GCOE Discussion Paper Series
Global COE Program

Human Behavior and Socioeconomic Dynamics
Discussion Paper No. 277

One male offspring preference: evidence from
Vietnam using a split-population model

Tien Manh Vu

August 2012GCOE Secretariat
Graduate School of Economics

OSAKA UNIVERSITY

1-7 Machikaneyama, Toyonaka, Osaka, 560-0043, Japan

One male offspring preference: evidence from
Vietnam using a split-population model
Tien Manh Vu
Osaka School of International Public Policy, Osaka University
1-31 Machikaneyama, Toyonaka, Osaka 560-0043, Japan.
Tel.: +81-(0)90-1717-9773
Fax: +81-(0)6-6850-5656
E-mail: t-vu@osipp.osaka-u.ac.jp

Abstract This paper examines sex preferences for children in Vietnam using the birth cohort from1990 to 2008. We specify the sex–birth order composition of existing children using a splitpopulation model. The model better fits the data by relaxing the assumption in conventional hazard
models that all mothers would eventually have another child. Our results indicate a strong
preference for families having precisely one male offspring. In addition, we observe a mixed sex
preference at the fourth birth order and find that the involvement of mothers in economic activities
does not significantly affect the fertility timing decision until the fourth childbirth. We also findthat a 1 percent increase in household income adjusted by household size reduces the probabilityof having children by 35.3–51.9 percent. The same income increment lowers the level of son
preference by 49.8 percent at the second birth order. However, income has only a minor impact on
the son preference at higher birth orders. Together, these results suggest that the importance placedon economic reasons for a son preference will gradually weaken as economic development
proceeds in Vietnam.
JEL Classification J11, J12, J13
Key words Son preference, Sex composition, Birth spacing, Birth order, Split-population model1

1 Introduction
During the period 1990–2008 in Vietnam, the combination of improvements inhealth, a lower fertility rate, and a higher economic growth rate should have
weakened the economic foundations of the family preference for a son. In
evidence, Vietnamese gross domestic product (GDP) grew at approximately 5
percent annually during this period (GSO 2010). At the same time, the mortality
rate of children under 5 years of age in Vietnam fell from 51 per 1,000 live births
in 1990 to just 29 in 2005 (WHO 2011). Similarly, the annual population growthrate declined from 1.8 percent in 1990 to just 1.1 percent in 2008, and average life
expectancy increased from 65 years in 1990 to 74 years in 2008 (World Bank
2011b, 2011c). Interestingly, however, the participation rate of women in the
Vietnamese labor force remained at about 70 percent throughout the same period(World Bank 2011a). These facts encourage further investigation of the case ofVietnam in terms of families’ preference for a son.
The purpose of this paper is to examine sex preferences for children in the
1990–2008 birth cohort using data from the 2008 Vietnam Household Living
Standard Survey (VHLSS). Unlike previous research in this area, we examine thefertility timing decision up to the fourth birth order conditional on the sex–birthorder composition of all preceding offspring using a split-population model. We
also analyze the impact of household income on the level of son preference. We
find that the split-population model is superior to conventional hazard models
when estimating the probability of having another child in each parity progression.
This is because it not only fits the data better but also relaxes the assumption of
conventional hazard models that all mothers will eventually have another child.
We obtain four major findings as follows. First, during the period 1990–
2008, parents in Vietnam ultimately desired precisely one male offspring. For thisreason, mothers without a son have the highest probability of having an additionalchild every month after ninth months since the delivery of the previous child.
Second, we also find a mixed sex preference in parity progression to the fourth
birth. Third, whether mothers are involved in economic activities has minimal
influence on fertility timing up to the third childbirth. Fourth, a 1 percent increasein household income reduces the probability of having additional children by up
to 51.9 percent and the level of son preference by up to 49.8 percent during theparity progression to the second childbirth. However, household income has only
a minor impact on the level of son preference at all other birth orders. Together,
these results suggest that the importance placed on economic reasons for a son
preference will gradually weaken as economic development proceeds in Vietnam.
The remainder of the paper is organized as follows. Section 2 details theexisting evidence on sex preference in families, especially in Vietnam. Section 3
introduces the data used and Section 4 describes our empirical methodology.
Section 5 presents our findings. Section 6 discusses our results and provides ourconclusions.

2 Sex preference literature
Substantial research into sex preference—the tendency for families to favor a
specific sex for an unborn child—has taken place in both developing anddeveloped countries. For instance, in many developing countries in South Asia,
Southeast Asia, and North Africa, there is evidence of a strong son preference(Basu and De Jong 2010). A preference for a mixed sex family also exists. For2example, in the Nordic countries, Danish, Norwegian, and Swedish parents have adaughter preference, whereas Finns exhibit a son preference for their third-born
child (Andersson et al. 2006). Preferences also appear to change over time. For
example, Japanese parents during the period 1920–1939 exhibited a son
preference, but this disappeared in subsequent decades, replaced by a mixed sex
preference among parents with two children (Kureishi and Wakabayashi 2011). In
contrast, although South Korea displayed a strong decline in the fertility rate from
6.0 in 1960 to 1.6 in 1990, the son preference remained strong (Larsen et al. 1998).
Das Gupta et al. (2003) suggest that cultural and economic factors are thetwo main influences on the son preference. Cultural factors include a patrilineal
kinship system, commonly strong in northern India, China, and South Korea,
which can increase a family’s desire for a son. Moreover, in both China and Korea,
ancestor worship—the belief that one should take care of the souls of one’s
ancestors after their death—motivates the apparent need to have a son.
Furthermore, in India and China, possible economic reasons for preferring maleoffspring include a need to increase the workforce for family farming and tosupport parents in their old age. High dowry costs in India can also explain alower preference for female children. Finally, Das Gupta et al. (2003) and Chungand Das Gupta (2007) claim that urbanization, the increased participation of
women in the labor force, and social and legal reform movements potentially leadto a decline in the level of son preference.
The consequences of a son preference, although not our focus, include thephenomenon of ‘missing women’ (Sen 1990) and/or a skewed sex ratio at birth.
Parents then engage in prenatal or postnatal discrimination to select the sex theywant, accordingly neglecting any children of the other sex (Das Gupta 1987).
However, it is not easy to estimate the effect of each factor including sex-selective
abortions, female infanticide (as in the works of Sen 1990 and Das Gupta 1987),
and Hepatitis B infection of women (as in studies by Oster 2005 and 2010, and
Das Gupta 2005, 2006 and 2008) to the outcome of skewed sex ratio at birth.
Additionally, Edlund (1999) argues that skewed sex ratios return to normal
through the marriage market. Moreover, Chung and Das Gupta (2007) suggestthat unbalanced sex ratios in South Korea would transit toward the global average
because of the widespread development of nonfarm employment andimprovements in gender perceptions. Das Gupta et al. (2009) also provide
evidence that the number of ‘missing girls’ in China and India has begun to
decline.
Investigation of the evidence attached to sex preference is common inexisting empirical studies, where researchers typically search for behavioral
evidence, rather than merely analyzing the outcome of a specific questionnaire on
individual preferences. For example, Yamaguchi (1989) calculates the average
number and birth order of boys in a family under both population homogeneityand heterogeneity in the probability of having a boy. The sex difference in birthorder is only found in population heterogeneity while the sex difference in thenumber of siblings exits in both types of populations. Haughton and Haughton(1998) construct eight different tests under limited information circumstances forfamilies that have completed childbearing. Notably, this line of research suggests
specifying the time interval between a given birth order and the next in a hazard
model. Furthermore, Basu and De Jong (2010) identify a common son-targeting
fertility behavior in developing countries, with the outcome being that girls
generally have more siblings and more often appear in lower birth orders.
In Vietnam, the son preference has been examined by Haughton and3

Haughton (1995, 1996, 1998) and Bélanger (2002b). Using quantitative data on
500 families in a rural village in northern Vietnam and qualitative information on
100 individuals, Bélanger (2002b) suggested that parents prefer to have sons fortheir social, symbolic, and economic value. In earlier work, Haughton andHaughton (1995) employ a subsurvey in the 1992–1993 wave of the Vietnam
Living Standard Survey (VLSS) of 2,636 women aged 15–49 years to argue that
although the son preference in Vietnam remains relatively strong, it has only aminor impact on the fertility rate. By investigating the birth spacing between
families’ second and third births, Haughton and Haughton (1996) apply two
separate Weibull regression models under the hypothesis of heterogeneous
preferences. Their results indicate that half of the surveyed parents preferred sons,but that the preference was difficult to confirm for the remainder. Most recently,
from eight different types of tests, Haughton and Haughton (1998) propose that asimple progression parity model and table are very effective for evaluating thepreference for sons if information on sex by birth order is available.
Although these existing studies provide a useful foundation for the
analysis of sex preference in Vietnam, they have some key limitations. To start
with, most of the data in use employ a certain restrictive sampling method in thatcounting the aggregate number of boys and girls in specific types of families in acertain birth order in the sample does not guarantee coverage of all necessary
conditions for a son preference in other sample data sets as well as in the
population. In addition, it is an unrealistic assumption that parents decide both thetotal number of children and the number of boy(s) before any childbirths havetaken place. Parents cannot perfectly control the sex of the child so their decisions
will change conditional on the sex of any existing children. Moreover, there would
be bias in our estimations if we were to specify overlapping sex composition as anindependent variable. For example, Lee (2008) specifies a dummy variable for thechildren in a two-child family of different sexes. If having a first male child werepreferred more than a first female child (a type of sex–birth order preference), theinterpretation obtained from the estimates of this single dummy variable would beless persuasive.
In addition, most studies rely on a combination of standard hazard models
for women of a fertile age (15–49 years) and logistic models for older womenassumed to have completed their period of fertility. This conventional method
makes it difficult to interpret results if there is a difference in the birth cohorts ofthe mothers, the distributional assumptions, or both. Moreover, demographers are
generally unlikely to consider interactions between the son preference andhousehold income because collecting information on household income
substantially increases the survey cost, especially given that demographic surveys
commonly have large sample sizes. Among the few studies that consider this,Gaudin (2011) employs the household asset score as a proxy for wealth and finds
a strong negative correlation between wealth and son preference in India.
However, as the assets owned by all household members are included in the asset
score, it does not adjust for the family size effect.

3 DataThe data we employ are from the 2008 Vietnam Household Living Standard andConsumer Price Index Survey, commonly known as the 2008 VHLSS. The 2008
VHLSS is similar to earlier waves of the survey; it receives technical support
from the World Bank and is undertaken nationwide by the General Statistics
4

Office of Vietnam (GSO). The data set in use is the country sample referred to as
Sample 1, which consists of 45,945 Vietnamese households. Sample 1 includes asampling weight for every household. In these households, our analysis
investigates the fertility of parents, one of whom is the household head. Children
included in the survey are then the children of the household head, and we obtain
this information from a specific question in the survey questionnaire.
We select the data using several specific criteria to prevent problems
arising with our sample observations. First, we identify both the son and his
spouse as ‘children’ of the household head in the survey. Second, in Vietnam, awoman does not change her family name when married and she may reside in her
spouse’s family home. Thus, we select parents for our sample whose children are
all single according to their declared marital status. All children must also havethe same initial letter of their family name as their father and we restrict the age ofthe eldest co-residing children to be less than 191 years to obtain the birth cohort
of interest. Third, we omit families where the age of the mother at childbirth isless than 15 years or more than 49 years to reduce the probability of including
stepmothers in the analysis. However, the remaining likelihood of errors fromerroneously including stepparents is relatively low. Just 0.24 percent of the fathers
and less than 0.01 percent of the mothers in the Sample 1 are divorced.
In addition, we include additional data containing information on allfamily members working and living away from the household 6–12 months before
the commencement of the survey2. However, we do not have information on
children that may have left the household more than a year before the survey.
Finally, we limit mothers to those aged 49 years or less. In total, 14,406
households meet all of our sample selection criteria. Table 1 provides descriptive
statistics for the sample households. As shown, the mean number of children per
couple is 2.1, which is close to the total fertility rate for Vietnam reported in 2008by the United Nations Population Fund (UNFPA) (2009a).
[INSERT TABLE 1 HERE]As shown in Table 2, we perform a mean comparison test of the hypothesisthat our selection differs from households having at least one child given
geographic distribution and income. We select the proportion of households living
in urban areas and the father’s wage in the last 12 months prior the survey as thecriteria for the comparison. The test results indicate that the differences are small.
[INSERT TABLE 2 HERE]
We recognize two problems with our sample selection. First, selecting only
households with an eldest co-residing child younger than 19 years could bias our
results. However, our interest lies in sex preferences during the economictransition period 1990–2008, during which time some demographic characteristicsof the population changed significantly. Second, some older children may haveleft the household more than a year before the sampling, which could result in
1

We define age as at the time of the survey. Households in Sample 1 were surveyed at two
different times: May/June 1989 and September 2008. Therefore, the actual childbirth cohort in thedata ranges from July 1989 to September 2008, which we refer to in this paper as the 1990–2008
birth cohort. The legal marriage age for women in Vietnam has been 18 years since 1987.
2
Children who are learning far away or still dependent on their parents are considered by the2008 VHLSS as household members and information about them is included.
5

error in defining the birth order3. Nevertheless, we preferred this option to theomission of some very important explanatory variables, such as sex composition
by birth order, household income adjusted by the square root of household size,and birth spacing in months. These records would be difficult to obtain from otherdemographic surveys.

4 Empirical models and specifications
In the parity progression to the second, third, and fourth childbirths, we examine
the sex–birth order composition of all previous children as a key independent
variable affecting the outcome of having a next child. We consider both theprobability of having additional children and the timing of fertility, that is, theprobability (hazard rate) of having a next child in any month after a given birthsequence.
We include several assumptions on sex preference in our analysis. To start
with, there are many possible measures aimed at prenatal and postnatal sex
selection, including sperm selection, abortion, infanticide, and neglect, often
appearing as an excessive mortality rate of the less preferred sex in early life (Das
Gupta 1987). However, we assert that having more children or shortening the
spacing of births are among the most common methods for a wide range of people
to obtain a child of the preferred sex. Thus, the interaction between an
independent variable and the less preferred sex is also an indicator of the level ofsex preference across that independent variable.
4.1 Empirical models
4.1.1 Standard hazard model for fertility timing

The study period is the time interval for parity progression. For each parity
progression, the period of study starts from the ninth month after the motherdelivered the preceding offspring. The study period ends either when the motherdelivers the next child or in 2008 if otherwise. In the standard model, if themother does not have a next child until the survey ends, she is included as acensored observation because she could have had more children after 2008.
Suppose that the time interval for having an additional child follows 𝐹(𝑡).
The survival function, indicating the probability that a woman does not have morechildren at time 𝑡, is then 𝑆(𝑡) = 1 − 𝐹(𝑡) = 𝑃(𝑇 > 𝑡). 𝑆(𝑡) = 1 at 𝑡 = 0.
The hazard function4, ℎ(𝑡), is the instantaneous rate of failure or the rateof having a next child in a small period of time. It is then the probability of having
a next child at a certain point in time:𝑃⁡(𝑡+∆𝑡>𝑇>𝑡|𝑇>𝑡)𝑓(𝑡)ℎ(𝑡) = lim∆t→0= 𝑆(𝑡).
(1)∆𝑡
The cumulative hazard function is𝑡𝑡 𝑓(𝑢)
𝐻(𝑡) = ∫0 ℎ(𝑢)𝑑𝑢 = ∫0 𝑆(𝑢) = −ln⁡(𝑆(𝑡)).

(2)

However, unlike the conventional literature on sex preference analysis, we do not
apply standard hazard models to our empirical work, but instead use a splitpopulation model.
We check the seriousness of this problem by testing the sex ratio of children aged 6 –18 to beequal to unity in the Appendix.
4
We simplify all functional forms without displaying covariates. For example, h(t) is usedinstead of h(t; ⁡X), where 𝑋 denotes independent variables.
36

4.1.2 Split-population model

The standard hazard model for fertility timing implies that all mothers that do not
progress to the next birth within the study period will eventually have anotherchild sometime after the study period ends. However, this assumption is
unrealistic in that some part of the censored data set will never have additionalchildren during their lifetime. The literature typically refers to these cases as‘cured’ or ‘immune’ (Maller and Zhou 1996) compared with ‘die’ or ‘failure’
events. In economics, models dealing with ‘immune’ cases are referred to as splitpopulation models. In addition, split-population models allow the independent
variables to influence both the probability of failure and the time of failure forthose that will ultimately arrive at a failure event (Schmidt and Witte 1989).
Lambert (2007) assumes that the survival function for all causes 𝑆(𝑡) is a
product of the expected survival function, 𝑆 ∗ (𝑡) , and the relative survival
function, 𝑅(𝑡):𝑆(𝑡) = 𝑆 ∗ (𝑡). 𝑅(𝑡).
(3)
The corresponding hazard function of all causes ℎ(𝑡) becomesℎ(𝑡) = ℎ∗ (𝑡) + 𝜆(𝑡)(4)where 𝜆(𝑡) is the excess hazard rate dealing with the event of interest. 𝜆(𝑡) has
an asymptote at zero.
There are two principal ways of estimating the ‘immune’ fraction. The first
approach is to obtain the expected survival rate, 𝑆 ∗ (𝑡), and/or the expected hazard
rate, ℎ∗ (𝑡), from national statistics as estimated from other data sources. However,
our empirical model could not proceed in this way because of difficulties in
obtaining such information in Vietnam, even data as simple as the expected
probability of having a next child at a given age for the mother. The alternative is
to fit the expected value using standard cure models (Lambert 2007). For thereasons given, we adopt the second approach.
The literature reports two types of model for the second measure, namely,
mixture and nonmixture cure models. The mixture cure fraction model assumes
that the relative survival rate is𝑅(𝑡) = π + (1 − π). S𝑏 (𝑡)(5)and𝑆(𝑡) = 𝑆 ∗ (𝑡). 𝑅(𝑡) = 𝑆 ∗ (𝑡). [π + (1 − π). S𝑏 (𝑡)](6)where 𝜋 is the fraction of women that will never have a next child (‘immune’)and S𝑏 (𝑡) is the survival function for those who eventually have another child(‘failure’). The corresponding excess hazard rate becomes(1−π).f (t)𝑏𝜆(𝑡) = π+(1−π).S
(𝑡)

(7)

𝑏

and

(1−π).f (t)𝑏ℎ(𝑡) = ℎ∗ (𝑡) + 𝜆(𝑡) = ℎ∗ (𝑡) + π+(1−π).S
.
(𝑡)

(8)

𝑏

In the nonmixture cure model, the relative survival rate is assumed to be𝑅(𝑡) = π𝐹𝑧 (𝑡) = exp(ln(π). 𝐹𝑧 (𝑡)) = π + (1 − π) (π𝐹𝑧 (𝑡) −π
1−π

)

(9)

and
π𝐹𝑧 (𝑡) −π𝑆(𝑡) = 𝑆 ∗ (𝑡). 𝑅(𝑡) = 𝑆 ∗ (𝑡). {π + (1 − π) (
)}
(10)
1−π
where 𝐹𝑧 (𝑡) is the cumulative distribution function of the progression to the next
birth. We select 𝐹𝑧 (𝑡) = 1 − 𝑆𝑧 (𝑡) and 𝑆𝑧 (𝑡) as the standard parametric survival
function. The excess hazard rate can then be expressed as
𝜆(𝑡) = − ln(π) . 𝑃𝑟𝑧 (𝑡)
(11)
and
7

ℎ(𝑡) = ℎ∗ (𝑡) + 𝜆(𝑡) = ℎ∗ (𝑡)− ln(π) . Pr𝑧 (𝑡)
(12)
(𝑡)
(𝑡).
where 𝑃𝑟𝑧is the probability distribution function for 𝐹𝑧
The general likelihood function for the two models for the ith household is𝑆(𝑡 )𝐿𝑖 = (ℎ(𝑡𝑖 ))𝑑𝑖 . 𝑆(𝑡 𝑖 )(13)0𝑖where 𝑑𝑖 is a censoring indicator, indicating 𝑑𝑖 = 0 if censored and 𝑑𝑖 = 1 if
not. For a sample of n households with sampling weights, 𝑤𝑡45,ℒ = ∏𝑛𝑖=1(𝐿𝑖 ∗ 𝑤𝑡45𝑖−1 ).
(14)Thus, the log-likelihood function can be expressed asln⁡(ℒ) = ∑𝑛𝑖=1[ln(𝐿𝑖 ) − ln(𝑤𝑡45𝑖 )].
(15)
Each ln⁡(𝐿𝑖 ) can be computed from𝑙𝑛(𝐿𝑖 ) = 𝑑𝑖 . ln(ℎ(𝑡𝑖 )) + ln⁡(𝑆(𝑡𝑖 )) − ln⁡(𝑆(𝑡0𝑖 )).
(16)
In our empirical model, in the ninth month after delivering a child in a given birthorder, all mothers enter the study time. Therefore, ln⁡(𝑆(𝑡0𝑖 ))=0 for all mothers.
In the mixture cure model, we replace (8) and (16) with (15) and have
(1−π𝑖 ).f𝑏 (t𝑖 )ln(ℒ) = ∑𝑛𝑖=1[𝑑𝑖 . ln {ℎ∗ (𝑡𝑖 ) + π +(1−π⁡} + ln⁡{𝑆 ∗ (𝑡𝑖 )} + ln{π𝑖 +).S (𝑡 )
𝑖

𝑖

𝑏

𝑖

(1 − π𝑖 ). S𝑏 (𝑡𝑖 )} − ln(𝑤𝑡45𝑖 )].
(17)
Similarly, in the nonmixture cure model, (15) becomesln(ℒ) = ∑𝑛𝑖=1[𝑑𝑖 . ln{ℎ∗ (𝑡𝑖 )− ln(π𝑖 ) . Pr𝑧 (𝑡𝑖 )} + ln⁡{𝑆 ∗ (𝑡𝑖 )} + 𝑙𝑛⁡(π𝑖 ) −ln(π𝑖 ). S𝑧 (𝑡𝑖 ) − ln(𝑤𝑡45𝑖 )].
(18)
4.2 Specifications

In general, we set f(π) = 𝑔(⁡𝑋𝑖 , 𝑊𝑖𝑗 , 𝛽, 𝛼). 𝑊𝑖𝑗 is a set of dummies indicating
the sex–birth order composition of all preceding children and 𝑋𝑖 are control
variables, including parental demographic characteristics, income, and economic
geography. We also add to 𝑋𝑖 the product of a dummy indicating ‘all children arefemale’ and the natural logarithm of household income adjusted by the square rootof household size. We include the product dummy in separate estimations.
More specifically, when 𝑗 = 1, 𝑊𝑖1 is 𝐺 when the first child is female
and the base is 𝐵 when the first child is male. When 𝑗 = 2, 𝑊𝑖2 includes 𝐺𝐺
when both the first and second children are female, 𝐺𝐵 (𝐵𝐺) when the first childis female (male) and the second child is male (female), and the base is 𝐵𝐵 whenboth the first and second children are male. The sex–birth order composition of
the children is similarly specified when 𝑗 = 3.
The control variables, 𝑋𝑖 , can be specified as follows.
𝑎𝑔𝑒𝑚𝑢𝑚1, 𝑎𝑔𝑒𝑚𝑢𝑚2, 𝑎𝑔𝑒𝑚𝑢𝑚3 which are corresponding maternalages (in years) at the time of the first, second, and third childbirths.
𝑊𝑤𝑜𝑟𝑘𝑖𝑛𝑔 is a dummy variable indicating a working mother. In the 2008
VHLSS, ‘working’ is defined as either working for a wage/salary or participatingin household production or services in planting, animal husbandry, forestry, or
aquaculture or undertaking business for the household. This variable could reduceinconsistent estimates in hazard models caused by unobservable heterogeneity(Nickell 1979, Heckman and Singer 1984, Honoré 1990).
𝐻𝑒𝑑𝑢 (𝑊𝑒𝑑𝑢) is schooling (in years) of the father (mother).
𝑙ℎℎ𝑖𝑛𝑐𝑜𝑚𝑒𝑝𝑐 is the logarithm of household income adjusted by thehousehold⁡income
square root of household size, where 𝑙ℎℎ𝑖𝑛𝑐𝑜𝑚𝑒𝑝𝑐 = log⁡(). We√household⁡size
appreciate that fertility and the family’s income level can be endogenous(Rosenzweig and Wolpin 2000). For instance, poor households may choose alarger family size because more children increase the probability for parents to be8

supported in their old age. Therefore, parents may rush to have additional children,
regardless of any son preference. The variable ⁡𝑙ℎℎ𝑖𝑛𝑐𝑜𝑚𝑒𝑝𝑐 could help tocontrol for this factor as household size includes all of the children of thehousehold head.
𝑢𝑟𝑏𝑎𝑛 is a dummy indicating the type of residential area.
𝑎𝑟𝑒𝑎1 − 𝑎𝑟𝑒𝑎8 are dummies indicating the eight economic regions in
Vietnam. We use these to control for differences in development, ethnicity, andculture.
𝐺𝑙ℎℎ𝑖𝑛𝑐𝑜𝑚𝑒𝑝𝑐, 𝐺𝐺𝑙ℎℎ𝑖𝑛𝑐𝑜𝑚𝑒𝑝𝑐, and 𝐺𝐺𝐺𝑙ℎℎ𝑖𝑛𝑐𝑜𝑚𝑒𝑝𝑐 are thecorresponding products of 𝐺, 𝐺𝐺, 𝐺𝐺𝐺 and 𝑙ℎℎ𝑖𝑛𝑐𝑜𝑚𝑒𝑝𝑐.
In the nonparametric analysis, we use only sex composition by birth order,
𝑊𝑖𝑗 , and the smoothed hazard estimates to compare the hazard difference in agiven parity progression. In the parametric models, we include the full set ofcontrol variables.
We assume the cure fraction function, 𝑓(𝜋), can take a variety of forms,
πincluding linear, π = 𝛽′𝑋 + 𝛼′𝑊, logistic, ln⁡(1−π) = 𝛽′𝑋 + 𝛼′𝑊, and log(-log),ln⁡(− ln(π)) = 𝛽′𝑋 + 𝛼′𝑊. For the empirical analysis, we employ the add-on
module for Stata provided by Lambert (2007). To our best knowledge, thismodule provides most combinations of the various assumptions5 concerning thecure fraction functions and the distributions of the parametric survival functions(including the Weibull, lognormal, and gamma distributions, a mixture of two
Weibull distributions, and a mixture of the Weibull and exponential distributions)in both the mixture and nonmixture split-population models.
4.3 Goodness of fit in the parametric models

We assess model fitness using the Akaike Information Criterion (AIC). In general,
𝐴𝐼𝐶 = 2𝑘 − 2ln(𝐿) where 𝑘 is the sum of the number of model covariates andthe number of model-specific distributional parameters, and 𝐿 is the maximized
value of the log-likelihood function from the estimated model (Akaike 1974). The
lowest AIC value indicates the most preferred model.
For each analysis of parity progression (to the second, third, and fourthchildbirths), we use the same control variables and sex–birth order composition
set and combine these with the cure fraction function and the parametric survival
function distributions supported by the module. We estimate the AIC for eachcombination to choose the best-fitted models.

5 Results
Among the several models estimated, the nonmixture split-population model witha combination of a gamma distribution for the parametric distribution and alogistic form for the cure fraction yields the lowest AIC for all parity
progressions6. The generalized gamma in use has an accelerated failure time
metric7. The interpretation of the coefficients for the logistic form of the cure5

STRSMIX/STRSNMIX command (Lambert 2007) supports linear, logistic, and log(-log) formsof the cure fraction. We apply this command with a standard cure model where the baseline hazard,ℎ∗ (𝑡𝑖 ), is fitted by creating a variable called rate comprising all zeros.
6
Other combinations with a higher AIC are not reported.
7
The parameter generalized gamma survivor function is
1 − I(γ, u)⁡if⁡κ > 0sign(κ).[log(t)−μ]S(t) = { 1 − Φ(z)⁡if⁡κ = 0 , where 𝜇𝑖 = 𝑋𝑖 𝛽, γ = |κ|−2 , z =, u = γ. 𝑒 |κ|𝑧 , Φ(z)𝜎
I(γ, u)⁡if⁡κ < 09πfraction is similar to that for the odds ratio in the logistic model, where eb = 1−πis the ratio of ‘cured’ observations to ‘uncured’ observations. If eb ≥ 1, themother has a lower probability of having a next child, while the reverse applies if
eb < 1. Thus, we also can apply the tips in Buis (2010, 2012) for interpreting theinteraction term. The use of these tips can avoid both misinterpretation of theinteraction terms (Ai and Norton 2003) and some of the complications associatedwith testing hypotheses (Greene 2010) in nonlinear models.
5.1 Preference for a son
5.1.1 Evidence of a son preference

Both the graphical display of smoothed hazard estimates and the split-population
model estimates of the probability of having one more child indicate that parents
have a son preference in the 1990–2008 birth cohort. As shown in Figures 1–3, thehazard curves for parents having only female children (𝐺, 𝐺𝐺, 𝐺𝐺𝐺) lie above allother curves of the remaining sex–birth order compositions for almost every
month after a given childbirth order. This indicates that women who have only
female children are more likely to have a next child than other women. Before
rising to the top sometime before the first 50 months, the 𝐺, 𝐺𝐺, and 𝐺𝐺𝐺
curves are steeper than the other curves, thereby indicating an accelerating desire
to have a next child during this stage.
[INSERT FIGURE 1 HERE][INSERT FIGURE 2 HERE][INSERT FIGURE 3 HERE]
Similarly, in all of the estimations, the coefficients for parents having only
female children are statistically significant, less than unity, and smallest among
the other coefficients for sex–birth order composition. Thus, mothers who have
only female children exhibit the greatest probability of having a next child in eachgiven childbirth order. For instance, in analysis (1) in Table 3, mothers having afemale first child, 𝐺, are 52 percent more likely to have a second child thanmothers having a male first child, 𝐵.
[INSERT TABLE 3 HERE][INSERT TABLE 4 HERE][INSERT TABLE 5 HERE]
5.1.2 Preference for one male offspring

The results also indicate that parents prefer to have precisely one male offspring
until the third birth order. As shown in analysis (1) in Table 4, the coefficients for
𝐺𝐵 and 𝐵𝐺 are statistically insignificant. The likelihood ratio test of whether themodel without 𝐺𝐵 and 𝐵𝐺 variables can be nested in model (1) supports theis the standard normal cumulative distribution function, and I(. ) is the incomplete gammafunction. κ and 𝜎 are ancillary parameters estimated from the data.
10

null hypothesis. Thus, mothers who have two male children display the sameprobability of having a third child as mothers with one male child (𝐺𝐵 and 𝐵𝐺).
We can still find evidence of this preference for one male offspring in the fourth
birth order with 𝐺𝐺𝐺 mothers 68.6 percent more likely than 𝐵𝐵𝐵 mothers tohave a fourth child (see analysis 1 in Table 5).
5.2 Mixed sex preference at parity progression to the fourth birth

In addition to the preference for a single male child, we observe a mixed sex
preference at the fourth birth order8. This evidence is consistent for both theparametric and nonparametric analyses. In Figure 3, the 𝐺𝐺𝐺 and BBB curves
are located above the other curves. The mixed sex preference can reflect a desire
to have children of both sexes, either with or without a balancing number. For
instance, the presence of either extreme of having the first three children of thesame sex, 𝐵𝐵𝐵 and 𝐺𝐺𝐺, makes it more likely that there will be a fourth child,to obtain a family comprising children of both sexes. One motivation for theremaining mothers may be the desire for a balanced number of the two sexes.
The differences in the sex–birth order compositions are also significant. As
shown in Table 5, we reject the likelihood ratio test of the null hypothesis (H0:model with only 𝐺𝐺𝐺 can be nested in the model with the full set of sex–birthorder composition). However, the underlying reasons for a different preference inthe sex–birth order composition are complicated and we possibly require further
qualitative study to provide some insight.
5.3 Household income and son preference

Our analyses indicate that high-income families tend to have fewer children. As
shown in Tables 3–5, a 1 percent increase in household income adjusted byhousehold size explains about a 35.3–51.9 percent decline in the probability of
having a next child. In particular, high-income families exhibit a lower level ofson preference at the second birth order. Nevertheless, the level of son preferenceshows no difference across household income for the remaining birth orders. As
indicated in analysis (2) in Tables 3–5, the interaction term 𝐺𝑙ℎℎ𝑖𝑛𝑐𝑜𝑚𝑒𝑝𝑐 isstatistically significant whereas 𝐺𝐺𝑙ℎℎ𝑖𝑛𝑐𝑜𝑚𝑒𝑝𝑐 and 𝐺𝐺𝐺𝑙ℎℎ𝑖𝑛𝑐𝑜𝑚𝑒𝑝𝑐 arenot. 𝐺𝑙ℎℎ𝑖𝑛𝑐𝑜𝑚𝑒𝑝𝑐 can explain about 49.4 percent of the decrease in theprobability of having a second child. If we combine this with the baseline value( 𝑐𝑜𝑛𝑠𝑡 ) of 0.000000152, the odds ratio changes from 0.000000152 to
0.000000075 (= 0.000000152  0.494) for a 1 percent increase in householdincome adjusted by the square root of household size. Note that both 𝐺 and𝑙ℎℎ𝑖𝑛𝑐𝑜𝑚𝑒𝑝𝑐 are statistically significant. Thus, the increment in income itself
provides a 27.7 percent reduction in the probability of having a second child aswell as lowering the level of son preference by 49.4 percent. This result concurs
with Gaudin (2011) and suggests that the level of son preference in Vietnam will
decline because of ongoing economic development.
5.4 Other influencing factors on birth spacing

Involvement in economic activities by women aged 15–49 years displays a weak
impact on the fertility timing decision. In our selected sample, 95.3 percent ofmothers are working mothers. As shown in Tables 3 and 4, working (𝑊𝑤𝑜𝑟𝑘𝑖𝑛𝑔)8

We acknowledge that it is difficult to distinguish between families having a son preference andothers having a mixed sex preference among 𝐺𝐺𝐺 families.
11does not have any significant influence on fertility timing at the second and third
birth orders. However, it does at the fourth childbirth. We also find that schoolingand the age of the mother have a greater influence on the fertility timing decision
than those for fathers. For example, an additional year in school by the motherreduces the probability of having a second, third, and fourth child by 7.8, 16.8,
and 14.0 percent, respectively. Similarly, a year older at the time of the previous
child delivery of the mother can explain for decreases the probability of a second,
third, and fourth child by 30.8, 17.8, and 14.0 percent, respectively. Consequently,
older mothers are less likely to engage in childbearing or shorten the birth spacing
if they want to have more children. These results are consistent with those in
Yamaguchi and Ferguson (1995), Gray et al. (2010), and Basu and De Jong (2010).
The age and education of the father exhibit smaller effects. For example, the ageof the father has no impact on the decision to have a second child but does explain
about 7.6 and 5.6 percent of the respective probability of having a third and fourthchild. In all likelihood, this is because men do not have the same strict age-related
bounds of biological fertility as women. Lastly, an additional year in school forthe father lowers the probability of having a second and third child by 4.8 and12.2 percent, respectively.

6 Discussion and conclusions
After constructing the full set of sex–birth order composition, this paper examinessex preference, birth spacing, and household income in Vietnam using a splitpopulation model. When we control for the number of children, the full set ofsex–birth order composition best specifies the order of sex in the sex composition.
At the same time, the split-population model helps both to overcome theunrealistic assumption that all mothers will proceed to have another child and to
fit the data better. The models deal with the probability of having a child eachmonth after a given preceding birth order in three separate parity progressions, up
to the second, third and fourth childbirths.
The results show a preference for a son until the third childbirth, while weobserve an additional preference, mixed sex, at the fourth childbirth. Involvementin economic activities by the mother has minimal impact on fertility timing until
the fourth childbirth. The income effect is consistent across the analysis andreduces the probability of having a next child. Higher-income families especiallydisplay a lower level of son preference at the second birth order, while there is nodifference in son preference across income levels for the remaining birth orders.
Sex-selective abortion in Vietnam is unlikely to affect our findings. In
evidence, UN World Abortion Policies (2007, 2011) reports that abortions for
women aged 15–44 years in Vietnam decreased from 35.2 per 1,000 females in2000 to 18.4 in 2007. In addition, the most common reasons given for abortion in
Vietnam include a decrease in the preferred family size, the reliance on a single
method of contraception (intrauterine device), the poor availability of alternative
methods of contraception, the low cost of abortion, and the increasing rate ofsexual activity among unmarried women (Goodkind 1994). Furthermore, there isno evidence that sex-selective abortion is widespread (Bélanger 2002a). Reportingfrom various data sources in Vietnam, UNFPA (2009b) finds that the absolutevalue of the sex ratio at birth (average number of newborn boys per 100 girls) has
been increasing to above 105 since 2000. The report hypothesizes that thisincrease could be due to sex-selective abortion as a result of the wider availabilityof sex-determination facilities. However, the report does not provide any evidence,12

such as the proportion of abortion cases for sex-selective reasons among all causes.
In addition, the report does not explain why the sex ratio at birth is below 105 in
2003.
To verify this issue in the selected sample of the 2008 VHLSS, we use aone-sample mean 𝑡-test to determine whether the sex ratio, R=B100/G, equals
105.5 for children under 6 years of age for each birth order. The test results
provide weak evidence of an abnormally skewed sex ratio (see the Appendix).
There are some cases where 𝑅 is above 105.5, such as when the first child isaged 3 and 5 years, the second child is aged 2, 3, or 4 years, the third child aged isaged 0 years, and the fourth child is aged 4 years. The variation by age and birthorder weakens the existence of an unusually skewed sex ratio in the selected
sample. If parents did pursue prenatal sex selection, the actual level of son
preference in Vietnam would be even higher than that indicated in our study.
Despite these previously discussed economic changes and improvements
in health indicators, the preference for having precisely one male offspringremains in Vietnam. Our result is consistent with that of Larsen et al. (1998), in
which South Korea exhibited a son preference despite a low fertility rate. Almost
certainly, when the total fertility rate falls to approximately two (UNFPA 2009a),
especially when the mortality rate in early life is also low (WHO 2011), parents
would not need to have more than one male offspring as a backup. It is also notnecessary to have two or more sons for the purposes of family lineage and old age
support. Moreover, the ‘price’ of having children is increasing alongside economic
development and urbanization. Therefore, it would be reasonable to have apreference for precisely one male child for both economic and cultural reasons.
In contrast, the high participation rate of Vietnamese mothers in economic
activities has a minimal impact on fertility timing until the third childbirth. This
lies contrary to our usual expectations. This is likely because, up to 2008, therelative cost of having more children to being absent from the workplace issufficiently low until the third childbirth. However, we expect this factor tocontribute more to making family size smaller when the ‘price’ of a child and/or
nonfarm work transition accelerates in the future.
Finally, our findings concerning a decline in the level of son preference forhigh-income families suggest that past economic reasons for a son preference,such as the need for laborers for farming activities and support in old age, may belosing substance with the ongoing economic development in Vietnam. In contrast,
cultural reasons for son preference, such as the lineage of the family name andancestor worship, remain despite these economic changes.
Acknowledgments The authors acknowledge the useful suggestions of Hisakazu Matsushige,
Tsunehiro Ootsuki, and Charles Yuji Horioka of Osaka University, and participants at the Labor
Economics Conference held in Awajishima, Japan, September 4–6, 2011 and the Fall Meeting of
the Japanese Economic Association held at Tsukuba University, Japan, October 29–30, 2011. The
authors would especially like to thank Shoshana Grossbard and two anonymous referees forvaluable comments and suggestions made during the reviewing process. All remaining errors are
ours.

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15Appendix: Sex ratio by age and birth orderFirst birth orderOne-sample t-test
Total
R1=G/(B+G) Pr(T < t)Conclusion
R=B100/G
123
123.640.447
0.191
Accept H0
202
104.040.490
0.539
Accept H0252
104.880.488
0.519
Accept H0
310
123.02
0.448
0.089
Reject H0343
106.630.484
0.461
Accept H0438
122.340.450
0.061
Reject H012,738109.130.478
0.000
Reject H014,406
109.690.477
0.000
Reject H0
Second birth order
0402
114.970.465
0.195
Accept H01
437
107.11
0.483
0.437
Accept H02
482
131.73
0.432
0.008
Reject H03
518
118.57
0.458
0.092
Reject H04
641
118.77
0.457
0.067
Reject H0
5
663
97.32
0.507
0.850
Accept H0
6–18
8,421
104.54
0.489
0.021
Reject H0
Total
11,564106.91
0.483
0.000
Reject H0
Third birth order
0205130.340.434
0.066
Reject H01
203125.560.443
0.109
Accept H02
221114.560.466
0.271
Accept H0
3
247
96.03
0.510
0.769
Accept H0
4
253
96.12
0.510
0.770
Accept H05
237
117.430.460
0.206
Accept H0
6–18
2,195
102.120.495
0.312
Accept H0
Total
3,561
105.6
0.486
0.052
Reject H0
Fourth birth order
056
115.380.464
0.371
Accept H01
77113.890.468
0.370
Accept H02
72111.760.472
0.404
Accept H0
3
83
97.62
0.506
0.637
Accept H04
76145.16
0.408
0.085
Reject H05
66106.250.485
0.489
Accept H0
6–18
464
95.78
0.511
0.679
Accept H0
Total
894
104.11
0.490
0.274
Accept H0
Notes: H0: R1 = 0.4867 (R = 105.5), Ha: mean < 0.4867 if age < 6 years. H0: R1 = 0.5 (R = 100),
Ha: mean < 0.5 if age > 5 years.
Age
0
1
2
3
4
5
6–18
Total

16

0

.005

.01

.015

.02

Figure 1 Smoothed hazard estimates for parity progression to the second birth

0

50

100
Analysis time (in months)
G

150

200

B

17

0

.002

.004

.006

.008

.01

Figure 2 Smoothed hazard estimates for parity progression to the third birth

0

50

100
Analysis time (in months)
GG
BG

150

200

GB
BB

18

0

.002

.004

.006

.008

.01

Figure 3 Smoothed hazard estimates for parity progression to the fourth birth

0

50

100
Analysis time (in months)
GGG
GBG
BBG
GBB

150

GGB
BGG
BGB
BBB

19

Table 1 Descriptive statistics
Variables
Descriptions
nchildNumber of children of the household head
G
B
GG
GB
BG
BB
GGG
BBG
BGG
BGB
GGB
GBG
GBB
BBB
Wage
Age of the mother (in years)
agemum1
Maternal age at first childbirth
agemum2
Maternal age at second childbirth
agemum3
Maternal age at third childbirth
Wedu
Years of schooling for the mother
Wworking
Mother involved in economic activities(yes/no)Hage
Age of the father (in years)
Hedu
Years of schooling for the father
lhhincomepc
Logarithm of annual household income percapita adjusted by square root of household
size
urban
Residing in urban area (yes/no)
area1
Red River Delta (yes/no)
area2
North East (yes/no)
area3
North West (yes/no)
area4
North Central Coast (yes/no)area5South Central Coast (yes/no)
area6
Central Highlands (yes/no)
area7
Southeast (yes/no)
area8
Mekong River Delta (yes/no)Obs.
14,406
14,406
14,406
14,406
14,406
14,406
14,406
14,406
14,406
14,406
14,406
14,406
14,406
14,406
14,406
14,406
14,406
11,5643,561
14,406
14,406

Mean
2.133
0.477
0.523
0.191
0.204
0.197
0.211
0.045
0.026
0.025
0.026
0.049
0.024
0.026
0.026
35.56523.36626.82229.4327.630
0.953

Std. Dev.
0.857
0.499
0.499
0.393
0.403
0.398
0.408
0.207
0.160
0.157
0.158
0.217
0.153
0.159
0.159
5.959
4.164
4.438
4.301
3.926
0.212

14,406
14,406
14,40638.475
8.186
9.745

6.289
3.896
0.711

14,406
14,406
14,406
14,406
14,406
14,406
14,406
14,406
14,406

0.231
0.194
0.175
0.066
0.103
0.089
0.074
0.122
0.178

0.421
0.395
0.380
0.247
0.304
0.284
0.262
0.327
0.382

20

Table 2 Two-group mean comparison test
Criteria
Selected sample (1)Urban
Father’s wage

Obs.
14,4065,530

Mean0.230820,814

Nonselected sample
(2)
Obs.
Mean
11,2850.2343
2,961
20,871

H0: diff = 0
diff = mean(2) – mean(1)Pr(|T| > |t|) Conclusion
0.5114
Accepted H00.8855
Accepted H021

Table 3 Split-population model for parity progression timing of the second birth
(1)
(2)
_t
exp(b)
Std. Err.
exp(b)
pi
G
0.480***
0.048
0.009***
agemum1
1.308***
0.030
1.309***
Wedu
1.078***
0.017
1.079***
Wworking
0.990
0.176
0.994
Hage
0.993
0.008
0.993
Hedu
1.048***
0.016
1.049***
lhhincomepc
1.519***
0.122
1.277***
urban
1.634***
0.177
1.631***
area2
1.204
0.170
1.211
area3
0.843
0.186
0.833
area4
0.293***
0.065
0.291***
area5
0.601***
0.110
0.601***
area6
0.195***
0.053
0.196***
area7
1.215
0.183
1.218
area8
5.215***
0.890
5.240***
Glhhincomepc
1.494***
const
0.000***
0.000
0.000***
ln_sigma
0.234***
0.057
0.237***
kappa–1.764***0.184–1.771***mu
4.366***
0.040
4.370***
Number of obs.
14,406
14,406Log likelihood–57,674.4–57,667.793
AIC
115,386.7
115,375.6

Std. Err.
0.010
0.030
0.017
0.177
0.009
0.016
0.115
0.178
0.171
0.185
0.064
0.110
0.053
0.184
0.901
0.172
0.000
0.057
0.185
0.041

Robust standard errors in parentheses (*** p < 0.01, ** p < 0.05, * p < 0.1).

22

Table 4 Split-population model for parity progression timing of the third birth
(1)
(2)
_t
exp(b)
Std. Err.
exp(b)pi
GG
0.151***
0.020
0.100**
GB
1.036
0.089
1.036
BG
0.907
0.079
0.907
agemum2
1.178***
0.013
1.178***
Wedu
1.168***
0.017
1.169***
Wworking
1.199
0.206
1.200
Hage
0.924***
0.007
0.924***
Hedu
1.122***
0.014
1.122***
lhhincomepc
1.353***
0.076
1.341***
urban
1.614***
0.149
1.614***
area2
1.640***
0.175
1.641***
area3
1.145
0.171
1.143
area4
0.279***
0.036
0.278***
area5
0.459***
0.059
0.458***
area6
0.210***
0.033
0.208***
area7
0.481***
0.063
0.480***
area8
1.590***
0.179
1.589***
GGlhhincomepc
1.043
const
0.002***
0.002
0.002***
ln_sigma
0.097
0.060
0.101*
kappa–2.195*** 0.248–2.212***mu
4.002***
0.039
4.003
Number of obs.
11,564
11,564Log likelihood–21,427.2–21,427.1
AIC
42,896.3
42,898.1
Likelihood ratio test
LR chi2(2) Prob>chi2(H0: model without 𝐺𝐵 and 𝐵𝐺 can= 2.54= 0.281
be nested in the original model)

Std. Err.
0.110
0.090
0.079
0.014
0.017
0.206
0.007
0.015
0.082
0.150
0.176
0.171
0.036
0.059
0.033
0.063
0.180
0.114
0.002
0.061
0.254
0.040

Robust standard errors in parentheses (*** p < 0.01, ** p < 0.05, * p < 0.1).

23

Table 5 Split-population model for parity progression timing of the fourth birth
(1)
(2)
_t
exp(b)
Std. Err.
exp(b)pi
GGG
0.314***
0.062
0.586
BBG
1.435*
0.302
1.434*
BGG
0.693*
0.143
0.694*
BGB
1.761***
0.380
1.760***
GGB
1.619**
0.306
1.618**
GBG
1.217
0.256
1.217
GBB
2.064***
0.453
2.062***
agemum3
1.140***
0.017
1.140***
Wedu
1.153***
0.024
1.152***
Wworking
1.672*
0.502
1.673*
Hage
0.944***
0.011
0.944***
Hedu
1.030
0.019
1.030
lhhincomepc
1.367***
0.122
1.387***
urban
1.512**
0.275
0.937**
area2
1.631**
0.329
1.510**
area3
0.983
0.230
1.625
area4
0.529***
0.095
0.981***
area5
0.833
0.174
0.529
area6
0.574***
0.114
0.831***
area7
0.764
0.161
0.573
area8
2.174***
0.477
0.762***
GGGlhhincomepc
2.173
const
0.004***
0.004
0.003***
ln_sigma–0.228*** 0.088–0.231***kappa–1.577*** 0.364–1.566***mu
3.711***
0.050
3.711***
Number of obs.
3,561
3,561
Log likelihood–5,440.1–5,440.1
AIC
10,930.3
10,932.1
Likelihood ratio test
LR chi2(6) Prob>chi2(H0: model with only 𝐺𝐺𝐺 and other= 38.05= 0.000
control variables can be nested in theoriginal model)

Std. Err.
1.016
0.302
0.143
0.379
0.306
0.256
0.452
0.017
0.024
0.501
0.011
0.019
0.136
0.169
0.275
0.328
0.229
0.094
0.174
0.114
0.160
0.477
0.004
0.087
0.361
0.050

Robust standard errors are in parentheses (*** p < 0.01, ** p < 0.05, * p < 0.1).

24