Theoretical Economics Letters, 2013, 3, 9-17
http://dx.doi.org/10.4236/tel.2013.35A3002 Published Online October 2013 (http://www.scirp.org/journal/tel)
An Empirical Analysis of Retirement and
Marriage in Taiwan
Wen-Shai Hung
Department of Business Administration, Providence University, Taichung, Chinese Taipei
Received July 18, 2013; revised August 18, 2013; accepted August 28, 2013
Copyright © 2013 Wen-Shai Hung. This is an open access article distributed under the Creative Commons Attribution License,
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
ABSTRACT
This paper investigates the factors influencing changes in marriage following retirement in Taiwan. The data used are
from the Survey of Health and Living Status of the Middle Aged Elderly in Taiwan. The Weibull models are used to
estimate the hazard rates of divorce or separation after retirement. The factors of unobserved heterogeneity are also
examined for the influences of divorce or separation after retirement. The main empirical results find that Mainlanders,
Aboriginals, people with better educational attainments, people with poor health or poor relationship with family have
higher hazard rates of divorce or separation than others. In contrast, people with more children and persons with higher
income have lower hazard rates of divorce or separation than others. After considering unobserved heterogeneity, most
estimated coefficients on the marriage hazard regressors are larger in magnitude than the corresponding coefficients in
the reference model.
Keywords: Divorce; Separation; Weibull Model; Unobserved Heterogeneity
1. Introduction
This paper examines the factors influencing changes in
marriages following retirement in Taiwan. According to
the 2012 survey of Ministry of the Interior, the highest
proportion rates of divorce were concentrated at the 10 -
14 years of marriage duration and the trends gradually
declined during the recent 10 years. In contrast, the
trends of divorce rates over 20 years were gradually in-
creased during the same period. This implies that the
changes in marriages and retirement behavior may have
some special relationships and it is interested to do a
deeper research.
Most previous studies on retirement behaviour in Tai-
wan were focused on the health status and health-care
utilisation, living arrangements, and the economic
well-being of the elderly. For example, Schoenbaum [1]
used the Survey of Health and Living Status of the Mid-
dle Aged and Elderly in Taiwan data to test the effect of
health on labour force transition among the elderly using
four different measures1. He concluded that health is a
major determinant of labour force transition, regard-
less of how it is measured. Individuals in poor health are
significantly more likely to retire than people in good
health. In addition, Chen [2] used the 1989 Labour Force
Survey by the Directorate-General of Budget, Account-
ing and Statistics in Taiwan to examine the effect of
health status and health-care utilisation among the elderly.
He noted that the proportion of old-old population was
relatively low. Taiwan’s elderly were more inclined to
use health-care facilities than elderly in other developed
economies.
Chang [3] used the data from the Survey of Health and
Living Status of the Middle Aged and Elderly to examine
the changes in living arrangements of the elderly in Tai-
wan between 1989 and 1995. He found that reduction in
widowhood would be favorable for the elderly to live
with a spouse only. Increases in educational attainments
and economic independence will alter the elderly to live
alone. In addition, the increasing age at marriage means
that unmarried children are likely to be in the parental
home for a longer period and thus minimize the strong
trend toward independent living of the elderly.
1The four types of health measures considered in his paper include: 1)
a summary measure of limitations on activities of daily living (ADL),
such as shopping and lifting; 2) a summary measure of health condi-
tions, such as stroke and dizziness; 3) a summary measure of mood and
depression using the Centre for Epidemiologic Studies Depression
Scale (CES-D) that can measure how people have been feeling in the
p
ast week; and 4) health indices, such as crude birth rate, crude death
rate, life expectancy at birth (years) constructed using an instrumental
variables framework.
Hermalin, Roan, and Chang [4] also used the data
from the Survey of Health and Living Status of the Mid-
dle Aged and Elderly in 1996 to test the effect of demo-
graphic and socioeconomic trends on the economic
well-being of the elderly. The data combined two panels,
C
opyright © 2013 SciRes. TEL

W.-S. HUNG 10
including the first panel 2669 respondents aged 67 and
over and the second panel 2462 respondents aged 50 to
66 in 1996. In general, those who relied on children as
their major source were reported lower incomes than
those who relied on other major sources.
Furthermore, Yu and Chang [5] investigated the re-
tirement behavior of public sector employees. They used
the matched data sets from the Taiwan Manpower Utili-
zation Survey from 1986 to 2002. They analyzed the
incentive effects of public-sector retirement regulations
on the retirement timing of public sector employees.
Further, they examined whether the sample attrition bias
was serious in their framework. Their empirical results
found that the regulations on retirement age and tenure
had significant effects on the choice of retirement timing.
Hung [6] examined the determinants of retirement
among the middle aged and elderly workers in Taiwan.
The data used were from two waves of Survey of Health
and Living Status of the Middle Aged and Elderly in
Taiwan in 1996 and 1999. He considered the models
without and with time-varying covariates on estimated
retirement. He found that the model without time-varying
covariates, older workers, female workers, Mainlander
workers, and workers with eligible pension have higher
hazard rates of retirement, and workers with better edu-
cation have a lower hazard rate of retirement. Further-
more, for the model with time-varying covariates, work-
ers with poor health have a higher hazard rate of retire-
ment, in particular as workers being in poor health in-
crease the hazard rates of retirement, other things being
equal.
For the other developed countries, some early studies
on the effects of retirement on marital satisfaction pro-
vide limited support for the view that retirement has a
negative impact on marital wellbeing. For example,
Moen, Kim and Hofmeister [7] used two waves of the
Cornell Retirement and Well-Being Study in US in
1994-1995 and 1996-1997 to investigate whether cou-
ples’ employment/retirement circumstances predict marital
quality differently for men and for women. They found
that initially, the retirement transition led to decreased
marital satisfaction and increased marital conflict for
men and women. The evidence complements the findings
that homemaker wives’ marital quality declines tempo-
rarily when their husbands retire. It is also consistent
with Szinovacz’s [8], who used the data from the Na-
tional Survey of Families and Households in US to ex-
plore the impact of couples’ employment/retirement pat-
terns on indicators of marital quality, including conflicts,
heated arguments, marital happiness. He claimed that
marital problems during the retirement behavior are
typically temporary and resolved within a few years after
retirement.
Vaus and Wells [9] showed the paper from Shaw, Pat-
terson, Semples and Grant [10], those who suggested that
after retirement a balance in the relationship must be
re-established based on a new set of routines and patterns
of communication. The evidence indicates that as cou-
ples settle into retirement, a new balance is generally
found and the role strain that couples experienced during
the retirement transition is reduced.
Pienta [11] used data from the 1992 Health and Re-
tirement Survey to compare the retirement behavior of
husbands and wives. He found that the wives’ retirement
status is related to familial factors, economic resources,
and spouses’ personal characteristics supporting the new
modes of retirement hypothesis. Husbands differ mainly
in that familial and spousal attributes have more limited
relationships with retirement behavior according to the
usual modes of retirement hypothesis.
Smith and Moen [12] investigated factors related to re-
tirees’ and their spouses’ individual and joint retirement
satisfaction using decision-making theory and a life
course perspective. The sample included retired respon-
dents (ages 50 to 72) and spouses from the Cornell Re-
tirement and Well-Being Study in US in 1994-1995 and
1996-1997. Although 77% of retirees report retirement
satisfaction, only 67% of their spouses are satisfied; even
fewer couples (59%) report joint satisfaction. Multivari-
ate logistic regression analyses reveal that retirees’ and
spouses’ individual and joint reports of retirement satis-
faction are related to perceptions of spousal influence on
the retirement decision, with effects varying by gender.
In sum, few papers analysed the issues of changes in
marriages and retirement, particularly for exploring the
related questions of the impacts of retirement on the do-
mestic divisions of labour and on marital quality in this
domain in Taiwan. This paper will use the duration
analysis and micro data to fill this gap. First, it describes
the factors influencing changes in marriages, including
divorce, separation, or spouse’s deceased following re-
tirement in Taiwan. Second, it estimates the hazard rates
of changes in marriages among the middle aged and eld-
erly. Third, in addition to investigating the effect of un-
observed heterogeneity of changes in marriages follow-
ing retirement, it is well known that the duration analysis
produces incorrect results if unobserved heterogeneity is
ignored (Lancaster, [13])2, and it is to find useful policies
for retirement and marriage in Taiwan.
2. Some Facts about Marital Status among
the Middle Aged and Elderly in Taiwan
Marital status always affects individual participation in
work and retirement behaviour. For instance, once a man
is married, he tends to have more opportunities to work,
2See Hosmer, Lemeshow and May [14] and Cleves, Gould, and
Gutierrez [15] for a description of the frailty models.

W.-S. HUNG 11
and perhaps an increased desire or need to work as he is
likely to be the main earner for his family. In contrast, a
married woman might do more housework and have a
lower desire (less need or opportunity) to work. The sur-
vey of Taiwan and Fujian Areas shows that the propor-
tion of the population who are married decreased with
increasing age from 85.4% aged 50 to 54 to 39.3% aged
80 and over. In contrast, the proportion whose spouse
was deceased increased with age from 5.7% aged 50 to
54 to 57.3% aged 80 and over in 2005. The proportion of
the population divorced or separated decreased with in-
creasing age from 6.2% aged 50 to 54 to 1.6% aged 80
and over. In particular, for the Taiwanese traditional so-
ciety, most people prefer to only marry once during their
lives.
Therefore, this paper is interested to examine some
hypothesis of changes in marriages following retirement
in Taiwan: for example, does marriage improve or get
worse following retirement? Do men and women report
different marital outcomes following retirement? What
happens to the division of labour between married men
and women following retirement? May the hazard rates
of separated or divorced after retirement be higher than
before retirement?
3. Research Methods
3.1 Data Source
The data used are from the Survey of Health and Living
Status of the Middle Aged and Elderly in Taiwan (here-
after, SHLS) to analyse retirement and marriage issues.
The SHLS is an important and unique survey in Taiwan,
the first large-scale panel data set collected and produced
by the Taiwan Provincial Institute of Family Planning
(TPIFP)3 and the Population Studies Centre in the Uni-
versity of Michigan (PSC, UM), and is available for the
period from 1989 to 2007. The project was initiated in
1989 with a survey of 4049 respondents aged 60 and
above. These respondents were interviewed four times
including a major follow-up interview in 1993. The
SHLS survey was extended by a second panel of indi-
viduals aged 50 to 66 in 1996. The two 1996 question-
naires were very similar. The sample size for the first
panel was 2669 individuals aged 67 and over, and the
second panel had 2462 respondents aged 50 to 66. In
1999 the first panel comprised 2310 respondents aged 70
and over, and the second panel had 2130 respondents
aged 53 to 73. In 2003 the first panel comprised 1743
respondents aged 74 and over, the second panel had 2035
respondents aged 57 to 73, and the SHLS survey was
again extended by a third panel of individuals aged 50 to
56. Until 2007, the first panel comprised 1268 respon-
dents aged 78 and over, the second panel had 1864 re-
spondents aged 61 to 77 and the third panel had 1402
individuals aged 54 to 60.
The main data used are from the second panel of
SHLS and the sample aged 50 to 66 in 1996. In particular,
the voluntary retirement can be taken at age 50 if indi-
viduals have worked for 25 years, or reached age 55 and
worked for more than 15 years. The first panel in 1989
did not cover those aged 50 to 60. For this reason the first
panel has been discarded for this study, and instead this
uses the second panel. The SHLS data represents a na-
tional random sample, the detailed information includes
individuals, family, marital status, health, social support,
employment, and economic status.
3.2 Variables Specification
3.2.1. Dependent Variable
According to the SHLS data, the sample consists of two
groups, namely the currently married and the divorced or
separated, except widowed. The former group remains
married during the sample period and are known as
“right-censored” of marriage duration. The latter group
includes those divorced and separated during the sample
period, and the date on which an individual started their
last marriage and the exact age at which their marriage
ended were observed. These are known as the “uncen-
sored” of marriage duration. Therefore, marriage dura-
tion includes the period from when an individual first
married to the end of the marriage for the “uncensored”
duration spells, and they continue married for the
“right-censored” duration spells. This variable can be
categorized as a dependent variable. The uncensored
variable is coded 1 for divorced or separated and 0 oth-
erwise.
3.2.2. Explanatory Variables
The explanatory variables recorded in the SHLS data
include 1) Demographic characteristics of respondent:
age, gender, race, educational attainment, and health
status. 2) Family structure and support: number of chil-
dren, relationship with family, and residence status. 3)
Economic and employment factors: household income
and retirement.
First, the demographic characteristics of respondents
are explored. The effect of ageing alone is important in
explaining why people losing their married status. In
particular, as people become older, they are more likely
to die or lose their partner. From the SHLS data, age can
be categorised into four groups: Age1 (aged 50 to 54),
Age2 (aged 55 to 59), Age3 (aged 60 to 64), and Age4
(aged 65 to 66). In addition, females always have a
longer life expectancy than males in Taiwan. That is, the
numbers of females who lose their husbands are is
3The Taiwan Provincial Institute of Family Planning was merged into
the Bureau of Health Promotion, Department of Health in July 2001.

W.-S. HUNG 12
greater than males who lose their wives. The Gender
variable is coded 1 for female and 0 for male. Next, the
Race variables have four groups, namely Race1 (Fuji-
anese), Race2 (Hakka), Race3 (Mainlander), and Race4
(Aboriginal). For the education variable is divided into
four levels of schooling, namely Edu1 (informal school-
ing), Edu2 (primary level: 1 to 6 years), Edu3 (high
school level: 7 to 12 years) and Edu4 (college level: 13 to
17 years). For the health assessment, the SHLS survey
identifies five levels including excellent, good, average,
not so good, and poor. The Poorh variable is coded 1 for
poor health, including “not so good” and “poor” health,
and 0 for otherwise.
Second, the variables of family structure and support:
the number of children can reflect marriage duration and
living support. In particular, the traditional Chinese cul-
ture in Taiwan suggests that people with more children
expect more family support in old age. There are 0 to 11
children for this variable. Next, the definition of rela-
tionship with family includes that people sharing, con-
cerning, communicating, and caring with their family;
particularly for the sickness, if the respondents could not
believe or depend on their family and the variable can be
defined as Poorla4, that is people with poor relationship
with their family. The variables of residence status in-
clude Area1 (people living in urban), Area2 (people liv-
ing in town), and Area3 (people living in rural). Basically,
people with more children have lower hazard rates of
divorce or separation. In contrast, respondents with poor
relationship from their family have a higher hazard rate
of losing their marriage.
Third, the economic and employment factors cover
household income and retirement. If people have a better
economic status or higher income, they might have a
lower hazard rate of ceasing to be married. For the em-
ployment variables, the Retirement variable is coded 1
for respondent’s retired and 0 for otherwise. Basically, if
the retired people without earnings or pension benefits
have higher hazard rates of losing their marriage.
However, the main limitation of this study is the sur-
vey data, the response rates on earnings and pension in-
come were low, reflecting the reluctance of participants
to divulge their true income. One more hidden danger of
the SHLS data is the unknown accuracy of the responses
given by the participants. No obvious means of verifying
these responses exists. To solve the limitation of the
SHLS is the lack of data on the interviewees’ wages and
their assets. This paper only uses the household income
as an indicator of income to facilitate further analysis of
changes in marriages following retirement. The descrip-
tive and summary statistics are given in Ta ble 1.
3.3. Estimation Method: Duration Model
Duration analysis has been developed in the field of
bio-statistics to describe the timing of events. It has be-
come a subject of increasing interest to applied econom-
ics, such as retirement issues in labour economics (Dia-
mond and Hausman, [16]; Hung, [17]), and divorce top-
ics in marriage economics (Hung and Ho, [18]). There-
fore, this paper uses duration analysis and considers mar-
riage duration in two groups, including right censoring
(individuals who remain married during the sample pe-
riod), and event or failure time (individuals do not re-
main married, including divorce or separation during the
sample period). From these two sets of marriage duration,
we can calculate the hazard rates of divorce or separa-
tion.
3.3.1. M ode l without Unobserved Heterogenei ty
Weibull distributions are widely used as models for dura-
t ion analysis. The hazard function of marriage duration
without unobserved heterogeneity is specified as



0
11
.
ii

x
i
htxtt e





 (1)
Empirically, the parameters λ and α in the Weibull dis-
tribution can be estimated by maximum likelihood. The
parameter λ depends on the explanatory variables xi, thus
providing us with a more flexible hazard function. For
example, the hazard function is increasing if α > 1, de-
creasing if α < 1, and constant if α = 1. For observed du-
ration data, 12 the log-likelihood function can
be formulated and maximized to include censored and
uncensored observations. Combining the Weibull model
into a general parametric likelihood yields:
;, ,
n
tt t




1
1,,
ii
ncc
ii ii
i
LftxStx 


 

 (2)
where


,

 
i
c
, and represents uncensored
observations,
1
i
c
0

represents right-censored observa-
tions (Cleves, Gould, and Gutierrez, [15]). To obtain the
maximum likelihood with respect to the parameters of
interest, β, then maximise the log-likelihood function4:





1
lnln,1 ln,
n
iiii ii
i
LcftxcStx 









(3)
The procedure to obtain the values of maximum like-
lihood estimation requires taking derivatives of


ln L

with respect to β, the unknown parameters, setting these
equations equal to zero, and solving for β.5
3.3.2. M ode l with Unobs erved Heterogeneity
After considering unobserved heterogeneity on estimated
individual marriage behaviour, the hazard function can
4Since the log function is monotone, maxima of (2) and (3) occur at the
same value of β; however, maximizing (3) is computationally simpler
than maximizing (2).
5See Klein and Moeschberger [19], for a description of the numerical
methods for implementing multivariate Newton-Raphson methods.

W.-S. HUNG 13
Table 1. Descriptive statistics of variables.
Variable Description Mean Std. Dev.
Duration Duration of marriage between 1 and 50 years. 32.032 7.755
Censor 1 = Uncensored, 0 = Otherwise. 0.029 0.167
Age96 50 - 66 years old in 1996. 57.411 4.733
Age1 1 = aged 50 to 54, 0 = Otherwise. 0.323 0.468
Age2 1 = aged 55 to 59, 0 = Otherwise. 0.326 0.469
Age3 1 = aged 60 to 64, 0 = Otherwise. 0.256 0.436
Age4 1 = aged 65 to 66, 0 = Otherwise. 0.093 0.291
Gender 1 = Female, 0 = male. 0.437 0.496
Race1 1 = Fujianese, 0 = Otherwise. 0.728 0.444
Race2 1 = Hakka, 0 = Otherwise. 0.185 0.388
Race3 1 = Mainlander, 0 = Otherwise. 0.072 0.259
Race4 1 = Aboriginal, 0 = Otherwise. 0.013 0.115
Edu1 1 = Informal education, 0 = Otherwise. 0.251 0.433
Edu2 1 = 1 to 6 years of schooling, 0 = Otherwise. 0.463 0.498
Edu3 1 = 7 to 12 years of schooling, 0 = Otherwise. 0.210 0.407
Edu4 1 = 13 to 17 years of schooling, 0 = Otherwise. 0.075 0.263
Health1 1 = Excellent Health, 0 = Otherwise. 0.205 0.403
Health2 1 = Good Health, 0 = Otherwise. 0.237 0.425
Health3 1 = Average Health, 0 = Otherwise. 0.331 0.470
Health4 1 = Poor Health, 0 = Otherwise. 0.203 0.402
Health5 1 = Very Poor Health, 0 = Otherwise. 0.023 0.150
Poorh 1 = Poor and Very Poor Health,
0 = Otherwise. 0.226 0.418
Children 0 - 11 children 3.791 1.453
Poorla4 1 = Poor relationship with family, 0 = Otherwise. 0.052 0.222
Area1 1 = People living in urban, 0 = Otherwise. 0.381 0.485
Area2 1 = People living in town, 0 = Otherwise. 0.265 0.441
Area3 1 = People living in rural, 0 = Otherwise. 0.353 0.478
Income1 1 = Less than NT$99,999, 0 = Otherwise. 0.159 0.366
Income2 1 = NT$100,000 - 299,999, 0 = Otherwise. 0.334 0.472
Income3 1 = NT$300,000 - 599,999, 0 = Otherwise. 0.294 0.455
Income4 1 = NT$600,000 - 999,999, 0 = Otherwise. 0.127 0.333
Income5 1 = Larger than NT$1,000,000, 0 = Otherwise. 0.084 0.277
Retirement 1 = retired, 0 = Otherwise. 0.311 0.463
Note: 1) The effective sample has 1556 observations, including 45 divorced or separated, and 1511 people who remain married. 2) The exchange rate was US$1
= NT$27.457 in 1996.
be defined as The other calculation procedures are same with the pre-
vious model without unobserved heterogeneity.


0
11
,ii

x
u
ii
htxutte





 (4)
4. Empirical Results
where u can represent unobserved heterogeneity, the dif-
ferences between observations are introduced via a
multiplicative scaling factor. This is a random variable
taking on positive values, with the mean normalised to
one and finite variance 2

. A crucial assumption in the
model is that u is distributed independently of xi and t.
4.1. Model without Unobserved Heterogeneity
Table 2 shows the estimated coefficients and hazard ra-
tios of divorce or separation by Weibull model. For the
benchmark individuals, all explanatory variables take a

W.-S. HUNG 14
Table 2. Estimation by Weibull model.
Variables Coefficient Standard Error Hazard Ratio Standard Error
Age96 −0.034 0.035 0.965 0.034
Gender −0.293 0.359 0.745 0.268
Race2 0.012 0.497 1.012 0.503
Race3 1.365*** 0.434 3.916*** 1.702
Race4 1.895*** 0.629 6.657*** 4.190
Edu2 0.866* 0.503 2.377* 1.196
Edu3 1.531*** 0.573 4.626*** 2.654
Edu4 1.020 0.836 2.774 2.319
Poorh 0.782** 0.329 2.186** 0.719
Children −0.506*** 0.123 0.602*** 0.074
Poorla4 1.225*** 0.367 3.406*** 1.250
Income2 −0.917** 0.397 0.399** 0.158
Income3 −1.339*** 0.440 0.261*** 0.115
Income4 −1.578** 0.651 0.206** 0.134
Income5 −2.703** 1.107 0.066** 0.074
Retirement 0.196 0.347 1.217 0.422
Constant −4.317** 2.155
/ln_

0.135 0.142 0.135 0.142
α 1.145 0.163 1.145 0.163
1

0.872 0.124 0.872 0.124
Log likelihood −205.652 −205.652
LR chi2 (16) 83.55 83.55
Notes: 1) The effective samples are 1,556 observations. 2. Effects are significant at *p ≤ 0.10, **p ≤ 0.05, ***p ≤ 0.01. 3) Goodness of fit: the result of
Log-likelihood ratio test can reject the hypothesis that all coefficients except the intercept are 0 at the 0.01 level.
value of zero. That is, the benchmark individuals in all
cases are relatively young Fujianese men with lower
education attainments, no child, good health, with lower
household income, and not retire. The hazard rate of di-
vorce or separation estimates can be derived from the
Weibull model of




0
ˆˆ0
11
0.145
;
1.145exp 4.317
i
i
htxtt e
t







(5)
In particular, 1.145 1



and , which
indicates the hazard rate has positive marriage duration
dependence,
15t0
0dhtdt . And

ln 10.135  , the
estimate suggests that the hazard rate of divorce or sepa-
ration is increasing over time. As marriage duration gets
longer, the hazard rate increases and people are more
likely to divorce or separate.
First, for the age variables of respondents, Table 2
shows that the estimated coefficient of Age96 is negative
and has lower hazard rates ceteris paribus, but statisti-
cally insignificant. The hazard ratio for Age96 is 0.965.
This implies that older Taiwanese have 3.5% lower haz-
ard rates than otherwise and they are less likely to di-
vorce or separate, ceteris paribus. The estimated coeffi-
cient of Gender is negative and has lower hazard rates
ceteris paribus, but also insignificant. The hazard ratio
for Gender is 0.745. This implies that women have
25.5% lower hazard rates than otherwise and they are
less likely to divorce or separate, ceteris paribus. In con-
trast, the estimated coefficients of Race3 and Race4 are
positive and statistically significant and have higher haz-
ard rates ceteris paribus. The hazard ratios for Race3 are
3.916, and Race4 is 6.657. This implies that Mainlanders
have 391.6% and Aboriginals have 665.7% higher hazard
rates than Fujianese and they are more likely to divorce
or separate, ceteris paribus. Furthermore, the estimated
coefficients of Edu2 and Edu3 are positive and statisti-
cally significant and have higher hazard rates ceteris
paribus. The hazard ratios for Edu2 are 2.377, and Edu3
is 4.626. This implies that people with primary education
have 237.7%, junior and senior high school have 462.6%

W.-S. HUNG 15
higher hazard rates than people with informal education
and they are more likely to divorce or separate, ceteris
paribus. For the variables of health status, Table 2 shows
that the estimated coefficient of Poorh is positive and
statistically significant and has higher hazard rates ceteris
paribus. The hazard ratio for Poorh is 2.186. This implies
that people with poor health have 218.6% higher hazard
rates than otherwise and they are more likely to divorce
or separate, ceteris paribus.
Second, for the variables of family structure and social
networks, Table 2 shows that the estimated coefficient of
Children (number of children) is negative and statisti-
cally significant and has lower hazard rates. Especially,
the hazard ratio for Children is 0.602. This implies that
respondents with children have 39.8% lower hazard rates
than respondents without children and they are less likely
to divorce or separate, ceteris paribus. Further, the esti-
mated coefficient of Poorla4 (poor relationship with
family) is positive and statistically significant and have
higher hazard rates ceteris paribus. The hazard ratio of
Poorla4 is 3.406. This implies that people with poor rela-
tionship from their family have 340.6% higher hazard
rates than otherwise and they are more likely to divorce
or separate, ceteris paribus.
Third, for the variables of economic status and em-
ployment, Table 2 shows that the estimated coefficients
of Income2, Income3, Income4, and Income5 are nega-
tive and statistically significant and have lower hazard
rates. The hazard ratios for Income2, Income3, Income4,
and Income5 are 0.399, 0.261, 0.206, and 0.066 respec-
tively. These show that people with higher household
income have lower hazard rates than otherwise and they
are less likely to divorce or separate. In contrast, the es-
timated coefficient of Retirement is positive and have
higher hazard rates ceteris paribus, but statistically in-
significant. The hazard ratio of Retirement is 1.217. This
implies that Retirement has 21.7% higher hazard rates
than not retired and they are more likely to divorce or
separate, ceteris paribus.
4.2. Model with Unobserved Heterogeneity
Frailty is a random component designed to account for
variability due to unobserved individual-level factors of
divorce or separation that are otherwise unaccounted for
by the other predictors in the marriage duration model.
Of particular note is the Poorla4 variable, which shows
that 5.2% of people with poor relationship from family.
When people are sick, they do not believe or depend on
their careing.
Table 3 shows that the frailty model of all samples is
assumed to follow a gamma distribution with mean 1 and
variance equal to theta (θ). The estimate of theta is 0.269.
A variance of zero (theta = 0) would indicate that the
frailty component does not contribute to the model. A
likelihood ratio test for the hypothesis theta = 0 is shown
directly below the parameter estimates and indicates a
chi-square value of 3.31 with 1 degree of freedom yield-
ing a highly significant p-value of 0.034. Notice how all
the parameter estimates are altered with the inclusion of
frailty. The estimate for the shape parameter is now
1.143, different from the estimate 1.138 obtained from
the model without frailty. The inclusion of frailty not
only has an impact on the parameter estimates but also
complicates their interpretation. Some estimated coeffi-
cients of the variables of Race4 (Aboriginals), Children
(number of children), Income2, Income3, Income4, and
Income5 are slightly larger in magnitude than the corre-
sponding coefficients in the reference model. The
Weibull distribution shape parameter α is also slightly
larger in the frailty model than in the reference model.
Therefore, the effects of unobserved heterogeneity are
important for examining the duration of marriage. There-
fore, people need to consider the factors of unobserved
heterogeneity and to improve the relationship with their
families, they may be able for reducing the rates of di-
vorce or separation in the modern society.
5. Conclusions
This paper investigates the factors influencing changes in
marriages following retirement in Taiwan. The data used
are from the 1996 Survey of Health and Living Status of
the Middle Aged Elderly in Taiwan and the sample aged
50 to 66.
First, for the demographic characteristics, the empiri-
cal results show those Mainlanders, Aboriginals, people
with better educational attainment, and those in poor
health have higher hazard rates and they are more likely
to divorce or separate, ceteris paribus. Second, for the
economic status and employment, people with higher
household income have lower hazard rates and they are
less likely to divorce or separate. In contrast, respondents
retired have higher hazard rates and they are more likely
to divorce or separate. Third, for the family structure and
social networks, people with more children have lower
hazard rates of divorce or separation. In contrast, the re-
spondents with poor relationships from family have
higher hazard rates and they are more likely to divorce or
separate.
After considering the effect of unobserved heterogene-
ity from the factors of poor relationship (including diffi-
cultly sharing, concerning, communicating, and caring
from their family), the estimated theta is larger than the
model without unobserved heterogeneity. This implies that
the influence of divorce or separation is more affected by
the factors of unobserved heterogeneity. Particularly for
the sickness, the respondents could not believe or depend
on their family. To reduce the rate of divorce or separa-
tion, people may consider the factors of unobserved het-

W.-S. HUNG 16
Table 3. Estimation by Weibull models without and wi th unobse rved heterogene ity.
Without Unobserved Heterogeneity With Gamma-Heterogeneity
Va ri ab le s
Coefficient Standard Error Coefficient Standard Error
Age96 −0.039 0.035 −0.035 0.035
Gender −0.222 0.352 −0.274 0.356
Race2 −0.027 0.495 0.001 0.496
Race3 1.404*** 0.447 1.376*** 0.435
Race4 1.842*** 0.626 1.885*** 0.627
Edu2 0.868* 0.495 0.867* 0.501
Edu3 1.672*** 0.571 1.566*** 0.573
Edu4 0.971 0.818 1.007 0.831
Children −0.533*** 0.124 −0.512*** 0.123
Poorhealth 0.846*** 0.324 0.799** 0.327
Income2 −1.111*** 0.389 −0.966** 0.397
Income3 −1.538*** 0.440 −1.387*** 0.442
Income4 −1.957*** 0.641 −1.674** 0.654
Income5 −2.879*** 1.094 −2.745** 1.103
Retirement 0.180 0.343 0.192 0.345
Constant −3.689* 2.075 −3.543 2.194
/ln_

0.129 0.142 0.134 0.138
/ln_the −1.311 1.196
α 1.138* 0.162 1.143* 0.158
1

0.878* 0.125 0.874* 0.121
theta 0.269* 0.322
Log likelihood −210.266 −208.611
LR chi2 (15) 74.32 65.57
Notes: 1) The effective samples are 1,556 observations. 2) Effects are significant at *p ≤ 0.10, **p ≤ 0.05, ***p ≤ 0.01. 3) Goodness of fit: the result of
Log-likelihood ratio test can reject the hypothesis that all coefficients except the intercept are 0 at the 0.01 level. In particular, Log-likelihood ratio test of theta
= 0: chibar2 (01) = 3.31, Prob > = chibar2 = 0.034.
erogeneity and how to improve their relationship with
their family.
the Korea National Research Foundation for providing
partially funding of this research. The number is: NRF-
2011-220-B00027.
For the future work, this study will continually use
the 1996-2007 panel data with the time-varying covari-
ates analysis. People with poor health have higher hazard
rates of divorce or separation, in particular as people be-
ing in poor health increase the hazard rates after retire-
ment, other things being equal. Few changes in earnings
or household’s income may provide a stable marriage
following retirement.
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