Discussion Paper No.369

Child Migration and the Health Status of Parents
Left Behind

Fengming CHEN

May, 2017

TOHOKU ECONOMICS RESEARCH GROUPGRADUATE SCHOOL OF ECONOMICS AND
MANAGEMENT TOHOKU UNIVERSITY
27-1 KAWAUCHI, AOBA-KU, SENDAI,
980-8576 JAPANChild migration and the health status of parents left behind
Fengming Chen1
cfmdbdx@gmail.com
Graduate School of Economics and Management, Tohoku University
27-1,Kawaauchi Aoba-ku, Sendai, Miyagi 980-8576,Japan.

Abstract
I investigate the causal effect of child migration on the health status of their parents
left behind. I mainly focus on the respondents who are more than 50 years old and have
only two children to simplify the situations of child migration. Using 2010 wave ofChina Family Panel Studies (CFPS), I employ propensity score matching method tocorrect the problem of self-selection and evaluate the causal effect of having migrantchildren on the health status of the elderly left behind. Results show that, in the case of
one child migrating for work, child migration has no impact on the health status of theirparents. As the substitutive relationship exists among child siblings, the child staying at
home would provide more support to their parents and cancel out the impact of childmigration. The incentive of free riding for migrant children is very strong, which
reduces the benefit of remittances for the elderly.

Journal of Economic Literature Classification Numbers: D13, F24, I12, O15
Keywords: Self-selection, Migrant children, Health status, Free riding, Propensity scorematching

1. Introduction
With the development of the economy, the economic inequality between eastern
coastal areas and western inland areas in China is increasing and is becoming the main
reason that young members of the labor force migrate to eastern coastal cities such as
Beijing and Shanghai. Moreover, the acceleration of urbanization and the developmentof transportation systems are not negligible factors influencing the migration of young
1

I am greatly indebted to Professor Hiroshi Yoshida for his kind advice and encouragement when writing this paper.
I would also like to thank Associate Professor Midori Wakabayashi and Associate Professor Kentaro Nakajima for
their helpful advice and comments. I also benefited from discussions with participants at various seminars in Tohoku
University. I am grateful to the Institute of Social Science Survey (ISSS) of Peking University for allowing me to use
CFPS data. Any errors are my own. This paper is a part of Analysis on the Impact of Population Aging on Economic
Society Evidence from China and Japan (doctoral dissertation of Fengming CHEN).

1

cohorts. Although out-migration facilitates the increase in economic growth, it also
induces a great number of elderly people to be left behind. The issue of how to deal
with elderly people who are left behind has attracted the interest of policymakers andeconomists. Because the social security systems in China are weakly developed, theelderly mainly depend on support from their adult children, including financial support,
physical support, and emotional support. However, because the existence of aregistration system limits access to health resources or other public resources for theelderly from emigrant areas, it is difficult for the elderly to accompany their adultchildren to eastern coastal cities (He & Ye, 2009). Child migration may reduce theprovision of economic support (short-term) and physical and emotional support(long-term) for the elderly who are left behind, and thus may cause a deterioration ofhealth status for frail parents. Because child migration prevails in many developing
countries, such as China, a growing number of researchers are interested in therelationship between child migration and the health status of parents left behind.
Many previous studies have documented this topic. Marcus, Ruth, and Tobias(2015) and Kuhn, Everett, and Silvey (2011), provide some positive evidence that childmigration increases the health status of the elderly left behind. Antman (2010), Antman(2016), Adhikari, Jampaklay, and Chamratrithirong (2011), Lian, Li, and Huang (2014),
and Tse (2013) focus on the negative impacts of child migration, including physicalhealth and mental health. Although researchers are interested in the causal effect ofchild migration on the health status of the elderly left behind, the endogeneity of childmigration may contaminate estimation results. Thus, the main methodological obstacleof this topic is the issue of how to deal with the endogeneity of child migration. One of
the causes of endogeneity is positive self-selection based on health status. This kind ofself-selection may introduce some positive biases into the estimated results. For
example, if child migration is positively selected based on the health status of adultchildren and their parents, unobservable common genetic or regional food culture
factors that are positively associated with health status may induce some biases in thecomparison between parents of migrants and those of non-migrants (Antman, 2016). If
researchers cannot adequately control for positive self-selection, nonexperimental
estimates will tend to overstate the household-level benefits of having members migrate(Gibson, Mckenzie, and Stillman, 2011). Certainly, the problem of simultaneity orreverse causation for adult migration may also exist. This is especially true for poor
households, because they do not have sufficient economic resources to guarantee
medical expenditure for their frail parents, and the decline of parents’ health status
forces adult children to migrate to obtain additional funds for medical services.
2

As discussed, the question of how to deal with the endogeneity problem of childmigration is the core issue of this topic. Most previous studies try to make causal
inferences using the instrumental variable (IV) method to correct the endogeneity biasof child migration. With the development of econometric analysis, propensity scorematching (Kuhn et al., 2011) and FEIV (individual fixed effects and instrumental
variables estimation, Antman (2011)) are also applied to control the endogeneity of
migration. Especially by using a propensity score to match the treatment and control
groups, researchers can conduct a quasi-experiment to deal with the issue ofself-selection regarding child migration.
In the economics literature, remittances, as a potential channel to influence thehealth status of the elderly left behind, has attracted significant attention (Gibson et al.,2011; Marcus et al., 2015). Many previous studies indicate that remittances can increase
the disposable income of the elderly and lead to improvements in diet or an increase in
medical expenditure, which may potentially benefit the health status of the elderly(Adhikari et al., 2011; Marcus et al., 2015). On the other hand, some previous studies
indicate that child migration may not increase the disposable income of the elderly left
behind and may even lead to a reduction in household income per capita (Gibson et al.,2011). With the number of migrant children increasing, it has become more difficult to
identify this potential channel.
Although intergenerational transfers from children to parents are considered thecultural norm of filial piety, in exchange, the elderly are expected to provide grandchildcare for the migrants’ children (Cong & Silverstein, 2011). By providing grandchildcare, adult migrants can optimize their potential earnings and send more remittances totheir parents (i.e., the elderly’s decision to provide grandchild care services can be seen
as a strategic investment with an expectation that children will reciprocate). This isconsistent with the analysis of children as investment goods (Cochrane, 1975). If theburden of grandchild care exceeds the benefit of remittances, the decline of the healthoutcomes of the elderly may negatively influence child migration. Certainly, theprovision of grandchild care services is also an altruistic act by the elderly for the
betterment of the children of their progeny, and this hypothesis may temper theexchange process (Cong & Silverstein, 2011).
In addition to remittances and the provision of grandchild care services influencing
the health status of the elderly left behind, the living arrangements of the elderly arevery important factors for studying the problem of child migration. Per Connelly &Margaret (2016), the elderly who are alone in a village are most at risk, while thoseliving with other non-migrant adult children are much less affected by migration. At the3same time, informal social security networks of families are robust despite highopportunity costs, and they shield elderly people from some of the negative social
consequences of large-scale child migration. Particularly in the context of developing
countries, social security networks are weakly developed. The elderly are mainly
dependent on support from their adult children. Consequently, child migration behavior
may be conditioned on the cooperation of non-migrant children (Stohr, 2015). It isnecessary to highlight the potential importance of including information on nonresident
family members when studying the relationship between elder care requirements andthe labor supply decisions of adult children (Giles & Ren, 2007).
With the increase of child migration and an aging population, researchers
increasingly emphasize the causal effect of child migration on the health status of theelderly. Using diverse indicators such as self-reported health, BMI, depression, and
ADL to evaluate the health status of the elderly left behind may help us detect otherpotential channels of child migration. Controlling for the endogeneity of child migration
is another important issue. Although some previous studies use an IV design to deal
with the endogeneity of child migration, most IVs do not satisfy the two criteria of IV
analysis. It is necessary to find suitable IVs for child migration or use other econometricanalysis techniques to correct the endogeneity bias, such as panel data analysis andpropensity score matching (Antman, 2011; Antman, 2016; Kuhn et al., 2011).
Furthermore, health investments, including smoking and drinking, are also considered
to provide a potential channel for child migration to influence the health status of theelderly left behind. In the future, this channel should be addressed in an empiricalanalysis.
This paper examines the causal effect of child migration on the health status ofparents left behind. As the number of migrant children increases, it is difficult to control
all associated variables from migrant children. Thus, I mainly focus on respondents
having two children to relieve the bias from adult children as much as possible. Usingthe 2010 wave of the China Family Panel Studies (CFPS), I employ the propensity scorematching method to correct the issue of self-selection and evaluate the relationshipbetween having migrant children and the health status of parents aged 50 and above
who are left behind. According to our estimated results, in the case of one childmigration, child migration has no impact on the health outcome of the elderly.
The remainder of this paper is arranged as follows. Section 2 introduces the
hypotheses. Section 3 describes my econometric strategy. Section 4 introduces the data
used in this study. Section 5 presents my empirical results, and section 6 shows theresults of robustness check. Section 7 concludes the paper.
4

2. Hypothesis
Chen & Yoshida (2017) constructs a simple theory framework to explain therelationship between child migration and the health status of the elderly. The healthstatus of the elderly is determined by the provision of informal care and formal care.
The increases of wage for adult children benefit the health status of their parents.
However, with the increase of children’s number, it becomes difficult to detect thischannel. And the existing of free riding behavior will also influence the relationshipbetween child migration and the health status of the elderly. If migrant child is freeriding on the behavior of providing informal care service, child migration may not
influence the health status of the elderly. To obtain convincing evidence, I focus on the
respondents having two children to reduce the potential bias from children.
Hypothesis: in the case of one child migrating for work, child migration would not
influence the health status of the elderly left behind. According to Chen & Yoshida(2017), the elderly would benefit from child migration by receiving more remittances.
However, in the case of one child migrating for work, the incentive of free riding for
migrant child is very strong, because the other child would provide more informal careservices. Thus, the health status of the elderly would not be influenced by childmigration.

3. Data
3.1 Data source
The data used in this study comes from the CFPS. This longitudinal survey is anationally representative sample of 14,960 families, including twenty-five provinces in
Mainland China and designed and conducted by the Institute of Social Science Survey(ISSS) of Peking University. It adopts a stratified three-stage cluster sample design anduses administrative units and measures of socioeconomic development as the main
stratification variables (Xie, Qiu, & Lu, 2012). The CFPS covers a wide range of topics,
from the information of family structure to the information of individuals’ attributes.
CFPS collects the information of child migration including migrant places, whether
transfers are provided to parents, whether grandchild care is provided for migrantchildren, and the health status of the elderly, and thus provides an opportunity to
examine the impact of child migration on the health status of parents left behind. I use
the baseline of CFPS to examine the effect of child migration, and respondents aged5

over 50 years are used in this study. I delete some respondents due to missing values ofkey variables. I also exclude some respondents having obviously incorrect information,such as a negative number of age. The statistical analysis software used is Stata/SE 14.

3.2 Outcome of health status
Table 2 shows the descriptive statistics of the full sample of data used in this study.
I use self-reported health status to evaluate the health condition of parents left behind.
Because the alternatives are defined as “1 Healthy,” “2 Fair,” “3 Relatively unhealthy,”“4 Unhealthy,” and “5 Very unhealthy,” the options are ordinal categories. It is
unsuitable to treat self-reported health status as a continuous variable. Thus, I recode
health outcome as a dichotomous variable, which is assigned a value of one if the
respondent chooses “1 Healthy,” and otherwise zero. This new dependent variable iscalled “Health dummy”.

3.3 Pretreatment variables
CFPS collected affluent information associated with non-coresident children
including the reasons for leaving home (1. study away from hometown; 2. out-migration
for work; 3. monk; 4. visit friends or relatives; 5. in prison; 6. military service; 7.
abroad; or 8. others). Consequently, I can use these details to construct child migration
dummy variables. Because the number of migrant children increases, it is difficult tocontrol all associated variables from migrant children. Thus, I mainly focus on the
respondents having two children to relieve the bias from adult children as much as
possible.
I construct two dummy variables to represent the compositions of child migration.
Child migration 1 is assigned a value of one if the first child migrates for work and thesecond child stays in the hometown. Child migration 2 is assigned a value of one if thefirst child stays in the hometown and the second child migrates for work. By using thecompositions of child migration status, I examine the substitutable relationship amongchild siblings. If this kind of substitutable relationship exists, the other siblings would
provide support to their parents instead of their migrant sibling, and the health status of
the elderly may not be negatively influenced by child migration.
Because remittances represent the main potential channel influencing the healthstatus of the parents left behind, I try to consider the money transfers from children to
their parents. Because only a few respondents give the exact amount of money transfer,
I use a dummy variable to represent whether adult children give some money to theirparents. Per Gibson et al. (2011), child migration does not always benefit the6households. Especially at the beginning of migration, it is necessary to pay a huge costto migrate, including transaction fees and the risk of unemployment. Therefore, childmigration may reduce disposable income and adversely influence the health status ofparents. To control this effect, I use a binary variable to stress whether the elderly
parents provide money to their children.
For adult children, if they can receive some grandchild care from the elderly
parents, they will have a chance to work outside and optimize their earning potential.
For elderly parents, the decision of providing grandchild care services can be seen as a
strategic investment with an expectation that their children will reciprocate or visit themmore often. Certainly, it is possible that the burden of taking care of grandchildren
would exceed the benefit of remittances, inducing a decline in health status for elderly
parents. Accordingly, I construct a dummy variable to represent whether the elderly
parents provide some grandchild care services for their grandchildren.
Regarding the characteristics of the elderly, I control for age (Age) and thequadratic form of age (Age squares/1,000) to capture the nonlinear trend. The maledummy is measured dichotomously: the variable takes the value of one for a male
respondent and zero for a female respondent. We also control for household registration(Hukou dummy: agricultural=1 and non-agricultural=0) using a binary variable.
Educational attainment is described by a binary variable indicating whether the
respondents obtain a junior high school degree including higher degrees or not. The
married dummy represents whether the respondent has a spouse currently (yes=1 andotherwise=0). The working dummy indicates whether the elderly member works
currently (yes=1 and otherwise=0). Regarding economic conditions, we control the
logarithm form of personal income from all sources in the last year (Lnincome). The
chronic disease dummy represents whether the respondents have at least one kind ofchronic disease (yes=1 and otherwise=0). Table 2 represents descriptive statistics of thefull sample based on two situations of child migration.

4. Econometric Strategy
Our primary goal is to examine whether children migration can affect the healthstatus of parents left behind. If child migration is randomly assigned among respondents,
it is easy to obtain the causal effect by comparing the means of the migrant group andnon-migrant group (Khandker, Koolwal, & Samad, 2010). However, as discussed inprevious studies, child migration is an endogenous variable. The self-selection problem
may introduce some biases into my estimated results. Moreover, I do not know the7direction of potential bias. If child migrants are positively selected based on health, I
should expect a bias toward finding that parents of migrants have better health outcomesthan those of non-migrants. However, it is also possible that bad health outcomes force
adult children to migrate. If so, I should expect bias toward finding that parents of
migrants have worse health outcomes than those of non-migrants. Dealing with thisself-selection problem is very important in evaluating the impact of child migration. A
number of previous studies use IVs to correct the endogeneity bias of child migration.
The most common IV approach uses macroeconomic variables, such as
network-growth-interaction (Marcus et al., 2015; Stohr, 2015), unemployment rate
(Lian et al., 2014), and U.S. city-level employment statistics in two industries popularwith Mexican immigrants (Antman, 2013). However, such IVs, if they are available,
typically identify only between-community variation in migration activity, not variation
between households within the same community (Kuhn et al., 2011). Additionally, somescholars use the characteristics of children as IVs (Antman, 2016; Tse, 2013). However,these IVs seem to have direct effects on health and fail to satisfy the exclusion
restriction. Table 1 represents several IVs used in empirical studies.
In this paper, I use a counterfactual framework to detect the causal effect of childmigration on health outcomes of elderly parents left behind. The problem is that childmigration’s impact can truly be assessed only by comparing actual and counterfactual
health outcomes. However, the counterfactual is not observed. Accordingly, thechallenge is how to create a convincing and reasonable control group (Khandker et al.,2010). I employ the propensity score matching method to obtain a propensity score andmatch the child migrant group and a non-migrant group from multi-dimensions to one
dimension.
By applying a logit model, I predict the probability of child migration as follows:
Pr (Child Migration i =1) = ʌ (X i )(1),where X is the multi-dimensional vector of characteristics including Age, Agesquares/1000, Male dummy, Rural dummy, Hukou dummy, Education dummy, Married
dummy, Work dummy, Logarithm form of income (Lnincome), Chronic disease dummy,
Age of first child, Gender of first child, Marital status of first child, Educational
attainments of first child, Age of second child, Gender of second child, Marital status ofsecond child, Educational attainments of second child, Support to child1 dummy,
Support from child1 dummy, Grandchild care to child1 dummy, Support to child2
dummy, Support from child2 dummy, and Grandchild care to child2 dummy. ʌ is thelogistic cumulative distribution function. The propensity score is the predictedprobability of logit model. Because the estimated propensity score is continuous, it is8

impossible to find two respondents with the same propensity score. Several matching
methods are used in previous studies to deal with this problem. Nearest neighbormatching, radius matching, and kernel matching are widely used (Becker & Ichino,2002). Based on the propensity score, I can create pseudo-randomized experimental
data and make sure the treatment case is matched by one or several comparable
counterfactual cases. Here, there is an important assumption called the “area of common
support,” which is necessary to be valid. In addition, the treatment group and control
group are necessary to be statistically similar from propensity score to covariates. Thisis called the balancing assumption. I will check these two important assumptions in
section 5.
When completing matching, I will calculate the average effect of treatment on thetreated (ATT) by the differences in the potential outcomes of the treatment group andthe control group as follows:
ATT=E(y1i-y0i | child migrationi=1)=E(y1i|child migrationi=1)-E(y0i|child migrationi=1) (2),where y1i and y0i represent the potential outcomes of the treatment group and control
group, respectively. Child migration is a binary variable indicating the status of childmigration.

5. Empirical results
5.1 Propensity score (50+ with two children)
To employ a propensity score matching approach, I first estimate propensity scoreby using several pre-treatment characteristics of respondents. To get a good
specification of the model, I follow previous studies to control the covariates, including
individual characteristics and the characteristics of children. In addition, remittance andgrandchild care are potential channels influencing the health outcome of the elderly
parents left behind. Therefore, I incorporate the Support to child1 dummy, Support fromchild1 dummy, Grandchild care to child1 dummy, Support to child2 dummy, Support
from child2 dummy, and Grandchild care to child2 dummy. In this paper, I estimate thepropensity score using a logit model.
Table 3 shows the estimation results with logit models, including first childmigrating case, and second child migrating case. Because the purpose of estimating thepropensity score is to match the treatment group and the control group, it is very
important to improve the goodness of fit in a logit model. Although there is no
straightforward criterion to follow, the pseudo-R2 seems to be used widely in empiricalstudies. To get a good pseudo-R2, I try to incorporate many associated factors mentioned
in the literature. Based on the estimation results of Table 3, I find that Age, the Rural
9

dummy, Hukou dummy, Child1 age, Child1 male dummy, Child1 education dummy,Child1 married dummy, Support from child1 dummy, Child2 male dummy, Child2
married dummy, and Grandchild care to child 2 dummy are good predictors for childmigration. With the development of economy, the economic inequality between eastern
coastal areas and western inland areas in China is increasing. More and more young
cohorts living in rural area choose to work outside.
5.1.1 Sample matching results (50+ with two children)
In this part, I discuss the matching results based on the nearest neighbor matching
method. Figure 1 shows the kernel density of the migration and non-migration groups
before and after matching for the two cases. I find that before matching there are
significant differences between migration and non-migration groups, indicating that
migration and non-migration groups are totally different in the pre-treatment variables.
After matching, the kernel density functions of migration and non-migration groups
become closer. Based on Figure 1, I find that treatment observations have enoughcontrolling observations nearby in the propensity score distribution. The important
assumption of common support is satisfied.
5.1.2 Comparison of ATTS (50+ with two children)
Table 4 shows the estimation results of average treatment effect on the treated(ATT). To ensure the robustness of estimated results, I calculate the ATTS using threekinds of matching methods, including nearest neighbor matching, radius matching, andkernel matching. Becker and Ichino (2002) show the details of these matching methods.
In addition, I use a bootstrap with 500 replications to obtain the standard errors of ATTs.
Regarding the results of one child migrating for work, the estimated coefficientsare not statistically significant, consistent with my hypothesis. In the case of one childmigrating, because the sibling staying at home can provide more support for the parents
instead of the migrant child, the incentive of free riding is very strong for migrantchildren and they would only give few remittances to their parents. Because
substitutable relationship exists among siblings, the health status of the elderly parents
may not be influenced by one child migrating for work.
5.1.3 Balancing test results (50+ with two children)
Employing a propensity score matching analysis is necessary to test the balance
between the treatment group and the control group. The balancing test results using thenearest-neighbor matching method are shown in Table 5. I find that there are significant
10differences between the treatment group and the control group. However, after matching,
I find that the significant differences between the two groups disappear. None of themean differences is statistically significant, indicating that the balancing assumption issatisfied in my paper.

5.2 The estimation results (60+with two children)
Although using 50+ with two children sample provide some convincing evidence
to support my hypothesis, many respondents may not demand physical support fromtheir migrant children. Next, I will use the respondents aged 60 years and older tofurther test my hypotheses, because the elderly parents are old enough to demand
physical and emotional support from their children. I list the descriptive statistics of 60+
with two children sample in Table 6. To employ propensity score matching, I need toestimate the propensity score using a logit model. Regarding the pretreatment variables,
I incorporate the same factors used in the previous analysis. The estimation results of
the logit model are shown in Table 7. In the case of first child migrating, I exclude
child1 male dummy due to collinearity.
Regarding the matching results, I mainly use the matching results of a nearest
neighbor matching method. Figure 2 shows the kernel density of the migration andnon-migration groups before and after matching for the three migrant cases. Before
matching, there are significant differences in the two groups, indicating that migrationand non-migration groups have large variance among the pre-treatment variables. By
comparing the descriptive statistics shown in Table 6, I further confirm this fact.
However, after matching, the kernel density functions of migration and non-migrationgroups become closer than before, especially in the lower propensity score. From Figure
2, I also confirm that the common support assumption is satisfied.
Table 8 shows the estimation results of ATTs based on nearest neighbor matching,radius matching, and kernel matching. None of estimation results is statisticallysignificant providing convincing evidence for my hypothesis. In addition, I also confirm
that the sequence of the child sibling migrating for work does not influence the healthstatus of the elderly parents.
Regarding the results of the balancing test, I find that before matching there arehuge differences between the treatment and control groups among the pre-treatment
variables listed in Table 9. After matching, the results of the mean difference test showthat the mean differences between the treatment and control groups are not statisticallysignificant, indicating that the two groups match very well.

116. Robustness check
There is one disadvantage of propensity score matching method that I need tocontrol associated variables as many as possible. However, there are some unobservablevariables influencing child migration and health status of the elderly. This may
introduce some bias into my estimation results. By using DID-PSM, I try to control
some time-invariant unobservable variables and relieve the potential problem ofpropensity score matching method. To implement this robustness check, I use
two-period panel data from 2010 and 2012 waves of CFPS. Regarding propensity scorematching, I include the same pretreatment variables as above. The estimation results forfirst child migrating and second child migrating are shown in Table 10 and Table 11,
respectively. Neither of estimation results is statistically significant providing
convincing evidence for my hypothesis.

7. Discussion and conclusions
Out-migration for work prevails in developing countries such as China. The impact
of child migration on the health status of elderly parents has become an important issue.
However, regarding the impact of child migration, previous studies do not provide adefinitive conclusion due to the problem of self-selection of child migration.
This study employs the propensity score matching method to estimate the impact
of child migration on the health status of the elderly left behind, using data from the2010 wave of the CFPS. Because the social security system of China is weakly
developed, supporting the elderly in China mainly depends on adult children.
Consequently, child migration influences the provision of economic support, physicalsupport, and emotional support for the elderly and further influences the health status ofelderly parents. Because a substitutive relationship among child siblings exists in mosthouseholds, an increase in the number of child siblings complicates the issue of
supporting the elderly. To simplify my analysis, I chose respondents aged 50 years andabove with only two children as research objects. In this paper, one hypothesis is tested.
Hypothesis: in the case of one child migrating for work, child migration would not
influence the health status of the elderly left behind. According to my estimation results,
I find enough convincing evidence to support my hypothesis. Although the existing offree riding behavior for migrant children reduces the transfers for their parents, thesiblings staying in the hometown provide more informal care for their parents. Thus,
one child migration has no impact on the health status of the elderly left behind.
12

Because the social security system is weakly developed, supporting the elderly
depends mainly on adult children in China. With the implementation of the one childpolicy, the optimal number of children is limited. Traditional forms of support of theelderly have begun to collapse. However, with the enlarging of the economic gap
between coastal areas and inland areas, an increasing number of young people arechoosing to migrate for work. Therefore, we want to know how child migrationinfluences the health status of the elderly left behind in China. These findings canprovide evidence for policy making targeting the elderly who are left behind. Because
Chinese government abolished one-child policy and allowed young couples to have twochildren, in the future more and more elderly Chinese people will have two children.
Since the channel of remittance may positively influence the health outcome of theelderly, it is necessary to maintain access to the formal care market and the health caremarket for the elderly. If the elderly can easily purchase some services from the formalcare market or the health care market, the benefit of remittances will be extended.
However, the behavior of free riding may hinder the benefit of remittances. Therefore,
how to deal with free riding is strongly associated with the health status of the elderlyleft behind.
Although this study provides some convincing evidence for the impact of childmigration on the health status of the elderly left behind, there are some limitations. First,
because I chose respondents having only two children as research objects to simplify thesituation of child migration, the estimated results may not be applied to other situations.
Second, the propensity score matching method uses observable pretreatment variables
to estimate the propensity score. Although I incorporate many factors into the logit
model, I cannot deal with the problem of omitted variables. In the future, otherassociated analysis methods should be used to deal with this issue.

13

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Lian, Y., Li, W., Huang, B., (2014), The impact of children migration on the health andlife satisfaction of parents left behind, China Economic Quarterly, 14(1),185-202. (in Chinese)
Marcus, H.B., Ruth, P., Tobias, S., (2015), Alone but better off? Adult child migrationand health of elderly parents in Moldova, Journal of Health Economics, 39,
211-227.
Stohr, T., (2015), Siblings’ interaction in migration decisions: Who provides for theelderly left behind?, Journal of Population Economics, 28, 593-629.
Tse, W., (2013), Migration and health outcomes of left-behind elderly in rural China,
Working paper. Available at:
http://poseidon01.ssrn.com/delivery.php?ID=884112031001097102088
0171140170020240010240320070490530051211261020851120881140
8212112402505611511400512412603109909810311010102303905602
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EXT=pdf 2016.12.29 accessed.
Xie, Y., Qiu, Z., Lu, P., (2012), China family panel studies: Sample design for the 2010
baseline survey, In Technical Report Series: CFPS-1. Beijing: Institute ofSocial Science Survey, Beijing University. (in Chinese)

Table
Table 1 Endogeneity variables and Instrumental variables
Authors

Endogeneity

Instrumental Variables

Variable

Region1. the urban unemployment rate
Lian et al. (2014)

child migration

2. the change rate of employment structure

China(1985–2009)
1. the proportion of migration population
Tse (2013)

child migrationin the village
2. the female proportion of the adultChina

children
Antman (2016)

Antman (2011)

child migration

paternal
migration

Hildebrandt andpaternalDavid (2005)

migration

Marcus et al.

child migration

1. the fraction of female children
2. the fraction of married children

Mexico1. U.S. city-level employment statistics in
two industries popular with Mexican

Mexicoimmigrants
1. Historic state-level migration rate

Mexico1. Network-growth interaction

Moldova16

(2015)

2. Military base
1. Network-growth interaction

Stohr (2015)

child migration

2. Network-growth interaction × number

Moldovaof children

Table 2 Descriptive Statistics (50+ with two children)
First child migrating

Second child migrating

Treatment

Control

Treatment

Control

0.372

0.364

0.341

0.366

(0.484)(0.481)(0.475)(0.482)57.26559.34656.81059.343(5.534)(6.391)(4.745)(6.417)

3.310

3.563

3.250

3.563

(0.681)(0.809)(0.578)(0.812)

0.609

0.509

0.527

0.516

(0.489)(0.500)(0.501)(0.500)

0.719

0.526

0.732

0.528

(0.450)(0.499)(0.444)(0.499)

0.854

0.701

0.893

0.701

(0.354)(0.458)(0.310)(0.458)

Dependent variable
Health dummy
Individual characteristics
Age

Age squares/1,000

Male dummy

Rural dummy

Hukou dummy

17Education dummy

Married dummy

Working dummy

Lnincome

0.154

0.129

0.117

0.132

(0.362)(0.335)(0.322)(0.339)

0.945

0.910

0.927

0.912

(0.229)(0.286)(0.261)(0.284)

0.561

0.413

0.556

0.416

(0.497)(0.493)(0.498)(0.493)

6.578

5.815

5.800

5.886

(3.468)(4.076)(3.793)(4.050)

0.202

0.203

0.210

0.202

(0.402)(0.402)(0.408)(0.402)30.17833.69030.73233.588(6.154)(6.826)(5.534)(6.888)

0.850

0.636

0.546

0.662

(0.358)(0.481)(0.499)(0.473)

0.158

0.164

0.083

0.170

(0.366)(0.371)(0.276)(0.376)

0.581

0.834

0.839

0.811

(0.494)(0.372)(0.368)(0.392)

0.016

0.047

0.015

0.046

(0.125)(0.211)(0.120)(0.210)

0.087

0.077

0.020

0.082

(0.282)(0.267)(0.139)(0.275)

0.075

0.090

0.044

0.092

(0.264)(0.286)(0.205)(0.289)28.58930.72727.02030.806(6.805)(7.237)(5.361)(7.277)

0.395

0.543

0.810

0.510

(0.490)(0.498)(0.393)(0.500)

0.107

0.192

0.171

0.186

(0.309)(0.394)(0.377)(0.389)

0.696

0.707

0.454

0.725

(0.461)(0.455)(0.499)(0.447)

0.012

0.040

0.020

0.039

(0.108)(0.197)(0.139)(0.195)Chronic disease dummyChild characteristics
Child1 age

Child1male dummyChild1education dummy

Continued
Child1married dummy

Support to child1 dummy

Support from child1 dummyGrandchild care to child1 dummyChild2 ageChild2 male dummyChild2 education dummyChild2 married dummy

Support to child2 dummy18Support from child2 dummyGrandchild care to child2 dummy
Observations

0.059

0.077

0.024

0.080

(0.237)(0.267)(0.155)(0.271)

0.024

0.069

0.102

0.063

(0.152)(0.254)(0.304)(0.242)

253

2,719

205

2,676

Note: 1. Standard deviations are in the parentheses. 2. Data source: 2010 wave of China Family
Panel Studies.

Table 3 The Estimation Results of Logit Models (50+ with two children)
Dependent variable

First child migrating

Second child migratingChildmigration1

Childmigration2-0.302*0.128(0.183)(0.259)2.392-1.058(1.480)(2.141)0.121-0.035(0.156)(0.170)0.666***

0.421**(0.168)(0.185)0.354

0.970***(0.221)(0.272)

0.230

0.127

(0.212)(0.254)0.338-0.125(0.305)(0.301)

Individual characteristics
Age

Age squares/1000

Male dummy

Rural dummy

Hukou dummy

Education dummy

Married dummy

19Working dummy

Lnincome

0.038

0.107

(0.156)(0.168)0.037*-0.018(0.021)(0.021)

0.062

0.184

(0.175)(0.189)-0.076***-0.041(0.022)(0.029)1.074***-0.251(0.191)(0.160)0.229-0.534*(0.212)(0.288)-1.012***0.707***(0.171)(0.228)-0.7270.079(0.632)(0.760)Chronic disease dummyChild Characteristics
Child1 age

Child1male dummyChild1education dummyChild1married dummy

Support to child1 dummy

Continued
Support from child1 dummyGrandchild care to child1 dummyChild2 ageChild2 male dummyChild2 education dummyChild2 married dummy

Support to child2 dummy

Support from child2 dummyGrandchild care to child2 dummy
20

0.958***-0.849(0.361)(0.677)0.409-0.359(0.291)(0.414)0.020-0.020(0.021)(0.025)-0.448***1.286***(0.146)(0.189)-0.3420.221(0.236)(0.216)0.443**-0.942***(0.194)(0.197)-0.030-0.185(0.724)(0.680)-0.395-0.638(0.403)(0.629)-0.556

1.632***(0.454)(0.326)

Pseudo R2

0.142

0.157

Note: 1. Standard errors are in the parentheses. 2. ***, ** and * represent significance at 1%, 5%,
and 10% levels, respectively.

Table 4 Estimation Results of ATT (50+ with two children)

First childmigrated

Second childmigrated

Matching method

ATT

Bootstrap S.E.

Z

Nearest neighbor matching-0.017

0.047

-0.37

Radius matching-0.007

0.043

-0.17

Kernel matching-0.015

0.033

-0.46

Nearest neighbor matching

0.016

0.054

0.30

Radius matching-0.017

0.052

-0.33

Kernel matching-0.018

0.039

-0.47

Note: 1. ***, ** and * represent significance at 1%, 5%, and 10% levels, respectively. 2. Standard
errors are calculated using a Bootstrap with 500 replications.

21

Table 5 The Results of Balancing Test (50+ with two children)
First child migrating

Second child migrating

Treatment

ControltTreatment

ControltU

57.26559.346-5.010***56.81059.343-5.540***M

57.26556.9390.660

56.81056.665

0.320

U

3.310

3.563

-4.820***

3.250

3.563

-5.420***

M

3.310

3.273

0.610

3.250

3.232

0.330

U

0.609

0.509

3.050***

0.527

0.516

0.290

M

0.609

0.572

0.840

0.527

0.520

0.130

U

0.719

0.526

5.940***

0.732

0.528

5.670***

M

0.719

0.719

0.000

0.732

0.738

-0.150

U

0.854

0.701

5.160***

0.893

0.701

5.900***

M

0.854

0.868

-0.470

0.893

0.899

-0.220

U

0.154

0.129

1.130

0.117

0.132

-0.620

M

0.154

0.129

0.810

0.117

0.112

0.150

U

0.945

0.910

1.880*

0.927

0.912

0.740

M

0.945

0.949

-0.200

0.927

0.914

0.490

U

0.561

0.413

4.560***

0.556

0.416

3.910***

Individual characteristics
Age

Age squares/1000

Male dummy

Rural dummy

Hukou dummy

Education dummy

Married dummy
Working dummy

22

M

0.561

0.568

-0.150

0.556

0.533

0.460

U

6.578

5.815

2.880***

5.801

5.886

-0.290

M

6.578

6.646

-0.210

5.801

5.771

0.080

U

0.202

0.203

-0.050

0.210

0.202

0.250

M

0.202

0.178

0.680

0.210

0.207

0.080

U

30.17833.690-7.890***30.73233.588-5.800***M

30.17830.231-0.10030.73230.688

0.080

U

0.850

0.636

6.880***

0.546

0.662

-3.380***

M

0.850

0.850

0.000

0.546

0.515

0.630

U

0.158

0.164

-0.260

0.083

0.170

-3.250***

M

0.158

0.136

0.710

0.083

0.098

-0.520

U

0.581

0.835

-10.050***

0.839

0.811

0.990

M

0.581

0.560

0.480

0.839

0.837

0.040

U

0.016

0.047

-2.290**

0.015

0.046

-2.130**

M

0.016

0.014

0.120

0.015

0.010

0.450

Lnincome

Chronic disease dummyChild characteristics
Child1 age

Child1 male dummyChild1education dummyChild1married dummy

Support to child1 dummy
Continued
U

0.087

0.077

0.550

0.020

0.082

-3.240***

M

0.087

0.080

0.270

0.020

0.021

-0.120Grandchild care to

U

0.075

0.090

-0.800

0.044

0.092

-2.340**child1 dummy

M

0.075

0.076

-0.060

0.044

0.042

0.080

U

28.58930.727-4.520***27.02030.806-7.300***M

28.58928.4940.160

27.02026.909

0.200

U

0.395

0.543

-4.510***

0.810

0.510

8.400***

M

0.395

0.406

-0.240

0.810

0.828

-0.470

U

0.107

0.192

-3.350***

0.171

0.186

-0.530

M

0.107

0.109

-0.100

0.171

0.164

0.180

U

0.696

0.707

-0.390

0.454

0.725

-8.320***

M

0.696

0.668

0.670

0.454

0.488

-0.690

U

0.012

0.040

-2.280**

0.020

0.039

-1.440

M

0.012

0.013

-0.130

0.020

0.021

-0.120

U

0.059

0.077

-1.030

0.024

0.080

-2.880***

M

0.059

0.053

0.320

0.024

0.020

0.340

Grandchild care to

U

0.024

0.069

-2.800***

0.102

0.063

2.230**

child2 dummy

M

0.024

0.020

0.300

0.102

0.101

0.050

Support from child1 dummyChild2 ageChild2 male dummyChild2 education dummyChild2 married dummy

Support to child2 dummy

Support from child2 dummy

Note: 1. ***, ** and * represent significance at 1%, 5%, and 10% levels, respectively.
23

Table 6 Descriptive Statistics (60+ with two children)
First child migrating

Second child migrating

Treatment

Control

Treatment

Control

0.373

0.343

0.314

0.345

(0.488)(0.475)(0.471)(0.476)66.17666.29965.11466.335(4.934)(5.310)(4.490)(5.313)

4.403

4.424

4.259

4.429

(0.676)(0.743)(0.614)(0.743)

0.686

0.560

0.600

0.565

(0.469)(0.497)(0.497)(0.496)

0.765

0.403

0.657

0.413

(0.428)(0.491)(0.482)(0.493)

0.902

0.531

0.829

0.540

(0.300)(0.499)(0.382)(0.499)

0.039

0.142

0.086

0.139

Dependent variable
Health dummy
Individual characteristics
Age

Age squares/1,000

Male dummy

Rural dummy

Hukou dummy
Education dummy

24Married dummy

Working dummy

Lnincome(0.196)(0.349)(0.284)(0.346)

0.882

0.847

0.829

0.850

(0.325)(0.360)(0.382)(0.357)

0.392

0.220

0.457

0.221

(0.493)(0.415)(0.505)(0.415)

6.571

5.540

5.029

5.613

(3.109)(4.178)(3.454)(4.158)

0.216

0.235

0.286

0.232

(0.415)(0.424)(0.458)(0.422)37.07839.80137.97139.725(6.925)(6.457)(6.041)(6.517)

1.000

0.705

0.743

0.719

(0.000)(0.456)(0.443)(0.450)

0.098

0.173

0.029

0.175

(0.300)(0.379)(0.169)(0.380)

0.784

0.893

0.914

0.887

(0.415)(0.309)(0.284)(0.317)

0.078

0.133

0.086

0.132

(0.272)(0.339)(0.284)(0.338)

0.431

0.219

0.114

0.234

(0.500)(0.414)(0.323)(0.424)

0.373

0.256

0.257

0.262

(0.488)(0.437)(0.443)(0.440)35.94137.02033.31437.097(8.310)(6.692)(6.493)(6.759)

0.529

0.550

0.943

0.534

(0.504)(0.498)(0.236)(0.499)

0.078

0.208

0.057

0.207

(0.272)(0.406)(0.236)(0.405)

0.824

0.887

0.800

0.887

(0.385)(0.317)(0.406)(0.317)

0.059

0.115

0.114

0.112

(0.238)(0.319)(0.323)(0.316)

0.294

0.219

0.143

0.226

Chronic disease dummyChild characteristics
Child1 age

Child1male dummyChild1education dummy

Continued
Child1married dummy

Support to child1 dummy

Support from child1 dummyGrandchild care to child1 dummyChild2 ageChild2 male dummyChild2 education dummyChild2 married dummy

Support to child2 dummy
Support from child2 dummy

25

Grandchild care to child2 dummy
Observations(0.460)(0.414)(0.355)(0.419)

0.118

0.196

0.600

0.178

(0.325)(0.398)(0.497)(0.383)

51

957

35

973

Note: 1. Standard deviations are in the parentheses.2. Data source: 2010 wave of China Family Panel
Studies.

Table 7 Estimation Results of Logit Model (60+ with two children)
Dependent variable

First child migrating

Second child migratingChildmigration1

Childmigration2

0.512

0.212

(0.639)(0.906)-3.224-1.422(4.639)(6.638)

0.185

0.006

(0.362)(0.436)

0.918**

0.216(0.384)(0.438)1.530***

1.491***(0.578)(0.641)-0.8910.907(0.841)(0.775)0.392-0.380(0.518)(0.545)

0.015

0.234

Individual characteristics
Age

Age squares/1000

Male dummy

Rural dummy

Hukou dummy

Education dummy

Married dummy
Working dummy26

(0.347)(0.454)0.099**-0.056(0.049)(0.052)0.047

0.827*(0.387)(0.450)-0.100**0.050(0.041)(0.062)

Lnincome

Chronic disease dummyChild Characteristics
Child1 age

Child1male dummy-Child1education dummyChild1married dummy

Support to child1 dummy

0.297(0.471)0.419-0.945(0.602)(1.147)-0.846*0.883(0.435)(0.710)-0.2090.311(0.705)(0.859)Continued
Support from child1 dummyGrandchild care to child1 dummy

1.039***-0.623(0.392)(0.786)

0.935***-0.270(0.350)(0.472)0.074*-0.103*(0.038)(0.055)-0.0932.225***(0.331)(0.759)-0.372-0.613(0.605)(0.835)-0.488-1.006*(0.479)(0.552)

0.043

0.078

(0.806)(0.760)-0.271-0.532(0.423)(0.734)-0.4902.160***(0.494)(0.465)

Child2 ageChild2 male dummyChild2 education dummyChild2 married dummy

Support to child2 dummy

Support from child2 dummyGrandchild care to child2 dummy27

Pseudo R2

0.197

0.293

Note: 1. Childmigration1, which is also a discrete variable, equals one if the first child migrated forwork and the second child stays at home, and zero otherwise; The definition of Childmigration2 issimilar to Childmigration1, equals one if the second child migrated for work and the first child stays
at home, and otherwise 0. 2. ***, ** and * represent significance at 1%, 5% and 10% level,
respectively. 3. Standard errors are in the parentheses. 4. Child1male dummy is excluded due tocollinearity.

Table 8 Estimation Results of ATT (60+ with two children)

First child migrating

Second child migrating

Matching method

ATT

Bootstrap S.E.

Z

Nearest neighbor matching

0.065

0.106

0.62

Radius matching

0.076

0.138

0.55

Kernel matching-0.010

0.093

-0.11

Nearest neighbor matching-0.029

0.125

-0.23

Radius matching

0.070

0.203

0.34

Kernel matching

0.027

0.108

0.25

Note: 1. ***, ** and * represent significance at 1%, 5%, and 10% levels, respectively. 2. Standard
errors are calculated using a Bootstrap with 500 replications.

28

Table 9 Balancing Test (60+ with two children)
First child migrating

Second child migrating

Treatment

ControltTreatment

ControltU

66.17666.299-0.16065.11466.335-1.340M

66.17666.869-0.68065.11464.476

0.650

U

4.403

4.424

-0.190

4.260

4.429

-1.330

M

4.403

4.500

-0.680

4.260

4.171

0.660

U

0.686

0.560

1.770*

0.600

0.565

0.410

M

0.686

0.595

0.960

0.600

0.590

0.080

U

0.765

0.403

5.150***

0.657

0.413

2.880***

M

0.765

0.752

0.150

0.657

0.695

-0.340

U

0.902

0.531

5.260***

0.829

0.540

3.390***

M

0.902

0.902

0.000

0.829

0.819

0.100

U

0.039

0.142

-2.090**

0.086

0.139

-0.900

M

0.039

0.020

0.580

0.086

0.048

0.630

U

0.882

0.847

0.680

0.829

0.850

-0.350

M

0.882

0.810

1.000

0.829

0.800

0.300

U

0.392

0.220

2.850***

0.457

0.221

3.280***

Individual characteristics
Age

Age squares/1000

Male dummy

Rural dummy

Hukou dummy

Education dummy

Married dummy
Working dummy

29

M

0.392

0.399

-0.070

0.457

0.419

0.320

U

6.571

5.540

1.740*

5.029

5.613

-0.820

M

6.571

5.901

1.020

5.029

5.848

-0.920

U

0.216

0.235

-0.320

0.286

0.232

0.730

M

0.216

0.183

0.410

0.286

0.229

0.540

U

37.07839.801-2.920***37.97139.725-1.570M

37.07837.510-0.29037.97137.629

0.250

U

-

-

-

0.743

0.719

0.300

M

-

-

-

0.743

0.657

0.770

U

0.098

0.173

-1.400

0.029

0.175

-2.270**

M

0.098

0.059

0.730

0.029

0.029

0.000

U

0.784

0.893

-2.410**

0.914

0.887

0.500

M

0.784

0.758

0.310

0.914

0.933

-0.300

U

0.078

0.133

-1.120

0.086

0.132

-0.790

M

0.078

0.072

0.120

0.086

0.076

0.140

Lnincome

Chronic disease dummyChild characteristics
Child1 age

Child1 male dummyChild1 education dummyChild1married dummy

Support to child1 dummy
Continued
U

0.431

0.219

3.520***

0.114

0.234

-1.660*

M

0.431

0.438

-0.070

0.114

0.133

-0.240Grandchild care to

U

0.373

0.256

1.850*

0.257

0.262

-0.070child1 dummy

M

0.373

0.399

-0.270

0.257

0.200

0.560

U

35.94137.020-1.11033.31437.097-3.260***M

35.94137.105-0.75033.31432.714

0.400

U

0.529

0.550

-0.280

0.943

0.534

4.820***

M

0.529

0.484

0.460

0.943

0.943

0.000

U

0.078

0.208

-2.250**

0.057

0.207

-2.170**

M

0.078

0.078

0.000

0.057

0.038

0.370

U

0.824

0.887

-1.380

0.800

0.887

-1.580

M

0.824

0.869

-0.640

0.800

0.771

0.290

U

0.059

0.115

-1.240

0.114

0.112

0.040

M

0.059

0.059

0.000

0.114

0.124

-0.120

U

0.294

0.219

1.250

0.143

0.226

-1.160

M

0.294

0.294

0.000

0.143

0.171

-0.320Grandchild care to

U

0.118

0.196

-1.390

0.600

0.178

6.340***

child2 dummy

M

0.118

0.118

0.000

0.600

0.629

-0.240Support from child1 dummyChild2 ageChild2 male dummyChild2 education dummyChild2 married dummy

Support to child2 dummy

Support from child2 dummy

Note: 1. ***, ** and * represent significance at 1%, 5%, and 10% levels, respectively.
30

Table 10 DID-PSM estimation results for first child migrating(50 years old with two children)
Control

TreatedDiff (T-C)

Standard ErrorstBaseline

0.387

0.372

-0.015

0.017

-0.88

Follow-up

0.064

0.045

-0.019

0.032

-0.6

-0.004

0.037

-0.12

Diff-in-Diff

31

Table 11 DID-PSM estimation results for second child migrating(50 years old with two children)
Control

TreatedDiff(T-C)

Standard ErrorstBaseline

0.352

0.341

-0.011

0.017

-0.63

Follow-up

0.062

0.049

-0.013

0.029

-0.46

-0.003

0.034

-0.08

Diff-in-Diff

32

Figures
Figures 1 Kernel Density of the Migration and Non-migration Groups(50+ with two children)(1) Before Matching

first child migrating(2) After Matching

6

10

8

6

DensityDensity4

Migration
Nonmigration

Migration
Nonmigration

4

2

2
0

0

0.0

0.0

0.2

0.4
Propensity Score

0.6(3) Before Matching

0.2

0.8

second child migrating

0.4
Propensity Score

0.6

0.8

(4) After Matching

15

6

10

DensityDensity4
Migration
Nonmigration

Migration
Nonmigration

5

2

0
0.0

0.2

0.4
Propensity Score

0.6

0.8

0
0.0

33

0.2

0.4
Propensity Score

0.6

0.8

Note: 1) Matching method is nearest neighbor matching.

Figures 2 Kernel Density of the Migration and Non-migration Groups(60+ with two children)(1) Before Matching

first child migrating(2) After Matching

20
4

3

DensityDensity15

Migration
Nonmigration10

Migration
Nonmigration

2

5

1

0

0

0.0

0.2

0.4
Propensity Score

0.6(3) Before Matching

0.8

0.0

second child migrating

0.2

0.4
Propensity Score

0.6

0.8

(4) After Matching

50
4

40

Migration
Nonmigration
20

DensityDensity330
Migration
Nonmigration

2

1

10

0

0

0.0

0.2

0.4
Propensity Score

0.6

0.8

34

0.0

0.2

0.4
Propensity Score

0.6

0.8

Note: 1) Matching method is nearest neighbor matching.

35