One Child Policy and the Rise of Man-Made Twins*
Wei Huang,† Xiaoyan Lei‡ and Yaohui Zhao§
Abstract
This study examines birth behavior response towards one child policy by investigating the
relationship between one child policy and twining birth in China. Exploring data from population
censuses shows that one child policy accounts for over one third of the twins increasing since the
1970s. Further investigation finds that birth space between first and second deliveries is 0.08
year longer if the second birth is twins after one-child policy, and that one child policy increases
height difference within twins, for both same and different gender pairs, suggesting that parents
may report non-twining children as twins under one-child policy.
JEL Codes: J08, J11, J13
Keywords: Twins, One-Child Policy, China
*
We thank Gary Becker, David Cutler, Avraham Ebenstein, Richard B. Freeman, Edward
Glaeser, Claudia Goldin, James Heckman, Lawrence Katz, John Strauss, T. Paul Schultz, Fei
Wang and David Wise for their helpful suggestions. We also thank the discussants at PAA
conference, China Meeting of Econometric Society, CGEB/LAEF Conference on Economics and
Demography for their comments. All errors are ours.
†
Email: [email protected]. Department of Economics, Harvard University.
‡
Email: [email protected]. China Center for Economic Research, Peking University.
§
Email:
[email protected]. China Center for Economic Research, Peking University. “One is too few,” said a woman (in China) waiting at the hospital, “People want to have a
second child.” - By Elizabeth Grether, ABC News, Aug. 3rd, 2011
I. Introduction
Since Rosenzweig and Wolpin (1980a, 1980b), there has been an established strand of literatures
in economics using twins as tools to help to understand the economic phenomena and to derive
unbiased estimates with causal interpretation by ruling out confounding factors (Ashenfelter and
Krueger, 1994; Ashenfelter and Rouse, 1998; Rosenzweig, 2000; Behrman and Rosenzweig,
2002; Black et al., 2007; Royer, 2009; Angirst and Evans, 1998; Angirst et al., 2010; Ponczek
and Souza, 2012). The methodologies are further developed and followed by the studies in other
countries under different contexts. For example, there is a growing interest in current literatures
using twins data in China, like Chew et al. (2010), Zhang et al. (2007), Li et al. (2007, 2008,
2012, 2013) and Rosenzweig and Zhang (2012). These studies more or less presume that twins
are born randomly and unexpected before pregnancy across the population conditional on some
biological factors. In studies of demographics and medicine, the factors potentially influencing
twining births studied are restricted to observed demographic or medical variables, like fertility
drug using and mother’s age when giving birth. However, no previous study examined whether
the twining births are influenced by public fertility policies so far. The importance of the
question is emphasized by not only that it provides context and background to understand the
external validity for the twins studies in the relevant countries, but also that it helps to understand
individual behavior response towards the public policies.
1 China provides unique chance to answer the question. In the 1970s, after two decades of
explicitly encouraging population growth, policy makers in China enacted a series of measures to
curb population growth, especially to the Han ethnicity. In 1979, the one child policy was
formally conceived and firmly established across the country in 1980 (Croll et. al., 1985;
Banister, 1987). Meanwhile, the twin births in China have increased dramatically in the past few
decades, as Figure 1 shows. Twin births as reported in population censuses more than doubled
between the late 1960s and the early 2000s, from 3.5 to 7.5 per thousand births. Especially, after
the one-child policy in 1979, the increasing pace of the twins rate becomes faster. But China is
not unique in seeing rising twin births, in the U.S., for example, twinning rate increases from
18.9 to 33.3 per thousand births from 1980 through 2009 (Martin et al., 2012). Therefore, it is a
question that whether and to what extent that one child policy contributes to the twins birth
increase.
[Figure 1 about here]
If we find that one child policy is associated with the twining births increase in China, it is
important to understand the mechanism that how one child policy becomes a policy contributor
besides demographic factors. As the policy name suggests, one couple is allowed to have one
child, but twins are an exemption.1 If a mother delivers an illegal birth, the household may face
punishments from the government, like regulatory policy fines. Therefore, such a policy provides
1
It is “one and a half children policy” in many rural areas. That is, the parents are allowed to
give another birth if the first is a girl.
2 strong incentive for the parents to make twins by themselves if they want to have more children
without receiving punishment. How do they make them? There are two ways. The first one is to
take drugs. As ABC news reported, married women intentionally take fertility drugs to give birth
to twins.2 The mechanisms of these drugs are to induce ovulation, which are usually used to
treat infertility. Due to less restricted administration, it is available to purchase these drugs in
on-line medicine shops and private hospitals. The other way is to report fake twins, i.e. the
couples register non-twin children as twins.3 For example, they may give birth to a child first
without reporting to registration office, give another delivery and then report it together with the
first one as twins. An administrative department in Yunnan province found and identified 700
pairs of fake twins in 342 villages in 2000. More surprisingly, among 23 pairs of twins reported
born in 1999, 18 were identified as fake twins. Intuitively, both of the two twins-making methods
potentially lead to social wellbeing loss. On one hand, twin births have been known to be
associated with high maternal risks and low birth weights, which in turn is negatively associated
with later health and socio-economic outcomes. If, on the other hand, the twins are fake, then the
older child’s schooling will be delayed because the school entry age is determined according to
one’s registration, and the girls in such families, if any, are likely to receive unequal treatments
2
http://abcnews.go.com/Health/chinese-women-fertility-drugs-bypass-child-policy/story?id=142
19173 , accessed March 10th, 2013.
3
An example (in Chinese): http://www.wuhan.jcy.gov.cn/yasf/200905/t20090519_221490.html ,
accessed March 10, 2013
3 from parents.
This paper investigates the impact of one-child policy on twining births in China. We
explore the temporal and geographical variation in one child policy fine rates to investigate the
impact of one child policy on reported twin births in census data. We also use the start of the
one-child policy in 1979 and Han-ethnic minority difference to conduct a parallel analysis to
provide additional evidence. Both approaches yield a large impact of the one-child policy on
rising twinning rate in China. Specifically, the estimates suggest that one-child policy accounts
for at least one third of the twins increasing since 1970s. Further investigation indicates that
policy-associated twins are more likely to be born in rural areas and in the second birth order.
This study also investigates the mechanisms by which people make twins. Because the
impact thus identified may come from either real twining from fertility drugs or fake twins from
reporting non-twin siblings as twins, identifying either or both of the mechanisms will further
support the impact of one child policy on twins birth. In addition, distinguishing between the two
hypotheses would be helpful because welfare implications and policy suggestions are different in
the two cases. We then investigate the relationship between birth space and twining births. For
one thing, if parents want to make a pair of fake twins, they may give birth to a child first
without reporting to registration office, give another delivery and then report it together with the
first one as twins. For another, parents from two households may plan together to bear, and then
report the children together as twins in one certain household. Both of them could plan again to
give another delivery so that the other household will also have a pair of twins. However, the
birth date of the reported twins would be determined by the younger one because the parents
4 have to wait until both two kids have been born. There are also many other ways for the parents
to construct fake twins, but the time needed should be not shorter than a normal delivery.
Therefore, if the fake twins reporting happens in the second birth order, then the birth space
between first and reported second delivery will be longer if the second birth is twins. Different
from fake twins, the birth space may not change if the parents take fertility drugs to have twins
because it is also a natural delivery. Using a difference-in-difference identification strategy to
control for other confounding factors, we find that the birth space between first birth and second
twining delivery is 0.08 years longer relative to a singleton delivery after one child policy. This
finding is consistent with fake twins hypothesis as discussed above.
We further examine the height differences within twins identified from the China Health and
Nutrition Survey (CHNS) to shed light on the issue. The identification is based on the following
facts: 1) fertility drug use only results in more dizygotic twins; 2) same sex dizygotic twins are
more different than monozygotic twins; and 3) fake twins are different regardless of sex
composition. If one child policy is not relevant to twins birth, the height difference within twins
should be uncorrelated with one child policy. If one-child policy leads to more fertility drug use
rather than reporting fake twins, then we are likely to see greater difference only among
same-sex twins under one child policy. If there are reporting fake twins, greater difference is
expected among both same-sex and different-sex twins. The empirical analysis shows that one
child policy fines rate increase the height difference within twins of both same gender and
different gender, indicating that one child policy stimulate incentive of parents to report
non-twining children as twins in order to have more children with no or less punishment. It is
5 noteworthy there that these results also provide empirical support to studies using twins data in
China, like Zhang et al. (2007), Li et al. (2008, 2012) and Rosenzweig and Zhang (2012). Since
the data used in these studies carefully examined the observed characteristics of the twins, like
hair color and appearance, our results indicate that fake twins are ruled out in these studies.
The structure of the paper is as follows. Section 2 introduces the data used in this study and
provides background for the one-child policy. Section 3 shows the empirical results. Section 5
concludes with a discussion of findings and the policy implications.
II. Data
2.1 Census Data and Twins in China
The data used in this study include a 1% sample of the 1982, 1990, 2000 Population Census,
and 2005 Population Study sample. All the data sets contain variables including birth year,
region of residence, type of residence,4 sex, ethnicity, education, and relation to the head of the
household. The datasets after 1982 also include month of birth. For women older than 15, the
4
The 1990 Census does not provide the type of current residence. Instead, it provides whether
the respondents lived in the same place 5 years ago and what the type of residence was then.
Therefore, we constructed a variable to indicator the type of current residence. First, we keep
those who were in the same place. Then, we calculate the proportion of people in this sample for
each residence type 5 years ago. We use the residence type with highest proportion as the type of
current residence in the same area.
6 data provide information about their fertility history, including number of children ever born and
number of children alive.
For analysis of twin births and family background, we first keep only those households with
at least one child and with mother's information available. We then restrict the sample to those
households with equal numbers of reported children alive, children born, and children observed
in the survey to make sure that all the children are born by the mother observed in the household
and that the sample covers the information needed for the children in the family. In case we miss
children who have moved out of the household, we further drop households with children over
age 17 in the survey. We finally drop households where the mother's age when giving birth is
either younger than 15 or older than 50, as this sample may be too special or may just be due to
recording errors.5
We use samples of the children after the above restrictions, and twins are defined as children
in the same household with the same birth year and birth month.6 The observations are in the
birth level, so twins in the same birth are treated as a single observation. For each birth, we also
construct several variables including whether this birth is a twin, and if so whether this twin birth
5
We also drop Tibet data.
6
Because 1982 Census data do not have information on birth month, we just define twins in that
year as those children born in the same household with the same birth year only. Actually, the
results are almost the same if we drop the 1982 Census or define twins only using the year of
birth in all data sets.
7 is male, female, or different gender. Figure 1 plots the rate of twins by year of birth between
1965 and 2005. We can see that the variation before 1970 and after 1990 is larger because of
smaller sample size. Sampling weights are applied throughout the analysis.
2.2 One Child Policy
In the 1970s, after two decades of explicitly encouraging population growth, policy makers
in China enacted a series of measures to curb population growth, especially to the Han ethnicity.
The one child policy was formally conceived in 1979, but actual implementation had started in
some regions in 1978, and enforcement gradually tightened until it was firmly established across
the country in 1980 (Croll et. al., 1985; Banister, 1987; Qian, 2009)
The one-child policy, as the name suggests, restricted a couple to having only one child. The
strictness of the one-child policy was partly reflected in its enforcement. In 1978, FPP appeared
in the Constitution for the first time, and came up with more details in the 1982 amended
Constitution (Wang, 2012). Legal measures, such as monetary penalties and subsidies, also
ensured the effective enforcement of the one-child policy since 1979. Due to various
development levels in different regions in China, the Central Party Committee “Document 7”
devolved responsibility from central government to the local and provincial governments so that
local conditions could be better addressed. It actually allowed for regional variation in family
planning policies, like the amounts for monetary penalties or subsidies (Greenlaugh, 1986, 1992).
As the population was still growing rapidly in the 1980s, Chinese policymakers felt more
compelled to limit fertility, and emphasized the importance of this policy in several different
8 documents. Afterwards, local governments tightened enforcement by reducing land allotments,
denying public services, increasing unauthorized births, and so on.
However, it is worthwhile to note that the one child policy mainly focused on the Han
ethnicity, the largest ethnicity in China with over 90 percent of population. Although local
governments might enact different regulations for a local minority of people, these regulations
were less restrictive compared to those for Han. For example, regulations in Gansu province
allow minority parents a second birth, which is not allowed for those of Han ethnicity.7
The measure of the one child policy in this study is the average monetary penalty rate for
one unauthorized birth in the province-year panel from 1979 to 2000, which are from Ebenstein
(2008).8 The one child policy regulatory fine (policy fine) is formulated in multiples of annual
income (Ebenstein, 2008; Wei, 2010). Although the monetary penalty is only one aspect of the
policy and the government may take other administrative actions meanwhile, it is still a good
quantitative measure because an increase in fines is usually associated with other stricter policies.
Figure 2 shows the pattern of policy fines from 1980-2000 in each province.
[Figure 2 about here]
It is obvious that fines and bonuses in different provinces generally have different patterns,
both in timing and in magnitude. Liaoning Province has increased it from one year’s income to
five in 1992, while Guizhou Province raised it from two years’ income to five in 1998, and
7
http://www.mjrkj.gov.cn/html/gs-law/17_31_12_360.html
8
The details about the construction of this variable can be found in Ebenstein (2008),
9 Hunan increased it from one to two in 1989. The average level of the fine is higher in the 1990s
than in the 1980s, which is consistent with stricter policy enforcement in the 1990s. The
geographical and temporal variation helps us identify the effects of the one-child policy on
twining in empirical analysis.
Since approximately nine months are needed from the beginning of pregnancy until the birth
of the baby, the parents’ decision to have a baby, if any, should be made close to a year in
advance. For each birth, we construct an effective policy fine, which is the weighted mean value
of fine rate in the 12 months just before the pregnancy in the province. If a child was born in
Jiangxi Province in September in 1986, the mother is expected to start pregnancy in December,
1985. The effective policy fine is then equal to the weighted mean value of fine rate in Jiangxi
Province between December in 1984 and December in 1985, which equals to 0.083𝐹𝑖𝑛𝑒 !"#$ +
0.917𝐹𝑖𝑛𝑒 !"#$ . However, because 1982 census does not cover birth month information, we use
the simply assume the children surveyed in 1982 were born in June, the middle of the year, and
conduct the same procedure as above. It should be emphasized here that one child policy started
in 1979 so over 92 percent of the children surveyed in 1982 are born before one child policy, so
the effect fine rate is zero for them. It is noteworthy that the estimates do not reply on the one
child policy measure we constructed here. The results are consistent if we use the fine rate in the
local province one year before the child was born. Since the fine rate data covers from start of
one child policy till year 2000, we drop the children born after 2001. By doing the above
procedures, we presumably assume that the children observed are born in the current place they
are living. However, only the data surveyed collected after 1990 contain the information about
10 place of birth, but some evidence is still found to support this presumption. For example, the
proportion of the children living in the same province where they were born is 96.5 percent in the
2000 census sample, implying that the migration should not be first order issue in the analysis in
this study.
Table 1 presents the summary statistics. Column 1 shows that the reported twins rate in the
full sample is 5.8 per thousand among almost 6 million observations. We then divide the sample
by the parents' ethnicity: both of the parents are Han ethnicity and either of them belongs to
minority. For simplicity, the Han ethnicity means both of the parents being Han in this paper,
afterwards. Twins birth rate for the Han ethnicity is 5.9, higher than 4.4, that in the minority
sample. The mean age of the sample is around 8 years old and mother’s age while giving birth is
around 23, and there is only a minor difference between Han and Minority. In addition, over half
of the births are first deliveries. The proportion of second or above births in minority groups is
higher because one child policy mainly restricted the fertility of the Han people.
[Table 1 about here]
Table 2 simply compares twin birth rates before and after the one child policy, by parents’
ethnicity. For the Han ethnicity sample, twin birthrates increased from 0.39 to 0.67 by 0.28
percentage points. However, the twin birthrate increased by only 0.08 percentage points in the
minority group, which is less than one third of that in Han ethnicity. Although the twins birthrate
may be influenced by other factors like mother’s age while giving birth, this simple comparison
indicates the one child policy potentially accounts for a large proportion of the twin rate increase.
[Table 2 about here]
11 III. Empirical Results
3.1 One child policy and twining births
To estimate the effect of the one child policy on the twin birthrate, we estimate an equation
as below:
1 𝑇𝑤𝑖𝑛𝑠! = 𝛽! + 𝛽𝐹𝑖𝑛𝑒!"# + 𝜃𝑋! + 𝛿!" + 𝛿! + T! + 𝜀! where the dependent variable, 𝑇𝑤𝑖𝑛𝑠! , denotes whether birth i born in year y and province j
is twinning in province j and wave k. 𝐹𝑖𝑛𝑒!"# is the effective one child policy fines rate defined
above in province j for the children born in year y and month m. The main coefficient of interest,
𝛽,
gives the association of one child policy fines with reported twins birth rate, and is
interpreted as the impact of the one child policy. 𝑋! is a set of covariates, including dummies for
residence type (urban/rural), parents' ethnicity (both Han/either a minority), birth order, birth
month, mother's education level, and mother's age when giving birth. 𝛿!" is the set of dummies
for year of birth, year of survey and their interactions. The interactions capture the age effects
because the parents may not report the children when they are very young. 𝛿! and 𝑇! denote the
province dummies and provincial specific birth year linear trend.
Columns 1 to 3 in Table 3 report the OLS estimates for 𝛽 in equation (1) and provincial
clustered standard errors. Column 1 reports results for full samples, and Columns 2 and 3 report
those for Han ethnicity and minority samples, respectively. All coefficients are interpreted as
percentage points since the dependent variable has been multiplied by 100 to avoid too many
zeros in the coefficients. The results indicate that a one year’s income increase in the policy fine
12 is associated with over 0.067 percentage point increase in the twin birthrate in the whole
population. Consistent with expectation, the association and significance survives in Han
ethnicity and diminishes in minority group. Given that the effective fine rate increased from 0
before one child policy to 1.4, the mean value for those born after one child policy, estimate in
column 2 suggests that over 36 percent of the twins increase in Han ethnicity is contributed by
one child policy.
[Table 3 about here]
Based on the above results, we further interact policy fine with Han ethnicity and conduct the
following equation: 2 𝑇𝑤𝑖𝑛𝑠! = 𝛽! + 𝛽! 𝐹𝑖𝑛𝑒!"# ×𝐻𝑎𝑛! + 𝛽! 𝐹𝑖𝑛𝑒!"# + 𝜃𝑋! + 𝛿!" + 𝛿! + T! + 𝜀! where 𝐻𝑎𝑛! denotes whether both parents of birth i belong to Han ethnicity and all the
other variables have the same definition as Equation (1). This equation actually conducts a
further difference between Han and Minority and 𝛽! can be interpreted as impact of one child
policy on twins birth. Column 4 in Table 3 reports the estimates and provincial clustered
standard errors. Although the magnitude is a bit smaller than that in column 2, the difference is
insignificant. It also suggests that one child policy plays a very important role in twining births
increase in China.
However, Li et al. (2011) and Li and Zhang (2008) argued that the spatial and temporal
variations of the one-child policy may be endogenous, because they found that the level of the
fine increases with the community wealth level and the local government’s birth-control
incentives, but decreases with the local government’s revenue incentives. In particular, the
13 spatial and temporal variations in the one-child policy have been documented as being affected
by the fertility rate, which, in turn, may be correlated with twin incidence. So we test the
endogeneity of policy fines by using prior twin birthrates to predict future policy fines. If the
association is significant, then the endogeneity problem is worthy of concern. More specifically,
we use twins as independent variables, and take the policy fine of the next year, three or five
years later as dependent variables. Because the policy fine is assumed to be zero before 1979 and
we do not want this assumption to drive the results, we restrict the sample to those born after
1979, run the same regressions, and report the results in Table 4. The results suggest that twins
rate does not have predictive power the one policy fine over the next one, three or five years
conditional on the covariates in Equation (1), indicating that the endogeneity problem of policy
fines due to reverse causality may not be serious in this study.
[Table 4 about here]
Although there is no evidence that policy fine rates are endogenous due to reverse causality
in this study, we can still conduct another set of regression(s) to without using policy fine rates to
establish the relationship between one child policy and twining birth. Following Li et al. (2011),
we estimate:
3 𝑇𝑤𝑖𝑛𝑠! = 𝛽! + 𝛽! (𝑃𝑜𝑙𝑖𝑐𝑦!!!"#$ ×𝐻𝑎𝑛! ) + 𝜃𝑋! + 𝛿!" + 𝛿! + T! + 𝜀!
in which 𝑃𝑜𝑙𝑖𝑐𝑦!!!"#$ denotes an indicator of whether the birth i is born after 1980, and
𝐻𝑎𝑛! is an indicator for Han ethnicity. The sample used here is the same as the one used to
estimate equations (1) and (2). The OLS point estimate for 𝛽! is reported in the final column in
Table 3, which also provide strong evidence for the positive association of the one child policy
14 with twin incidence. This Difference-in-differences estimate indicates that the one child policy
explains over 58 percent of the twins increase, indicating our estimates in Table 3 may
underestimate the impact of the one child policy. This may be reasonable since the policy fine is
only one dimension for the regulations, which may miss many other useful variations.
It is worthy to note that the Difference-in-Differences (DID) estimations in equations (2) and
(3), require the trends in the treated group (Han ethnicity) and control group (Minority group) to
be similar. Figure 3 plots the twin birthrate by the parents' ethnicity group against year of birth.
The dashed lines plot lowess-smoothed trends with bandwidth 0.8. The figure shows that the
trends in the two groups are almost identical prior to the one child policy, marked by the vertical
dashed line.9 Although we derived robust results in the DID model of Equation (5), the minority
group may not be a perfect control group because they are also under the control of the one child
policy. The twins rate of the minority is possibly more or less influenced by the regulations. This
is why we use temporal and geographical variations in fines to estimate the effect.
[Figure 3 about here]
3.2 Heterogeneous Effects
9
Data before 1970 is not taken into account because of its small sample size. In this figure, we
do not drop those born after 2001. The larger variance after 2000 is mainly due to smaller sample
size in 2005 population study data. It is obvious that the trend between Han and Minority is
stable.
15 The one child policy is enforced differently in urban and rural areas. For example, the policy
in many rural areas allows a household to give a second birth if the first is a girl, called the “one
and a half” child policy. This varying enforcement, together with other differences between these
two areas, may result in heterogeneous effects. Those living in rural areas are generally more
poorly educated and may have stronger children or boy preferences, so they may have stronger
incentives to obtain more children and more sons. But one child policy is more strictly enforced
in urban areas, which may increase the incentive of people to make twins by themselves but
increase the risk of being exposed. Therefore, it is an empirical question that whether and to what
extent that one child policy increases the twining births in urban and rural areas, respectively.
We conduct the regressions for the urban and rural residents separately and report the
results in Panel A of Table 5. The results show that policy fine is positively associated with twins
in both urban and rural areas, and the effect of the one child policy in rural areas is larger. The
coefficient for the urban sample is not significant at 10 percent level but still large in magnitude,
indicating there possibly is a large heterogeneity.
[Table 5 about here]
In addition, since a couple is allowed to have an additional child if the first is a girl in most
rural areas, there may be heterogeneous effects of birth order in rural and urban areas. We
interact policy fines with birth order dummies, and report the coefficients of the interactions in
Panel B of Table 5. Estimates show that twins in the second birth order are mostly
policy-associated, and this association is mainly in the rural areas, which is consistent with the
fact that a large part of rural areas are governed by the “one and a half” child policy. The parents
16 may lack incentive to make twins in their first birth order.
3.3 Birth Space between first and second deliveries
The above results suggest that one child policy increased twining births in China in a large
magnitude but little has been done yet to open the “black” box that how couples can make twins
intentionally to bypass the regulations. As mentioned before, couples in China may report
non-twining children as twins to have more children with no or less punishment, or they may
also take fertility drugs intentionally to increase the probability to deliver multiple children in a
single birth. Although some medias have uncovered some phenomena in certain places, no
previous research ever found any statistical evidence for either or both of the household
behavioral responses towards the one child policy. In addition, we are able to further check and
back up the results in previous section by providing consistent evidence.
We test the hypotheses of reporting fake twins by examining the birth space between the
first and second deliveries, by whether the second birth is twining and whether the birth is born
after one child policy. The rationale is that it probably takes more time for the parents to make
fake twins. For example, they may give birth to a child first without reporting to registration
office, give another delivery and then report it together with the first one as twins. In this case,
the reported second birth is actually the third birth, and it is reasonable that the timing needed is
longer than normal. For another, parents from two households may plan together to bear, and
then report the children together as twins in one certain household. Both of them could plan
again to give another delivery so that the other household will also have a pair of twins. However,
17 the birth date of the reported twins would be determined by the younger one because the parents
have to wait until both two kids have been born. If the fake twins are reported in the second birth
order, then it is expected to see the birth space between first and reported second delivery will be
longer when the second birth is reported as twins. However, if the parents plan to bear twins by
taking fertility drugs, there is no reason why the parents will give the second delivery later than
normal.
Since twining births are more likely to happen when mother’s age while give birth is higher
and birth space is also likely to be influenced by one child policy, local social norms and other
factors, we conduct the following difference-in-difference regressions to rule out the possible
confounding factors:
3 𝐵𝑖𝑟𝑡ℎ 𝑆𝑝𝑎𝑐𝑒! = 𝛽! + 𝛽! 𝑃𝑜𝑙𝑖𝑐𝑦!!!"#$ ×𝑇𝑤𝑖𝑛𝑠! + 𝛽!! 𝑇𝑤𝑖𝑛𝑠! + 𝜃X!! + 𝛿!" + 𝛿! + T! + 𝜀!
Before conducting the above regressions, we restrict the sample to the second births because
results in Table 5 suggest that policy-associated twins are concentrated in the second births. Thus,
𝐵𝑖𝑟𝑡ℎ 𝑆𝑝𝑎𝑐𝑒! denotes the birth space between the first and second deliveries for birth i. 𝑇𝑤𝑖𝑛𝑠!
denotes whether birth i is twining or not, which captures the time difference between singleton
births and multiple births. The coefficient, 𝛽! , on the interaction term, 𝑃𝑜𝑙𝑖𝑐𝑦!!!"#$ ×𝑇𝑤𝑖𝑛𝑠! , is
of central interest here because it reflects the how much additional length of time needed to give
birth to twins than singletons after one child policy. The covariates 𝛿!" , 𝛿! and T! have the
same definitions as before. A new set of other covariates, denoted by X!! , include dummies for
residence type (urban/rural), parents' ethnicity (both Han/either a minority), mother's education
level, and mother's age when giving the first birth. We do not use the fine rate here due to its
18 undetermined impact on birth space. For one thing, the higher fine rate provides stronger
incentive for couples to make fake twins; for another, the higher fine rate also push the potential
fake twins makers to find/bear another twining member earlier.
Table 6 reports the OLS estimates for 𝛽! and 𝛽!! in different samples. Column 1 provide
positive and significant estimate for 𝛽! , showing that twins births after one child policy requires
more time to make preparation compare to singletons. After one child policy, the birth space
between first and second births is 0.08 years longer if the second birth is twining, providing
suggestive evidence for the reporting fake twins, as discussed above. The next two columns
provide results for Han ethnicity and minorities, respectively. The significant estimates only
survive in Han ethnicity. Compared to this, the coefficient for minority group is insignificant,
indicating large heterogeneity in this group. Indeed, one child policy may have heterogeneous
impact on fertility of minority as well. For example, government in Guangxi province allows
minority parents to have a second child, but the condition is at least 4 years’ birth space between
the first and second delivery. The policy varies by locations and ethnicities, and we do not have
detailed information for them.
3.4 Height difference within twins and one child policy
We provide further evidence by looking into the height difference within twins in this
section. To keep it concise, the detailed derivations of how to test these two hypotheses are put in
the appendix. Summarizing these derivations, we can use height differences of the two children
in same-sex twins and mixed-sex twins to test. If we find the height difference within
19 same-gender twins increases with policy fines and that within mixed-gender twins does not, then
it is likely that the increase in twin births are made by taking fertility drugs; if we find, however,
that height differences within mixed-gender twins increase with policy fines, then they are most
likely to be fake twins.
We turn to the China Health and Nutrition Survey (CHNS) data to do this work.10 Same as
before, twins are defined as children less than 18 years old with exactly the same birth year and
birth month within the same household. There are 85 pairs in total, including 60 same-gender
pairs and 25 mixed-gender pairs. We then define the height gap of one pair as the height of the
taller individual less that of the shorter one. Considering that the height gap may change as the
children grow up, we also introduced ratio of height gap to the mean height in the pair
(Gap/Height) as another measure of height difference. We also match the twins sample to the
10
The China Health and Nutrition Survey included 26,000 individuals in nine provinces, which
are Liaoning, Heilongjiang, Jiangsu, Shandong, Henan, Hubei, Hunan, Guangxi and Guizhou.
The nine provinces vary substantially in geography, economic development, public resources,
and health indicators. The nine provinces contain approximately 56% of the population of
mainland China. Data collection began in 1989 and has been implemented every 2 to 4 years
since (Jones-Smith and Popkin, 2010). We chose CHNS to conduct this study because it is
currently the largest and longest household panel data of China for public use and contains
detailed information on family background, demographic variables, and biological measures,
including height, for both adults and children. For children under 18, height is measured in
millimeters in each wave.
20 fines data, and drop those born after 2001, as we did for the census sample. Therefore, there are
72 pairs in total, with 53 of them are of same gender. Table 7 reports the summary statistics for
height gap and ratio of gap to mean height. The mean height gap is 2.2 centimeters and
gap/height ratio is 1.75 percent. As expected, different-gender twins have larger difference in
height.
[Table 7 about here]
To estimate the relationship between height difference and one child policy, we conduct the
following estimation:
4 𝐻𝐷! = 𝛼 + 𝛽! 𝐹𝑖𝑛𝑒!"# + 𝜌𝑍! + δ! + δ! + δ! + T! + 𝑒! where the dependent variable, 𝐻𝐷! denotes the height difference within twin pair i in province j
born in year y of wave k. It can be either the height gap or gap/height ratio as defined above. The
coefficient 𝛽! gives the association between the policy fine and the height difference of twins.
We control for a full set of covariates, 𝑍! , that are potentially correlated with height difference,
including indicator variables such as same-gender twin, urban residence, same-gender pair, the
boy being taller in different-gender twins, and also average height of pair i, the mother's age
when giving birth, age, and age squared of the twins. Because of the small sample size, we
combine the birth year into four groups (every five years as one group), δ! , to capture the birth
year effects. Province dummies and province-specific time trends are also controlled for.
Panel A in Table 8 reports the estimates of equation (3) and some of its extensions, with
standard errors clustered at provincial levels. The first column shows that increasing the fine by
one year’s income suggests an increase in twins’ height gap by 1.8 centimeters on average,
21 suggesting that couples may have employed methods to make twins by themselves (by taking
drugs or false reporting). We then add interactions of the fines variable with same-gender and
different-gender twins in the same regression to identify the one-child policy's impact on the
height difference of different types of twins. As shown in Column 2, policy fines are
significantly and positively associated with height differences for both same-gender and
different-gender pairs. Columns 3 and 4 also provide consistent results where the dependent
variable is the Gap/Height ratio. The results in the Panel A provide suggestive evidence to
support the fake twins hypothesis. Details are shown in Appendix A.2.
[Table 8 about here]
Since CHNS is a panel data and one certain pair of twins may be surveyed in different waves,
the height difference may change as the twins grow up because the individuals in one pair would
have different environmental influences throughout their lives. To avoid potential econometric
problems, we keep observations of the latest wave for each pair, run the same regressions as
above. Panel B in Table 8 reports the estimates for key variables, and the results provide a
consistent pattern as shown in Panel A, except for coefficients in larger magnitude.
IV. Conclusions
Using data from 1982, 1990 and 2000 census and 2005 1% population survey, this paper
documents that the birthrate of twins in China has more than doubled from the late 1960s
through the early 2000s, from 3.5 to 7.5 per thousand births. Though a similar phenomenon also
exists in other countries like the U.S. China may be a special case because of the one-child
22 policy. To those who prefer more children or those with a strong preference for boys, twins are
favorable because individuals are able to have more children, and have a higher probability of
having a boy without going against regulations. Given such a strong incentive, individuals are
likely to take measures to increase the probability of giving birth to twins, which may include
taking fertility drugs, asking for help from private hospitals, and even hiding older children and
registering them with younger ones as twins.
This paper aims to answer the question whether and how the one child policy and twins are
related. Above all, through matching census data to one-child policy regulatory fine data by
province and year, we find that an increase in policy fines by one year’s income is associated
with an approximately 0.07 per thousand births increase in the rate of twins. The estimates in our
preferred model indicates that at least one third of the twins rate increase since 1970s can be
explained by the one child policy. The results are robust to different model specifications. We
then divide the full sample into urban and rural groups and add interacts of fines with birth order
in the regressions. We find that the impact of the policy is larger in rural areas, and that the
policy increases the twin birthrate in the second births. These results indicate that
policy-associated twins may not be randomly distributed throughout the population.
In addition, we also provide some evidence on what ways those increase in twins comes
from. Using a difference-in-difference identification strategy, we find that the birth space
between first birth and second twining delivery is 0.08 years longer relative to a singleton
delivery after one child policy. This result is more consistent with the hypothesis that couples
report non-twining children as twins after one child policy. Furthermore, we also use CHNS data
23 to provide supplement evidence for this claim. Estimates show that height difference within
twins is positively associated with policy fines, and that the association exists in both same- and
different- gender twins. This finding is also consistent with the hypothesis that the one child
policy stimulated people’s incentives to have twins by reporting non-twinning children as twins.
However, it is important to note that our results do not rule out the possibility of the hypothesis
that couples may take fertility drugs intentionally to give birth to twins.
This is the first study to examine people’s behavior response against one child policy by
investigating the relationship of twining births with it. Our estimates indicate that one third of the
twinning births increase are contributed by one child policy, indicating a sizeable behavioral
response from Chinese couples. Since behavior response is usually correlated to social welfare in
public economics, our results motivate studies in the future to examine the individual behavior
responses towards other public policies in China, and to calculate the associated welfare gain or
loss in the largest developing countries. This study also helps to understand the context and
background of studies using twins data in China. Since twining births can be made by couples
intentionally to bypass one child policy, the distribution of reported twins in China may be not
random. However, our results also imply that the non-random distributed or policy-associated
twins can be screened out by carefully examining the observed characteristics of the twins,
which emphasizes the importance to check these characteristics and also backs up the results of
other studies with the careful examination.
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29 Appendix: The One Child Policy and Height Differences within Twins
In this section, different derivations of real “man-made” twins and fake twins hypothesis are
derived. For simplicity, we only use financial penalties (fine) to measure the one-child policy,
and assume it equals one when the financial penalty policy is established in the local province,
and zero if otherwise.
A.1 Real “Man-made” Twins Hypothesis
The man-made twins hypothesis indicates that individuals are motivated to take technologies,
like fertility drugs, to give birth to twins, under the one-child policy. But taking ferlity drugs
should be more reasonable because embryo technologies did not appear in China until the late
1990s. The mechanisms of these drugs are usually to induce ovulation, which is usually used to
treat infertility. When normal women take them, the possibility of multiple ovulation is increased,
and thus they are more likely to have twins. Though these drugs are classified as prescription
medicines, it is still possible for individuals to purchase them in certain private hospitals and get
prescriptions from certain doctors by bribing the doctors or tell lies.
Under the Man-Made Twins Hypothesis, individuals are more likely to take fertility drugs
(Take = 1) to have more children while avoid being punished under the one-child policy, that is,
Pr 𝑇𝑎𝑘𝑒 = 1 𝐹𝑖𝑛𝑒 = 1 > Pr 𝑇𝑎𝑘𝑒 = 1 𝐹𝑖𝑛𝑒 = 0). According to the medical literature and
stylized facts, we know that taking certain fertility drugs or using technologies really increases
the probability of giving birth to twins: Pr 𝑇𝑤𝑖𝑛𝑠 = 1 𝑇𝑎𝑘𝑒 = 1 > Pr 𝑇𝑤𝑖𝑛𝑠 = 1 𝑇𝑎𝑘𝑒 =
0). We also assume that, conditional on individuals' behaviors (Take), giving birth to twins is
30 independent of the one-child policy. In addition, the biological results of fertility drugs or
embryo technologies are to develop multiple zygotes in the uterus at the same time, rather than to
stimulate a single fertilized egg in the mother's body to divide into two or more embryos. Thus,
these actions only raise the probability of dizygotic (DZ) twins rather than that of monozygotic
(MZ) twins, that is,
Pr 𝐷𝑍 = 1 𝑇𝑎𝑘𝑒 = 1 > Pr 𝐷𝑍 = 1 𝑇𝑎𝑘𝑒 = 0)
and Pr 𝑀𝑍 = 1 𝑇𝑎𝑘𝑒 = 1 = Pr 𝑀𝑍 = 1 𝑇𝑎𝑘𝑒 = 0).
According to the medical literature, MZ twins are genetically nearly identical and they are
always of the same sex unless there has been a mutation during development. But it is possible
that same-gender twins are DZ. Certain characteristics of MZ twins become more alike as twins
age, such as IQ and personality (Segal, 1999). DZ twins, however, like any other siblings, have
an extremely small chance of having the same chromosome profile. DZ twins may look very
different from each other, and may be of different sexes or the same sex. The above also holds
for brothers and sisters from the same parents, meaning that DZ twins can be viewed as siblings
who happen to be of the same age. Therefore, we have Pr 𝐷𝑍 = 1 𝐷𝐺 = 1 = 1, Pr 𝑆𝐺 =
1 𝑀𝑍 = 1) = 1, 0 < Pr DZ = 1 SG < 1, and 0 < Pr MZ = 1 SG < 1.
An established strand of literature has proved that DZ twins tend to have more differences
than MZ ones as they grow up because of genetic disparity, including height (Fischbein, 1977;
Smith et al., 1973), weight (Stunkard et al., 1986), mental ability profiles (Segal, 1985), bone
mass (Smith et al., 1973) and so on. Specifically, Fischbein (1977) found that MZ twins have a
significantly higher concordance in height than for DZ pairs during puberty, for both boys and
31 girls, and yearly height increments are also more similar for MZ pairs, indicating that the height
spurt occurs more simultaneously for MZ twins in comparison to DZ twins. Thus, we presume
that the height difference (HD) within a DZ (same-gender) pair should be larger than that of a
MZ pair if other factors are equalized. Thus, 𝐸 𝐻𝐷 𝑆𝐺 = 1, 𝐷𝑍 = 1 > 𝐸(𝐻𝐷|𝑆𝐺 = 1, 𝑀𝑍 =
1).
Additionally, we also assume that the actions people may take do not influence twins' height
differences conditional on these twins' type (MZ or DZ). Based on the facts or assumptions
above, it can be shown that
(1) E(HD|Fine=1,Twins=1)>E(HD|Fine=0,Twins=1)
(2) E(HD|Fine=1,SG=1)>E(HD|Fine=0,SG=1)
and (3) E(HD|Fine=1,DG=1)=E(HD|Fine=0,DG=1)
Equation (1) tells us that twins' height differences would be larger under the one-child policy
because there will be more DZ twins due to the methods the individuals take in response to the
one-child policy. This response will increase DZ proportions in same-gender twins, and thus the
height difference in this group will become larger (Equation 2). However, different-gender twins'
height differences will not change because they themselves are DZ (Equation 3). Because we do
not know whether a woman took fertility drugs or not, equations (1) through (3) are important
because of height difference, one-child policy fine and twins' gender composition are all
observables, and thus allow for empirical tests.
A.2 Reporting Fake Twins Hypothesis
The fake twins hypothesis means that parents report non-twining children as twins in order
32 to avoid punishment under the one-child policy. It is somehow feasible under some special
circumstances in earlier China. First, many pregnant women gave birth at home in the 1980s, and
the population administration would not notice until parents report their infants, though they
were required to do so. Second, birth certificates did not launch until 1997, and the children's
birthdates were easy to revise before that. Third, children—especially siblings—look alike, in
particular when the age difference is not large. Though parents will face harsher punishment
once they are found to have reported fake twins, many parents may still choose to do so because
of strong children or boy preferences.
Under the fake twins hypothesis, the one child policy stimulates people's incentives to report
fake twins, that is, Pr(Twins*|Fine=1)>Pr(Twins*|Fine=0), in which Twins* denotes the
observed twins, including real ones and fake ones. For real twins (Twins), we assume all of them
are reported, that is, Pr(Twins*|Twins)=1.
The most important difference between fake twins and true twins is the age. For simplicity,
we only consider the factors of age, and do not take into account of the gender factor in height
differences in different-gender twins here because all the children are very young here. Due to
the age difference, the height difference within fake twins is supposed to be larger, so
E(HD|Twins*)>E(HD|Twins) if Pr(Twins|Twins*)<1.
The condition Pr(Twins|Twins*)<1 ensures that fake twins do exist. If parents have strong
children preference and do not care about the gender, then the gender composition of fake twins
should be random, so that height differences in both (observed) same-gender twins and
different-gender ones should be larger. However, if parents have a strong boy preference, they
33 are more likely to construct different-gender twins because they have less incentive to make fake
twins when they had a boy already. No matter which case it is, under the fake twins hypothesis,
we must have
(4) E(HD|Twins*,Fine=1)>E(HD|Twins*,Fine=0),
and (5) E(HD|DG*,Fine=1)>E(HD|DG*,Fine=0),
in which DG* denotes the observed different-gender twins. Same as before, equations (4)
and (5) are all based on observables so that can be tested in empirical analysis.
34 Figure 1. Twins birth rate against year of birth
Figure 3 Twins birth rates against year of birth, by parents' ethnicity
Table 1: Summary statistics
(1)
Variables
Full sample
Twins (%)
0.58
(7.58)
0.73
(0.45)
0.93
(0.26)
8.04
(4.67)
23.25
(2.97)
Rural area (Yes = 1)
Both parents Han ethnicity (Yes = 1)
Age
Mother's age when giving birth
Birth order
First
Second
Third or above
Observations
0.57
(0.50)
0.30
(0.46)
0.14
(0.35)
5,965,262
(2)
Parents are
Han
0.59
(7.65)
0.72
(0.45)
(3)
Either parent
is minority
0.44
(6.58)
0.81
(0.40)
8.08
(4.67)
23.28
(2.95)
7.62
(4.62)
22.82
(3.18)
0.57
(0.50)
0.29
(0.46)
0.14
(0.34)
5,553,384
0.51
(0.50)
0.32
(0.46)
0.18
(0.38)
411,878
Notes: Standard deviations in parentheses. The sample is restricted to the births before
2001.
Table 2: Twins birth in Han and Minority
(1)
(2)
(3)
Born no later than Born after
Difference
1979
1979
(2) - (1)
Twins birth rate in Han
0.39
0.67
0.276
(6.25)
(8.15)
Twins birth rate in Minority
0.38
0.45
0.075
(6.12)
(6.70)
Notes: Standard deviations are in parentheses, and standard errors are in
brackets.
Table 3: Twins birth and one-child policy fine rate
(1)
Sample
(2)
Full sample
Parents Han
(3)
Either Parent
Minority
Twins
0.0665*
(0.0380)
0.0717*
(0.0406)
0.0114
(0.0287)
Dependent variable
Effective Policy fine rate
Policy fine rate * Parents Han
(4)
Full sample Full sample
0.0527***
(0.0158)
Born after 1979 * Parents Han
Observations
R-squared
(5)
0.163***
(0.0299)
5,965,262
0.001
5,553,384
0.001
411,878
0.001
5,965,262
0.001
5,965,262
0.001
NOTE: Robust standard errors in parentheses are clustered in provincial level. *** p<0.01, ** p<0.05, * p<0.1. One child policy
fine is measred in years of local household income. Sampling weights are applied. Coefficients should be interpreted as percentage
because all dependent variables have been multiplied by 100. Covariates include residency type, province, birth order, mother's
education level, mother giving birth age, year of birth, survey year, and interactions between year of birth and survey year. Parents'
ethnity dummy is controlled for in columns 1, 4 and 5.
Table 4: One child policy fine predicted by prior twins rate in post-1979 births
(1)
(3)
(5)
Dependent variable
One Child Policy Fine
VARIABLES
1 year later
3 years later
5 years later
Twins
0.0102
(0.00628)
0.00833
(0.00543)
0.00133
(0.00656)
Observations
R-squared
4,286,030
0.752
4,118,084
0.775
3,913,326
0.800
NOTE: Robust standard errors in parentheses are all clustered in provincial level. ***
p<0.01, ** p<0.05, * p<0.1. Only post-1979 births are used. Covariates include
continuous variables like provincial time trend, and indicator variables, like residency
type, parents' ethnicity, province, birth order, mother giving birth age, year of birth,
survey year, and interactions between year of birth and survey year.
Table 5: Heterogenous effects of policy fine on twins birth
(1)
Parents Han
Panel A: Policy Fine
Policy fine rate
0.0717*
(0.0406)
Panel B: Policy Fine interacting with birth order
First
0.0400
(0.0402)
Second
0.151***
(0.0471)
Third and above
0.0718
(0.0468)
Observations
5,553,384
(2)
(3)
Subsamples by type of residence
Urban
Rural
Dependent variable is Twins
0.0591
(0.0407)
0.0842*
(0.0413)
0.0538
(0.0424)
0.0931
(0.0598)
0.0274
(0.0645)
0.0341
(0.0400)
0.167***
(0.0462)
0.0863*
(0.0442)
1,394,364
4,159,020
NOTE: Robust standard errors in parentheses are clustered in provincial level. *** p<0.01, ** p<0.05, * p<0.1. One
child policy fine is measred in years of household income. Sampling weights are applied. Coefficients should be
interpreted as percentage because all dependent variables have been multiplied by 100. Covariates include dummies
for residency type, parents' ethnicity, province, birth order, mother giving birth age, year of birth, survey year, and
interactions between year of birth and survey year.
Table 6: Age gap between first and second birth, twins and one child policy
(1)
(2)
(3)
Full sample
Parents Han
Either Parents Minority
Dependent variable
Age gap between first birth and second birth (in years)
Twins * Born after 1979
Twins
Observations
R-squared
0.078***
(0.027)
0.188***
(0.016)
0.077**
(0.028)
0.182***
(0.016)
0.100
(0.108)
0.288***
(0.096)
1,822,396
0.467
1,690,608
0.471
131,788
0.460
Note: Robust standard errors in parentheses are clustered in provincial level. *** p<0.01, ** p<0.05, * p<0.1. Sample is restricted to the
second births. Sampling weights are applied. Covariates include residency type, province, birth order, mother's education level, mother's
age when giving first birth, year of birth, survey year, and interactions between year of birth and survey year.
Table 7: Summary statistics in CHNS
(1)
Variable
Height gap (cm)
Mean of height (cm)
Gap/Height Ratio in percentage
Observations
All twins
2.18
(2.74)
121.15
(27.59)
1.75
(2.14)
72
(2)
(1)
By type of twins
Same gender
Different gender
1.30
(1.59)
119.58
(28.47)
1.02
(1.14)
53
4.65
(3.68)
125.55
(25.17)
3.78
(2.90)
19
NOTES: Standard deviations are reported in brackets. Data source is China Health and Nutrition Survey. Twins are
defined as children (aged below 18) born in the same household within the same month. For each pair of twins,
height gap is defined as the height of the taller member minus that of the shorter one. Gap/Height ratio is defined as
twins' height gap divided by the mean height of the pair, and the values reported are multiplied by 100.
Table 8: Height difference and one-child policy fine
(1)
(2)
Height Difference (cm)
Dependent variable
Panel A: Full sample
Fine in years of income
1.834***
(0.313)
Interactions
Same gender pair & Fine
2.075***
(0.380)
Different gender pair & Fine
0.706**
(0.240)
Observations
72
R-squared
0.631
Panel B: Only the latest wave is kept
Fine in years of income
3.284**
(1.079)
Interactions
Same gender pair & Fine
Different gender pair & Fine
Observations
R-squared
Year of birth group dummies
Wave dummies
Province dummies
Provincial time trend
72
0.640
(4)
(5)
Height Difference/Mean
1.698***
(0.229)
1.772***
(0.263)
1.348***
(0.252)
72
0.631
72
0.632
2.709***
(0.586)
3.368*
(1.565)
2.935
(1.946)
2.585**
(0.836)
3.226**
(1.158)
33
0.744
33
0.745
33
0.765
33
0.768
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Notes: Standard errors in parentheses are clustered in provincial level. *** p<0.01, ** p<0.05, * p<0.1. Data
source is CHNS. The twins sample used in this table are those born between 1979 and 2001. Height gap is
defined as the height of the taller twin minus that of the shorter one, and gap/height ratio is defined as twins'
height gap divided by the mean height of the pair. Each observation is derived from one pair of twins.