samples, Table 6 lists the total numbers of observations by
insurance groups in the general and balanced samples in 2005. For comparison, we also provide thecorresponding numbers in the nonswitching sample. In Table 6, in 2005, there are a little less than 1
million subjects in the nonswitching sample, but there are more than 1.47 million in the general sample. In
other words, the general sample is about 49% larger than the nonswitching sample. By contrast, there arejust over 0.42 million in the balanced sample, about 40% of the nonswitching sample.
Among the four insurance groups, the ratios of general sample size to nonswitching sample size is thelowest for Government Employee Insurance, at 1.07. Government employees appear to have higher job
stability. By contrast, the corresponding ratios of Labor Insurance and the uninsured are higher, at 1.45 and
1.79, respectively. Enrollees switching in and out of being employed and being unemployed seem to be
more common among those in Labor Insurance than those in either Government Employee Insurance or
Farmer Insurance. The balanced sample consists of enrollees in the nonswitching sample born between

37

1958 and 1962, so naturally the corresponding ratios between sample sizes are stable, at about 40% of all
insurance groups.14
Table 7 presents the summaries of difference-in-difference estimation results of the general andbalanced samples for enrollees in Labor Insurance, Government Employee Insurance, and Farmer
Insurance. For brevity, we present only total inducement and timing effects for hysterectomy;15 the effects
for all the other three surgeries are negligible.16 Again, we include results of the nonswitching sample foreasy comparison. From the first three rows in Table 7 for Labor Insurance, the inducement effect in thegeneral sample is measured at 7,172 hysterectomies out of a total 61,692; this is about 11.3%. The
inducement effect in the balanced sample is measured at 1,537 out of a total of 13,609; this is about 11.7%.
The corresponding percentage for the nonswitching sample is 11.6% (5,076/43,845). Thus, the percentagesof induced hysterectomy in total hysterectomy remain stable in these three samples. The estimated timing
effects in the three samples of Labor Insurance are in column (4) of Table 7. For each timing effect, we
also calculate it as a percentage of the inducement effect, and list all of them in column (5). The ratios oftiming to inducement effects for the general and balanced samples are 16.8% and 25.2%, respectively;
these compare with 19.9% of the nonswitching sample. Overall, the timing effects across the three samples
are similar.
Estimates of inducement and timing effects of the general sample of Government Employee Insurance
are also in Table 7. We do not include the results of the balanced samples for Government Employee
Insurance and Farmer Insurance because the explanatory variables in these small samples exhibit very
limited variations. For the general sample of Government Insurance enrollees, the total inducement effectmeasured as a percentage of total hysterectomy, and the timing effect measured as a percentage of
14 It is possible that an individual contributes to the numerator or denominator for the hazard rate of one

insurance group, say, Government Employee Insurance, in one year, but will contribute to that of anotherinsurance group, say, Labor Insurance, in the next year.
15
We plot the difference-in-difference estimates of 𝜌! of the general sample for hysterectomy, total oophorectomy,
partial oophorectomy, and myomectomy, in Tables A7 to A10, respectively (available online at
http://goo.gl/Aa7SjD). Except for hysterectomy, most estimates are insignificant, and there are negligible inducement
and timing effects.
16
Tables A11 to A14 (available online at http://goo.gl/3nqt7S), respectively, present the difference-in-difference
estimates of 𝜌! for hysterectomy, total oophorectomy, partial oophorectomy, and myomectomy for the balanced
sample. Again, the results are similar to those in Tables A7 to A10.

38

inducement effect, are 11.2% and 17.6%, respectively, whereas the corresponding percentages in the
nonswitching sample are 10.9% and 18.1%. These estimates confirm that results in the general andnonswitching samples are stable.
The last two rows in Table 7 are the summaries of the estimations of Farmer Insurance. The total
inducement effect in the general sample is small, at 241 hysterectomies, or 2.2% of total hysterectomies.
Although the number is even smaller than the total inducement of 347 in the nonswitching sample, theresults may be driven by the imprecise estimates of coefficients after age 45. For enrollees in Farmer
Insurance, the inducement effect in the general sample is 2.2% of total hysterectomies, and it is lower thanthe 3.8% in the nonswithching sample. For the timing effect, the general sample is about 20 percentage
points higher than the 81.6% (of the inducement effect) of the nonswitching sample.
Next, we turn to the nonparametric estimates. We only compare the results of the general and thenonswitching samples. Our nonparameteric method requires a 20-year sample window, but the data for
1997-2011 cannot track any individual for such a long time period, so we cannot construct a balanced
sample.
Table 8 summarizes the inducement and timing effects from the nonparametric estimates.17 For Labor
Insurance, the inducement effect is measured at around 11% of total hysterectomy for both nonswitching
and general samples. The timing effects are, respectively, 14.9% and 15.6% of the corresponding
inducement effects for the general and nonswitching samples. These measures indicate robustness of
estimates for the general and nonswitching samples.
For Government Employee Insurance, the inducement effects in the general sample and nonswitching
sample are, respectively, 10.4% and 11% of the corresponding total hysterectomy. The timing effects in
the general and nonswitching samples, as percentages of the corresponding inducement effects, are 11.5%
and 15.6%, respectively. Again, these results indicate robustness. Likewise, for Farmer Insurance, the total
inducement effects in the general and nonswitching samples are quite similar, measured at 3.1% and 2.9%

17

We present the nonparametric estimates of 𝜌! , using the general sample, for hysterectomy, oophorectomy, partial
oophorectomy, and myomectomy in Tables A15 to A18, respectively (available online at http://goo.gl/vDDQHw).

39

of the corresponding hysterectomy, with the timing effect being 21.4% and 26.3%, respectively. Again, asmaller timing effect is obtained from the nonparametric estimation, especially for Farmer Insurance.
6.2.

Inducement and insurance benefit
We now investigate the relationship between benefit amount and the inducement and timing effects.

This is an issue pertinent to current policy discussions because the Taiwanese government has been
considering reducing fertility disability benefits. Our method is to stratify our sample into five groups ofincreasing insurance salaries with roughly equal numbers of observations in each group.
We carry out this stratification analysis on enrollees of Labor Insurance for two reasons. First, from
Table 1, the sample size of Labor Insurance is at least 5 times larger than Government Employee Insurance,and 4 times larger than Farmer Insurance. The large sample size allows us to obtain more reliable estimates.
More importantly, in contrast with other insurance groups, we have more accurate information from labor
insurance because the disability-insurance salary is based on the enrollee’s full monthly salary. Therefore,
we can have a better understanding of the size of disability benefit (equal to 160 days or about 5.3 months
of insurance salary, up to the cap of NT$43,900) relative to one’s earning.
For each of the 5 groups, we use the difference-in-difference and nonparametric methods to estimate
the number of induced hysterectomies and the inducement rate, the ratio of induced hysterectomies to total
hysterectomies of enrollees between the ages of 40 and 49. Table 9 presents the results, with thedifference-in-difference and nonparametric method results in the upper and lower panels, respectively.
Column 1 lists the average insurance benefits for the 5 groups. The average insurance benefit of group 1 isaround NT$84,000, nearly one third of the average benefit of the highest group 5 which has an average ofalmost NT$220,000. Given that the maximum of disability benefit is approximately NT$232,600(5.3×NT$43,900), the average insurance benefits of group 5, only a little lower than the maximum
disability benefits, suggests that a sizable proportion of enrollees in this group have actual salaries above
the cap.
Columns 2 and 3, respectively, present the total number of hysterectomies undertaken by enrollees
between ages 40 and 49, and the estimated induced hysterectomies. Total hysterectomies of each group40

look similar, with the percentage difference between the highest and the lowest group being about 10%. By
contrast, the variation of induced hysterectomies is quite large among different benefit groups: induced
hysterectomies of group 5 are about twice that of group 1.
The estimated inducement rates are in Column 4. The inducement rate increases with average
insurance benefit: the rate ratio of induced hysterectomy increases modestly when moving from group 1 togroup 3 (from about 9% to11%), but accelerates when moving from group 3 to group 5 (from about 11% to15%). In total, in the difference-in-difference estimates, the highest benefit group’s inducement rate isabout 75% larger than the lowest income group (15.71% versus 8.93%). The corresponding results in the
nonparametric estimates are stronger, with group 5’s inducement rate being more than twice that of group
1 (14.45% versus 7.11%).
Our stratification analysis shows an inducement effect that is strongly and positively affected by thebenefit amount. Results in Table 9 shed some light on the possible impact of a policy change. The current
discussion may recommend a reduction of benefit by a half of the highest benefit. If insurance programs
were to cut the disability benefits by a half, for group 5 the average benefit would drop from NT$220,000
to NT$110,000, falling between the average benefit of group 3 and group 2. A simple projection will
therefore put the inducement effect at about 11%, which would be a reduction of more than 4.5 percentage
points from the current inducement effect of 15.71%.
Inducement effects are stronger among those enrollees who have a higher insurance salary, and,
therefore, are increasing in the benefits. If the benefit is paid at a fixed price, say the benefit level being set
at the third tier, we predict that inducement effects will be stronger among low-income enrollees, andweaker among high-income enrollees.
Our study here may shed some light on issues related to organ donations. Hysterectomy andoophorectomy do not involve donation or transplant. However, the disability insurance program does work
like paying someone a price for having an organ removed. We do recognize that the uterus and ovaries arequite different from the kidney, blood, or the bone marrow. The rationale behind the repugnance constraint(Roth, 2007) against financial rewards in organ donation is probably the worry that a price for organ41

donation adversely affects the poor more than the rich. Inducement effects being positively related tobenefits supports this rationale. A fixed price for donation may be more attractive to poor donors than richdonors.
6.3.

Social costs due to disability insurance
We now use our estimation results to assess social costs due to induced surgeries and insurance

benefit payments. Each induced hysterectomy is an unnecessary surgery, so the treatment cost is a
deadweight loss. Each induced hysterectomy qualifies an enrollee for benefit that otherwise would nothave been paid. One can plausibly argue that the benefit is a transfer, so does not entirely constitute a
deadweight loss. We make no judgment on the desirability or efficiency of the benefit transfers due toinducement, so we calculate separately the deadweight loss of surgical treatment and the benefit payments
due to inducement.
We adopt a lifetime-cost perspective. What are the inducement costs over a female insurance
enrollee’s lifetime? Most hysterectomies happen when females are between 40 and 50 years old. Our
sample and estimation results therefore are suitable for lifetime cost assessment. We use the balanced
sample because all enrollees’ experiences from their 40th to 50th birthdays happen within the data period of
1997 to 2011. This sample consists of all enrollees born between 1958 and 1962. We estimate the social
costs of the three programs separately because their inducement effects differ. Inducement effects have
only been estimated for the Labor Insurance balanced sample. (Recall that for Government Employee
Insurance and Farmer Insurance, explanatory variables have limited variations in the balanced sample.)
However, from Table 7, for Labor Insurance, the inducement effects for the nonswitching and balanced
samples are similar. We believe that the same would hold for the nonswitching and balanced samples in
Government Employee Insurance and Farmer Insurance. Hence, we simply use the inducement effectpercentages in the nonswitching sample.
To estimate the deadweight loss due to induced hysterectomies, we have to estimate the hysterectomy
reimbursements from National Health Insurance. It turns out that hysterectomies are classified by three42

broad surgical intensities (total, subtotal, and laparoscopic), as well as by three levels of teaching
characteristics of hospitals where the surgeries take place (major teaching, minor teaching, andcommunity). There are altogether 9 different classes of hysterectomies, and the National HealthAdministration sets a separate reimbursement rate for each class. Our data span 15 years, between 1997
and 2011, so we pick the mid-point, and use the reimbursement rates in 2005. For calculating surgery costs,
we multiply the number of hysterectomies in each of the 9 classes by the corresponding reimbursement
rate, and then sum over these 9 products. The details for the disaggregated numbers of hysterectomies andthe 2005 reimbursement rates are available in an online file at http://goo.gl/fEcRer.
Table 10 presents the aggregated data summary and the inducement costs. The first column lists thetotal number of enrollees in the balanced sample in the three programs. In other words, these are the total
enrollees in the 1958-1962 year cohorts in the three programs. The last entry, 303,229, is the total numberof enrollees in all three programs. The second column lists the average monthly insurance salary by
programs. For Farmer Insurance, the insurance salary is fixed at NT$10,200 per month, so it is the average
insurance salary. For Labor Insurance, the insurance salary is defined to be the lower of an enrollee’s
actual monthly salary and NT$43,900. Based on the insurance salaries of female enrollees who underwent
hysterectomies, we obtain the average insurance salary per month, NT$31,578.
For Government Employee Insurance, the insurance salary is the lower of an enrollee’s base monthly
salary and NT$53,900. However, National Health Insurance records include base salary and stipends. For
insurance benefit estimation, we use the average base salary for those who have worked for 10 years. Thisis NT$33,786 in the 2005 reports of Government Employee Insurance.
The third column lists the numbers of hysterectomies in the three programs, as well as the total in all
programs. Estimates of induced disability benefit payment and surgical costs are in the next two columns.
Recall the benefit is 6 months of insurance salary for Government Insurance and 5.3 months for Labor
Insurance and Farmer Insurance, so total payment is equal to the monthly amount multiplied by thecorresponding month in the program. Then we multiply the total payment by the inducement rates in each
insurance program in Table 7 to obtain the induced benefit payment. We follow a similar procedure to43

estimate the hysterectomy deadweight loss due to inducement. (Again, our online file http://goo.gl/fEcRer
lists the nine hysterectomy reimbursement rates and the corresponding cases.)
For the total of over 303 thousand enrollees, we estimate a lifetime cost of over NT$427 millions of
induced benefit payment, so the lifetime induced benefit payment is NT$1,410 per insured enrollee. We
estimate a lifetime deadweight loss due to induced hysterectomies is over NT$120 millions. This
corresponds to a lifetime cost of just under NT$400 per insured enrollee. To give a sense of the magnitudeof these numbers, we find that the 2016 reimbursement rates for mammogram and pap smear are,respectively, NT$1,245 and NT$80. Hence, the induced benefit payment would be more than enough tofund 1 mammogram, and the deadweight loss due to induced hysterectomy would fund 5 pap smears, overeach enrollee’s lifetime.
7.

Conclusions
We have studied enrollees’ response to the infertility coverage in three Taiwanese disability insurance

programs. Enrollees having hysterectomy or complete oophorectomy qualify for benefit, but the eligibility
ends at the 45th birthday. This program arguably can be likened to a natural experiment of putting a priceon the removal of a human organ. Compared to the uninsured, enrollees have about 11% more
hysterectomies, and about 20% of the induced hysterectomies could be classified as those expedited to beatthe deadline. Disability insurance has not led to any increase in oophorectomy.
The contrast between the different responses in hysterectomy and oophorectomy is striking. The
plausible explanation behind the difference is a cost-benefit calculus. Because organ removal is a discrete
choice, economic principle dictates that such an operation is undertaken if and only if the reward is above athreshold. If a policy goal is an amount of insurance that would not result in induced operations, then our
results indicate that in the Taiwanese case, the benefit is above the threshold for hysterectomy, but below
for oophorectomy. A policy implication, therefore, is that insurance coverage for infertility should depend
on whether the infertility is due to hysterectomy or oophorectomy.
One naturally questions the rationale behind the Taiwanese infertility coverage. In Chinese culture
and customs, children often take care of their parents, so infertility can be likened to a loss of future44

resources. Besides, infertility likely adversely affects a woman’s prospect in the marriage “market.” Bothreasons can be behind the government’s policy of protecting women from negative income shocks. We
have simply followed up with the economist’s methodology of analyzing the policy’s unintended effects.

45

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48

Table 1: Insurance program changes before hysterectomy
Insurance program in the year of hysterectomy

Insurance program in the year before
hysterectomy

(1)
Labor
Insurance(2)
Government
EmployeeInsurance(3)
FarmerInsurance(4)
Trade Union(5)
Uninsured

Total

Percentage changes(1) Labor Insurance

91.94%

0.03%

0.18%

3.54%

4.30%

100%

(2) Government Employee Insurance

0.95%

97.55%

0.06%

0.19%

1.26%

100%

(3) Farmer Insurance

1.66%

0.00%

96.54%

0.79%

1.01%

100%

(4) Trade Union

2.19%

0.01%

0.03%

96.93%

0.83%

100%

(5) Uninsured

5.81%

0.10%

0.64%

6.84%

86.61%

100%

Enrollees with hysterectomies in different
program (obs.)

67,7198,920

11,69353,91137,748

179,991

Table 2: Sample censoring and balance
Cohorts

Age at 1997

Age at 2011

1948
.
1952
1953
.
1956
1957
1958
1959
1960
1961
1962
1963
1964
.
1966
1967
.
1972

49
.
45
44
.
41
40
39
38
37
36
35
34
33
.
31
30
.
25

63
.
59
58
.
55
54
53
52
51
50
49
48
47
.
45
44
.
39

Years in sample
left-censored.
left-censoredleft-censored.
left-censoredleft-censoredbalancedbalancedbalancedbalancedbalancedright-censoredright-censored.
right-censoredright-censored.
right-censored

49

1
.
5
6
.
9
10
11
11
11
11
11
10
9
.
6
5
.
1

Data record at 45thbirthday
no
.
no
yes
.
yes
yes
yes
yes
yes
yes
yes
yes
yes
.
yes
no
.
no

Table 3: Summary statistics of female enrollees between 39 and 49 years old
Nonswitching Sample
2000
2005
2010

2000

Birth year
1950-54
1955-59
1960-64
1965-69
1970-74

37.7%
44.3%
17.9%
0.0%
0.0%

0.0%
33.0%
45.7%
21.4%
0.0%

0.0%
0.0%
29.9%
47.3%
22.8%

32.3%
46.9%
20.7%
0.0%
0.0%

0.0%
32.4%
47.2%
20.4%
0.0%

0.0%
0.0%
34.0%
46.4%
19.6%

Insurance programs
Government Employee
Labor
FarmerUninsured

9.6%
47.8%
11.7%
31.0%

10.2%
52.7%
9.0%
28.2%

9.6%
56.5%
6.3%
27.5%

7.3%
49.1%
9.7%
33.9%

7.3%
51.3%
7.5%
33.8%

8.1%
55.6%
6.2%
30.1%

Surgery incidence rate per 100,000
Hysterectomies
Myomectomies
Total oophorectomies
Partial oophorectomies
N (number of female enrollees at year end)

766.5
124.2
146.2
93.7
931,632

582.8
198.5
67.4
246.9
991,952

526.7
273.1
55.2
267.3
1,232,835

702.1
109.9
127.4
81.6
1,348,413

556.2
173.6
63.6
220.7
1,477,946

516.0
234.1
57.5
236.3
1,523,745

Standard errors in parentheses.

50

General Sample
2005
2010

Table 4: Difference-in-difference estimates of ρq for hysterectomy(nonswitching sample)(1)(2)
Government Employee
Insurance

Labor Insurance
Quarter to 45th birthday x Treatment group dummy (ρq )34.18**
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
7
Treatment group dummy
Log household income
Total number of children
Number of sons
Married(7.950)49.37**(8.231)27.68**(9.025)31.19**(7.053)69.09**(9.824)79.12**(8.240)47.85**(8.316)78.11**(10.81)97.91**(11.05)193.8**(14.95)-42.88**(9.071)-14.10(10.70)-4.997(8.992)-15.78*(7.703)-21.51*(8.839)-19.64*(9.068)-10.01(10.21)
1.204(7.572)8.764**(3.289)-12.10*(5.502)-20.34*(8.306)4.045(10.98)48.33*(18.66)
5,076
1,008
5,280

22.65
(12.06)39.66**(14.67)
13.19(12.78)46.67**(16.19)34.25**(11.08)55.79**(15.62)57.38**(16.96)70.66**(14.46)92.00**(15.91)179.2**(19.70)-36.57**(13.37)-21.98(13.94)-4.015(12.62)-3.447(13.86)-14.79(14.65)-9.188(14.54)-16.81(12.54)3.337(15.31)-17.23**(4.228)-8.788*(4.044)-11.82(8.496)0.544(10.57)38.68(21.29)
789
143
5,280

(3)
Farmer Insurance
15.70(15.01)41.90*(16.79)-10.03(13.61)40.20*(15.74)46.10**(15.98)38.98*(15.46)24.64(15.52)36.32**(13.09)34.47*(15.24)66.70**(15.91)-18.56(13.83)-9.601(16.11)
4.841(16.31)
0.480(15.61)
6.320(14.86)-12.71(15.06)1.950(15.08)-9.745(14.17)33.22**(5.825)-25.33**(5.940)-18.43*(7.395)-1.099(10.32)25.93(23.07)
347
283
5,280

Estimated inducement effect
Estimated timing effectObservations
Notes: The dependent variable is quarterly hazard of hysterectomy. Uninsured are used as control ineach regression. Other covariates are full sets of quarter dummies and data year fixed-effects. Robust
errors clustered at the birth cohort level are in parentheses. ** p<0.01, * p<0.05.

51

Table 5: Nonparametric estimates of ρq for hysterectomy (nonswitching sample)
Quarters to
age 45
-18
-17
-16
-15
-14
-13
-12
-11
-10
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6

(1)

(2)

Uninsured

Labor
Insurance

14.61*(6.95)
2.22(7.32)-10.15(7.40)-4.43(7.73)
6.90(7.40)-15.66(8.70)-9.19(8.50)
8.40(9.64)
1.27(8.82)-7.15(10.26)9.67(9.30)
4.55(7.95)-4.76(9.29)-9.24(9.11)
4.75(9.56)-6.23(10.70)-0.39(9.72)
11.72(10.25)0.69(10.68)-1.65(10.44)9.94(11.07)
3.71(9.55)
6.80(10.86)
13.15(10.45)
11.91(10.50)(-18, 6)

9.67
(7.33)
13.16(7.00)
13.75(8.18)
8.27(8.14)
20.73*(8.72)
27.13**(9.36)
33.64**(8.70)
28.55**(8.99)
26.96**(8.24)
55.91**(10.25)61.88**(10.45)44.50**(9.46)
65.06**(10.77)91.44**(10.60)201.20**(17.53)-47.24**(7.99)-20.55*(9.11)
0.42(8.79)-16.17*(6.98)-18.57*(8.66)-10.05(8.11)(3)
Government
EmployeeInsurance

19.20(11.55)18.82(13.07)27.08(15.16)
16.82(12.73)44.99**(16.03)22.92*(10.78)39.84*(16.09)55.15**(17.69)58.50**(15.43)86.19**(18.09)187.31**(22.06)-40.39**(11.31)-28.25*(12.27)0.20(11.63)(4)
FarmerInsurance

17.44(12.73)-17.75(12.68)29.01*(12.63)26.97*(12.59)16.66(12.55)
17.69(12.48)19.13(12.41)
23.41(12.34)68.64**(12.29)-27.49*(12.20)-19.43(12.12)
7.78(12.04)(-15, 5)(-11, 2)(-9, 2)
Optimal bounds (q L , q U )
4,842
756
280
Estimated inducement effect
-722
87
60
Estimated timing effect-4,483
4,498
4,474
4,481
Observations
Notes: The dependent variable is quarterly hazard of hysterectomy. The covariates are quarterly age withpolynomial order up to five. Robust errors are in parentheses. ** p<0.01, * p<0.05.

52

Table 6: Comparisons between nonswitching, general, and balanced samples in 2005
(1)

(2)

(3)

(4)

(5)

Nonswitching
sampleGeneralsample(2)/(1)

Balancedsample(4)/(1)Government Employee Insurance

100,745

107,696

1.07

43,577

0.43

Labor Insurance

522,462

758,9091.45

218,357

0.42

Farmer Insurance

88,782

111,550

1.26

41,295

0.47

Uninsured

279,963499,791

1.79

121,0140.43

991,952

1,477,946

1.49

424,243

0.43

Insurance programs

Standard errors are in parentheses.

Table 7: Hysterectomy inducement and timing effects from difference-in-difference estimates

Insurance types

Labor Insurance

Government
Employee Insurance

(1)

(2)

(3)

(4)

(5)

Total
hysterectomies
from 40 to 49

Total
Inducement
Effect(2)/(1)

Timingeffect(4)/(2)

Nonswitching sample

43,845

5,076

11.6%

1,008

19.9%

General sample

61,692

7,172

11.6%

1,202

16.8%

Balanced sample

13,609

1,537

11.3%

387

25.2%

Nonswitching sample

7,262

789

10.9%

143

18.1%

General sample

7,888

885

11.2%

156

17.6%

Nonswitching sample

9,100

347

3.8%

283

81.6%

General sample

10,987

241

2.2%

241

100.0%

SampleFarmer Insurance53

Table 8: Hysterectomy inducement and timing effects from nonparametric estimates

Insurance types

(1)

(2)

(3)

(4)

(5)

Total
hysterectomies
from 40 to 49

Total
Inducement
Effect(2)/(1)

Timingeffect(4)/(2)

Nonswitching sample

43,845

4,842

11.0%

722

14.9%

General sample

61,692

6,736

10.9%

1,053

15.6%

Nonswitching sample

7,262

756

10.4%

87

11.5%

General sample

7,888

864

11.0%

135

15.6%

Nonswitching sample

9,100

280

3.1%

60

21.4%

General sample

10,987

319

2.9%

84

26.3%

SampleLabor Insurance

Government
Employee Insurance

Farmer Insurance

Table 9: Hysterectomy inducement effects of stratified nonswitching Labor Insurance enrollees

Subgroup

(1)

(2)

(3)

(4)

Averageinsurance benefits

Total hysterectomies
between 40 and
49 years old

Inducedhysterectomies

Inducement rate(3)/(2)Difference-in-difference method
1
NT$84,592
2
NT$100,425
3
NT$133,435
4
NT$185,197
5NT$219,500
Nonparametric method
1
NT$84,592
2
NT$100,425
3
NT$133,435
4
NT$185,197
5NT$219,500

8,280

739

8.93%

9,145

1,060

11.60%

8,722

949

10.88%

9,049

1,319

14.58%

8,631

1,356

15.71%

8,280

589

7.11%

9,145

903

9.88%

8,722

848

9.72%

9,049

1,520

16.80%

8,631

1,247

14.45%

54

Table 10: Estimated social costs of disability insurance (balanced sample)
Insurance programs

Total number ofMonthlyenrolleesinsurance salary

Total number ofhysterectomies

Disability benefit
payment due toinducement

Surgical expenditure
due to inducement

Government Employee Insurance

43,577

NT$33,786

2,740

NT$60,543,000

NT$15,322,000

Labor Insurance

218,357

NT$31,578

14,946

NT$306,577,000

NT$89,732,000

Farmer Insurance

41,295

NT$10,200

2,740

NT$60,543,000

NT$15,322,000

Total for three programs

303,229

20,426

NT$427,663,000

NT$120,376,00055