This document summarizes a study that examines the impacts of parental migration on cognitive development in children left behind in rural China. Using test score data from over 5,000 children in rural China, the study finds: 1) Being left behind by both parents significantly reduces children's math and Chinese test scores by around 5 percentile points, while being left behind by only one parent has smaller and insignificant impacts. 2) Only the absence of both parents is associated with lower family investments in after-school tutoring according to cross-sectional evidence. 3) The results suggest that the absence of both parents, which is common in rural China, has more serious negative consequences for children's education than the absence of a single

1. The Impacts of Parental Migration on Children
Left-Behind: Evidence from Rural China
Hongliang Zhang, Jere R. Behrman, C. Simon Fan,
Xiangdong Wei, and Junsen Zhangy
September 2013
Abstract
Many children worldwide are left-behind by parents migrating for work –over 60
million in rural China, almost half of whom are left-behind by both parents. While
previous literature considers impacts of one parent absent on educational inputs (e.g.,
study time, school enrollment, schooling attainment), this study investigates directly
impacts on children’s learning outcomes (test scores) and distinguishes impacts of ab-
sence of one versus both parents. Using dynamic panel methods that control for both
unobserved heterogeneities and endogeneity in parental absence with data collected by
the authors from rural China, estimates indicate signi…cant negative impacts of being
left-behind by both parents on children’s cognitive development, reducing their con-
temporary achievements by 5.0 percentile points for math and 4.7 percentile points for
Chinese, but much smaller insigni…cant impacts of being left-behind by one parent.
Cross-sectional evidence indicates that only absence of both parents is associated with
substantially lower family inputs in after-school tutoring.
JEL Classi…cations: O15, J12, J13
Keywords: left-behind children, migrating parents, cognitive achievement, China
The authors are grateful to the funding support provided by the Hong Kong Research Grants Council
General Research Fund (No. 458910), the CUHK South China Programme and Grand Challenges Canada
Grant 0072-03. They also thank the Educational Bureau of the Longhui County in China for administrative
support and Jia Wu for excellent research assistance.
y
Hongliang Zhang, hongliang@cuhk.edu.hk, Chinese University of Hong Kong; Jere R. Behrman,
jbehrman@econ.upenn.edu, University of Pennsylvania; C. Simon Fan, fansimon@ln.edu.hk, Lingnan Univer-
sity; Xiangdong Wei, xdwei@ln.edu.hk, Lingnan University; Junsen Zhang, jszhang@cuhk.edu.hk, Chinese
University of Hong Kong.
1

2. 1 Introduction
One in three children under age 17 in rural China is living without one or both parents who
have migrated in search of work in cities. Almost half of these children have been left-behind
by both parents.1
Despite its degree and scale, the “left-behind children” phenomenon in
China remains understudied because of both theoretical ambiguities and empirical challenges.
The existing literature has long highlighted the various channels through which parental
migration can a¤ect the human capital development of children left-behind (e.g., Stark,
1993; Haveman and Wolfe, 1995; Dustman and Glitz, 2011). On the one hand, parents
increase their earnings through migration and remittances of these earnings can ease the
household budget constraint and thereby increase household spending on education and
reduce child labor.2
This theoretical prediction has been empirically supported by studies
on the e¤ect of remittances from migrants on children left-behind in El Salvador, Guatemala,
Mexico and Philippine (Cox Edward and Ureta, 2003; Adams and Cuecuecha, 2010; Alcaraz,
Chiquiar, and Salcedo, 2012; Yang, 2008). On the other hand, parental migration inherently
leads to parental absence from home, which can have negative e¤ects on children left-behind
through channels such as the loss of local earnings and labor, the lack of parenting inputs,
and the psychological cost associated with family separation.3
Moreover, parental migration
also increases the migration prospects of children and can induce more or less educational
investment in children depending on the di¤erence in the rates of return to human capital
between the migration destination and the place of origin (Beine, Docquier, and Rapoport,
2008). Therefore, the sign of the overall e¤ect of parental migration on the education of
children left-behind is a priori unclear and remains an empirical question.
Recently, there is a growing empirical literature that examines the e¤ects of parental
migration on the outcomes of children left-behind, focusing mainly on the dimensions of
time allocations and schooling attainment. Antman (2001), for example, …nds that a Mexican
father’s migration to the U.S. decreases study hours and increases work hours for children
left-behind. Chang, Dong, and Macphail (2011) and Chen (2013) both employ the China
Health and Nutrition Survey (CHNS) to examine the time allocations of left-behind children
1
See Section 2.1 for the source of these …gures.
2
For a survey of the remittances literature, see Rapoport and Docquier (2006) and Yang (2011).
3
See Antman (2013) for a survey of the literature on the adverse e¤ects of parental absence.
2

3. in China, and …nd that children of migrant households spend more time in household work.4
In contrast to the consistent results on children’s time allocations, …ndings on children’s
schooling attainment are mixed, even among di¤erent studies of the same context. For
example, in studying the impact of Mexican emigration to the U.S. on children’s schooling
attainment, McKenzie and Rapoport (2011) …nd a negative e¤ect of living in a migrant
household on schooling of older children left-behind, while Antman (2012) reports a positive
e¤ect of paternal migration on the schooling attainment for girls.5;6
This paper examines the immediate net impacts of parental migration on the cognitive
skills of their children left-behind in rural China. It makes two important contributions to
the existing literature. First, we are able to distinguish between absence of one versus both
parents and estimate their e¤ects separately because of the large numbers of children in
both categories. Clearly, the learning implications for children of a family structure with
one parent at home can be drastically di¤erent from that with neither parent at home. The
phenomenon of “left-behind children”elsewhere almost entirely refers to cases in which one
of the two parents (usually the father) is absent from home; in contrast, in rural China, often
both parents migrate simultaneously. If paternal and maternal inputs are closer substitutes in
the production of child human capital than those of other caregivers, such as grandparents,
the absence of both parents has larger impacts on child human capital and may deserve
greater policy attention than the commonly considered cases of the absence of a single parent.
Nonetheless, research on the impacts of migration of both parents on children left-behind
is very rare. As for the two previous studies on left-behind children in China, Chen (2013)
limits her analysis to households with fathers away from home only, and Chang, Dong, and
Macphail (2011) restrict the e¤ects to be linear in the number of parents away.
4
Chen (2013) also …nds that mothers spend less time in both household and income-generating activities
after fathers’ migration, and interpret the …ndings as mothers’ non-cooperative behaviors as a result of
fathers’imperfect monitoring after migration.
5
McKenzie and Rapoport (2011) match the observed decrease in schooling to increased housework for
girls and migration for boys, and link the latter to the increased migration prospects of boys and lower
returns to schooling in the U.S. for Mexican migrants. Antman (2012) interprets the di¤erential e¤ects of
paternal migration by gender as the outcomes of increased bargaining power for mothers who spend the
marginal dollars on the education of girls.
6
There are also studies on the e¤ects of the migration of family members other than parents on children’s
education. For example, Kuhn (2007) shows that the migration of brothers was associated with improvements
in children’s pace of school completion in Bangladesh, while the migration of sisters was not. Gibson,
McKenzie, and Stillman (2011) use a migration lottery program to study the e¤ects of Togan emigrants to
New Zealand on the remaining household members and …nd insigni…cant impact of the migration of some
household members, typically uncles and aunts, on children’s school enrolment and schooling attainment.
3

4. Second, we measure children’s educational outcomes by their cognitive skills as re‡ected
by test scores in math and Chinese. That is, we investigate directly the impacts of parental
migration on the outcomes of their children’s education (i.e., what they learn) rather than
being limited to inputs into education such as study time, school enrollment, and schooling
attainment, which are the main themes of previous research. This distinction is important
because parental absence may have very di¤erent impacts on the time children devote to
education than on what they learn if parents provide inputs that are complements to the
time children devote to education. In that case, it is possible that parental absence generates
positive impacts on the time children spend on education but still negative impacts on their
learning outcomes. To the best of our knowledge, the only other paper that examines the
e¤ect of parental absence on children’s academic achievement is in the context of military
deployments (Lyle, 2006), which …nds a tenth of a standard deviation decline in the test
scores of enlisted soldiers’children.
The data used in this paper were collected by the authors from Longhui County in Hunan
Province of China. The county was selected for this study to represent one of the country’s
poorest rural areas with a high prevalence of parental absence: per capita GDP is less than
a quarter of the national average7
and over two-thirds of children are left-behind by one or
both parents. Working with the county’s educational bureau, we randomly selected over
5,000 third to …fth graders (9 to 11 year olds) enrolled in the county’s primary schools, and
collected longitudinal information on their parental absence status and test scores in math
and Chinese for every school term since their enrollment in the …rst term of grade 1. The
identi…cation strategy used in this paper follows the same spirit as Andrabi, Das, Khwaja,
and Zajonc (2011) and Mani, Hoddinott, and Strauss (2012), who respectively apply dynamic
panel methods to evaluate the e¤ect of private schooling on student achievement in Pakistan
and the impacts of investments in early schooling in rural Ethiopia. First, to address the
possibility that the contemporary parental migration status and child outcomes are shaped
by common past factors such as genetics and experience, we adopt a value-added speci…cation
of human capital accumulation to control for the impacts of all historical schooling inputs
and heritable endowments on current child outcomes. Second, we further include child …xed
e¤ects in the value-added model to control for unobserved individual heterogeneity in the
7
In 2010, the county’s per capita GDP was RMB 6,992, less than a quarter of the national average of
RMB 29,748.
4

5. speed of learning. That is, for children whose parents’migration status changes over time,
we identify the e¤ect of parental absence by comparing a child’s achievement progress in
periods with parental absence to his/her achievement progress in periods without parental
absence. Finally, even after controlling for lagged achievement and individual heterogeneity
in learning growth, changes in parental absence status may still be correlated with changes in
the time-varying component of the unobserved determinants of learning. To further address
this concern, we employ a GMM framework and instrument changes in parental absence
with its longer lags.
Our estimates show signi…cant adverse e¤ects of the absence of both parents on the
cognitive achievements of children left-behind, reducing their contemporary test scores by 5.0
and 4.7 percentile points in math and Chinese, respectively. However, we …nd that the e¤ect
of the absence of a single parent is much smaller –only about one-third of the magnitude of
that of the absence of both parents –and insigni…cant, suggesting that there may be a high
degree of substitution between fathers and mothers in educating children. That is, when only
one parent is away, the remaining parent may assume the roles of both, resulting in little
reduction in family inputs on children’s education. This hypothesis is also consistent with the
cross-sectional evidence that only the absence of both parents is associated with substantially
lower family inputs in after-school tutoring. As previous research suggests a key role of the
persistence parameter in estimating the value-added achievement function, in addition to
estimating the persistence parameter empirically, we also allow it to be exogenously assigned,
varying from 1.0 to 0.4 with decrements of 0.2. Our conclusion that only the absence of both
parents has signi…cant adverse e¤ects on children’s cognitive achievement is robust to the
choice of the persistence parameter value. These results suggest that the absence of both
parents, which is quite common in rural China, is a much more serious problem in shaping
the educational outcomes of the next generation than the usually considered cases elsewhere
of the absence of a single parent, and therefore deserves greater policy attention. Further,
we test for heterogeneous e¤ects for sons versus daughters and …nd, if anything, stronger
e¤ects for sons though the di¤erence is not statistically signi…cant. Finally we investigate
whether past parental absence status matters for a child’s contemporary learning progress,
but …nd no evidence of signi…cant e¤ects.
The remainder of this paper is organized as follows. Section 2 provides the background of
the “left-behind children”phenomenon, describes our data set, and presents the “…rst-look”
5

6. evidence of the relationship between parental absence status and children’s cognitive achieve-
ment progress based on a di¤erence-in-di¤erences strategy. Section 3 introduces our empir-
ical framework, which employs dynamic panel methods to evaluate the e¤ects of parental
absence on children’s cognitive achievements in a value-added achievement function. Section
4 presents our main estimation results. Section 5 discusses the regression diagnosis, the
robustness of our estimation results, and the cross-sectional relationship between parental
absence status and family inputs. Section 6 provides some concluding remarks.
2 Background and Data
2.1 China’s rural-to-urban migration and left-behind children
China started its household registration system, commonly known as the Hukou system, in
the mid-1950s. Under this system, rural residents were barred from entering cities to look for
jobs from the mid-1950s to the end of 1970s. The main purpose of this system was to stem a
‡ood of rural migrants to cities that would paralyze the infrastructure and cause huge social
problems there. However, since China embarked its economic reform in the late 1970s, there
has been a rising demand for cheap labor in cities. The government then gradually relaxed
its control of this system and allowed rural residents to come to cities to work. Ever since
the relaxation of this system in the beginning of the 1980s, millions of rural migrant workers
have come to cities to …nd jobs. According to the latest 2010 Population Census, there are
an estimated 210 million rural migrant workers now working in the cities, constituting nearly
a third of China’s urban population (National Bureau of Statistics, 2012). Such a huge wave
of rural to urban migration is unprecedented and has been called the largest peace-time
migration in history (Roberts et al. 2004).
Despite the Chinese government’s decision to allow rural residents to work in cities, it
has not dismantled its Hukou system. The rural migrant workers are still being treated as
“second-class” citizens and are usually without entitlements for city welfare including free
public education for children (e.g., Chen and Feng, 2011). As a consequence, the majority of
migrant parents choose to leave their children behind in the countryside, leading to a huge
left-behind children phenomenon in the countryside. According to the All-China Women’s
Federation’s (ACWF, 2013) report based on the 2010 Population Census, there are over 61
6

7. million children aged 17 years or below left-behind by one or both parents in the countryside,
accounting for 37.7 percent of rural children and 21.9 percent of all children in China, of
which 46.7 percent are left by both parents.
2.2 Data
This study uses data collected by the authors in Longhui County of Hunan Province in
Central China, which is among the poorest counties in the nation. According to ACWF
(2013), Hunan is also among the six provinces in China with more than half of the rural
children left-behind by one or both parents.8
The population of the county is about 1.2
million in 2011 and 90% of the population are rural residents. Working with the educational
bureau of Longhui County, we randomly selected …ve townships (out of a total of 26 townships
within the county’s jurisdiction) and collected both administrative and survey information
on all third to …fth graders enrolled in the 20 primary schools in these townships in April
2011. We choose to focus our study on primary-school-aged children in these three grades
for three reasons. First, primary school students are more vulnerable to parental absence.
Second, grade 3-5 students have enough past academic achievement records for us to build a
panel data on student academic achievements. Third, many secondary schools in rural areas
provide boarding facilities for needy students, therefore making it hard to isolate the impact
of parental absence on student learning.
Our sample consists of over 5,000 students, accounting for roughly one-…fth of all of the
students enrolled in grades 3 to 5 in the study county. The data were collected from three
sources. First, a student information sheet was …lled out by the master teacher of each
class, with information from the school’s administrative records on each student’s …nal exam
scores in math and Chinese for every school term since the student enrolled in the school.9
These exams were designed by either the township’s school board or each individual school
to assess students’end-of-term mastery of academic subjects covered in each school term.
Although raw scores from di¤erent schools are not directly comparable due to di¤erences
in the exam contents, raw scores are still informative about students’relative performances
within the same school. Because students rarely switch classes in primary school, we thus
8
The other …ve provinces are Anhui, Chongqing, Jiangsu, Jiangxi, and Sichuan.
9
In China, a school year is divided into two school terms: Fall term (September to January) and Spring
term (February to June).
7

8. measure a child’s cognitive achievement by his/her percentile rank in class. Second, a student
survey was conducted in class under the instruction of our surveyors, collecting information
on birth date, height, weight, time allocations after school, whether parents or others helped
with study, and self-reported satisfaction levels on their relationships with parents, other
family members, teachers, and classmates. Third, a household survey was completed by stu-
dents’parents or primary caregivers when both parents were absent from home10
, collecting
information on family composition, parents’ages, schooling attainment, migration status,
main economic activities, and incomes. Very important to this study, we asked parents or
caregivers in the absence of parents to report retrospectively both the paternal and maternal
migration status for every school term since the children enrolled in the …rst term of grade
1.
We then linked the history of parental migration status from the household survey to the
longitudinal test scores from the student information sheet to construct a panel for up to …ve,
seven, and nine school terms for the third, fourth, and …fth graders, respectively. We impose
a set of restrictions to con…ne our analysis to students with complete histories of parental
migration status and test scores. First, we exclude 534 students (s10.1 percent) who started
schooling elsewhere and later transferred to their current schools.11
Second, we exclude 114
students (s2.2 percent) with missing test score information in one or more school terms.
As primary school enrollment is almost universal in China,12
the missing test scores were
mainly due to student absence on the exam days or temporary transfers to other schools.
Finally, we further exclude 6 students (s0.1 percent) with incomplete information on their
parental migration histories. Thus, our …nal data set consists of 4,653 students –1,702 third
graders, 1,584 fourth graders, and 1,367 …fth graders –for whom the full histories of parental
migration status and test scores are available since the beginning of primary school.
Table 1 shows the summary statistics for students in our …nal sample by their current
parental absence status. Throughout the paper, we de…ne a parent as absent from home in
a school term if he/she was away from home for more than half of the time. For the school
10
The primary caregivers were asked to verify the information with students’parents by phone when …lling
out the family survey.
11
The majority of these students started schooling in satellite school units in remote villages and later
transferred to the primary schools we surveyed. These satellite school units o¤er junior (usually …rst and
second) grade classes only.
12
According to China’s Ministry of Education, the primary school enrollment rate was 99.5% in 2008.
http://www.china.org.cn/government/scio-press-conferences/2009-09/11/content_18508942.htm.
8

9. term when the survey was conducted, only 28 percent of the children in our sample had both
parents present at home. Of the 72 percent of the children who were left-behind by at least
one parent, 39 percent had both parents absent from home, 28 percent had only mothers
at home, and the remaining 5 percent had only fathers at home. For children with both
parents away from home, 66 percent had paternal grandparents as the primary caregivers,
16 percent had maternal grandparents as the primary caregivers, and the remaining were in
the care of other close relatives, friends, neighbors, etc. In terms of cognitive achievement,
the subgroup of students with only fathers at home had the lowest mean percentile score
in both subjects (45.8 in math and 44.6 in Chinese), whereas the other three subgroups all
had mean percentile scores around 50 in both subjects. Families with only fathers at home
also had the lowest paternal and maternal schooling levels, suggesting that di¤erences in
children’s cognitive achievements by parental migration pattern may be in part driven by
observed, in addition to any possible unobserved, heterogeneity at the family level. We also
report the median family income of each subgroup based on households reporting non-zero
income for the previous year.13
Not surprisingly, the median annual income was highest
among families with both parents away as migrant workers (RMB 40,000) and lowest among
those with both parents staying at home (RMB 26,000).
2.3 Di¤erence-in-Di¤erences Estimates
In the dynamic panel model used in this paper, identi…cation is based on the 1,440 students
whose parental absence status changed during the observation period. Table 2 illustrates the
working of this identi…cation strategy by employing a di¤erence-in-di¤erences approach to
compare children’s test score changes over two periods when parental absence status varied.
Because of the small number of children who ever had fathers at home alone, we consolidate
throughout the paper paternal absence (only) and maternal absence (only) into a single
category of having (only) one parent absent from home. Thus, we subdivide transitions in
parental absence status into six categories by changes in the number of parents at home, as
illustrated in column (1) of Table 2. For children falling into each category, the di¤erence-
in-di¤erences approach compares the means of their test score changes between the period
immediately before and the period immediately after the transition took place. Taking cat-
13
89 percent of the households in our survey report non-zero income. The attrition rates are roughly the
same across di¤erent subgroups.
9

10. egories (1a) and (1b) as examples, among the 292 cases where a child had transitioned from
having both parents at home to having both parents away, the migration of both parents
is associated with 3.1- and 2.5-percentile-point reductions in the test score changes in math
and Chinese, respectively, whereas among the 252 cases where a child had transitioned in
the opposite way from having both parents away to having both parents at home, the return
of both parents is associated with 2.2- and 2.9-percentile-point increases in the test score
changes in math and Chinese, respectively. Due to the relatively small number of observa-
tions falling into each category, none of these di¤erences is signi…cant at conventional levels.
In column (6), we pool these two categories together and examine instead the di¤erence in
the means of test score changes when both parents are away versus when both parents are
present at home. This exercise shows that the absence of both parents is associated with 2.6-
and 2.7-percentile reductions in the test score changes in math and Chinese, respectively,
compared to the presence of both parents. Both estimates are signi…cant at the …ve percent
level owing to the reductions in standard errors with the sample pooling. In another exercise
comparing the means of test score changes when both parents are away and when only one
parent is away, we also …nd the di¤erence to be negative and signi…cant for both subjects.
However, the comparison between the absence of a single parent and the presence of both
parents shows only very small and insigni…cant di¤erences.
While the intuition of the di¤erence-in-di¤erences approach is clarifying, the consistency
of its estimates hinges on two critical assumptions, which are rather restrictive and may
not hold in this case. First, it requires that shifts in a child’s parental absence status over
time are exogenous to changes in the unobserved time-varying determinants of that child’s
achievement progress across periods. However, in practice, parents may change their resi-
dence/migration status in response to unobserved family-level shocks, which may also a¤ect
their child’s learning progress, thus violating the exogeneity assumption. Second, it essen-
tially adopts a canonical restricted version of the value-added model that assumes perfect
persistence of lagged achievement. However, it has been widely acknowledged in the litera-
ture that achievement exhibits mean reversion, which can be more salient in our context as
these exams mainly attempted to assess students’understanding of subjects covered in each
school term and varied substantially in content over time. We thus adopt a less restrictive
learning framework and apply dynamic panel methods in the next section to address both
of these concerns.
10

11. 3 Empirical Framework for Learning Dynamics
We adopt an educational production function approach and consider children’s knowledge
acquisition as a cumulative process that depends on the histories of family and school inputs
as well as on children’s inherited endowments. Following Boardman and Murnane (1979)
and Todd and Wolpin (2003), we model the cumulative production of cognitive achievement
as a dynamic process as follows
yit =
Pt
s=0(Xis t s + t s"is); (1)
where yit is the true cognitive achievement for child i at the end of period t (measured without
error), Xis is a vector of observed family and school inputs applied to child i in period s, "is
is the unobserved determinants (including both inputs and endowments) a¤ecting child i’s
learning in period s. t s and t s correspond to, respectively, the impacts of the observed
and unobserved factors applied t s periods prior to the time of assessment on a child’s
cognitive achievement. In particular, we normalize "it as the unobserved contemporary
component of yit such that 0 always equals unity. Underlying the educational production
function in Equation (1) is the assumption that the input coe¢ cients depend only on the
lead time when the inputs are imposed relative to when the achievement is measured (i.e.,
t s).14
Further assuming that all input coe¢ cients, both observed and unobserved, decline
geometrically at the same rate , i.e., t s 1 = t s and t s 1 = t s 8 s t 1 , we
can obtain a value-added speci…cation that relates a child’s current achievement to his/her
lagged achievement and the contemporaneous inputs as follows:
yit = yit 1 + Xit 0 + "it (2)
In this value-added speci…cation, lagged achievement yit 1 is considered to be a su¢ cient
statistic for all historical inputs including heritable endowments, and is linked to current
achievement through the persistence parameter . However, the estimation of the value-
added speci…cation in Equation (2) faces two additional challenges as discussed in Andrabi
et al. (2011). First, lagged achievement only captures individual heterogeneity in learning
14
A more general speci…cation of Equation (1) denotes the input coe¢ cients as t;s and t;sto allow them
to vary by both the timing of the inputs (s) and the timing of achievement measurement (t). However, such
a speci…cation is not empirically estimable with our data.
11

12. level at t 1, but talented children may also learn faster. Such individual heterogeneity in
learning dynamics, if it exists, would result in a common individual-level component in the
error term "it, i.e.,
"it = i + it
where i re‡ects the unobserved individual-level heterogeneity in the average speed of learn-
ing and it is the time-varying deviation in the unobserved individual-level learning speed
that has a zero mean across time for the same child. Second, we do not observe the latent
learning outcome (yit) but instead only a noisy measure (yit):
yit = yit + eit
where eit is independently distributed across both individuals and time. Speci…cally for
this paper, we measure a child’s cognitive achievement by his/her percentile rank in class.
In addition to circumventing the incomparability of raw test scores across schools, the use
of within-class percentile score has two additional advantages. First, as almost no student
in our sample ever switched classes once they were formed at school entry, the within-
class percentile score eliminates the e¤ects of any school inputs that have common additive
in‡uences on students within the same class. Thus, we can focus our attention on family
inputs only for the input vector X in Equation (1). In the context of this paper, we de…ne a
time period to be the same as a school term and proxy for a child’s family inputs in period
t by his/her parental absence status in school term t. Second, the within-class percentile
score also eliminates any transitory common shocks in the error component of test scores for
students from the same class so that there is no need to adjust standard errors for clustering
at the class or school levels.
Replacing latent achievements with its observed measures in Equation (2) yields
yit = yit 1 + Xit 0 + i + 'it (3)
where 'it = it + eit eit 1. To address individual-level heterogeneity in the speed of
learning, we can di¤erence Equation (3) as follows
12

13. 4yit = 4yit 1 + 4Xit 0 + 4'it (4)
where 4'it = it it 1 + eit (1 + )eit 1 + eit 2. Though the individual …xed e¤ect i
is gone, the lagged dependent variable 4yit 1 in Equation (4) is still potentially endogenous
to 4'it because it is correlated with it 1 and eit 1 through the yit 1 term and with eit 2
through the yit 2 term. In the standard dynamic panel model without measurement errors,
Arellano and Bond (1991) propose instrumenting for 4yit 1 using two or more period lags
of yit if the unobserved individual-level, time-varying shocks it are serially uncorrelated.
However, in our context, because of the existence of eit 2 , yit 2 is still endogenous to 4'it.
We thus use three or more period lags of yit to instrument for 4yit 1 in Equation (4). As eit
is independently distributed across both individuals and time by construction, the validity
of these higher order lags as instruments for 4yit 1 hinges only on the assumption of no
serial correlation in it, which we will test empirically using the Arellano-Bond test.
We next consider the possible endogeneity of 4Xit in the di¤erenced speci…cation, a
problem raised in Section 2.3. In our empirical estimation, Xit includes only parental migra-
tion status as proxy for family inputs, i.e. dummies for whether both parents are constantly
at home, only one parent is constantly at home,15
and both parents are constantly absent
from home. Hence, 4Xit measures the change of parental migration status in the current
period as compared to the previous period. We …rst exclude the strict exogeneity of Xit in
our context as parents are likely to adjust family inputs (i.e., their migration status) based
on observed past achievements, i.e., Xit is endogenous to yit s for 1 s t 1. Therefore,
Xit is also endogenous to all past shocks ( it s) and measurement errors (eit s). In terms of
the contemporaneous relationship, we assume that Xit is endogenous to it but exogenous
to eit, as the latter is purely random. Under these conditions, it turns out that only two or
more period lags of inputs, i.e., Xit 2 or higher order lags, are exogenous to 4'it if it is
serially uncorrelated.16
We thus implement our di¤erenced GMM estimation by instrument-
ing 4yit 1 and 4Xit using the three or more period lags of yit and two or more period lags
15
As discussed before in 2.3, we focus on whether both parents are absent versus one or none in our paper
as the group having father at home alone has very small sample size. We did explore separating maternal
and paternal absence but found no signi…cant di¤erence.
16
Note that even if Xit is assumed to be predetermined (instead of endogenous), the implementation of
the di¤erence GMM estimation still requires the use of two or more lags for this variable. This is because
Xit 1 is still endogenous to the error term in Equation (4) through its correlation with the eit 2 term in
4'it.
13

14. of Xit, respectively.
4 Empirical Results
Table 3 summarizes our main GMM estimation results, employing the three and higher order
lags of achievement and two and higher order lags of parental absence status as instruments in
the …rst-di¤erenced speci…cation. The dependent variables are within-class percentile scores
for math in columns 1-3 and for Chinese in columns 4-6. In columns 1 and 4, we summarize
parental absence status by two dummy indicators denoting the absence of (only) a single
parent (sit) and the absence of both parents (bit), respectively. The coe¢ cient estimates on
the latter dummy indicator are negative and signi…cant for both subjects, suggesting that the
absence of both parents lowers a child’s score in math and Chinese by 5.0 and 4.7 percentile
points, respectively, compared to having both parents at home. Though still negative, the
coe¢ cient estimates on the dummy indicator for the absence of a single parent are only one-
third of the magnitude of the coe¢ cient estimate on both parents absent and insigni…cant,
showing little evidence that the migration of a single parent (typically the father) has any
salient adverse e¤ect on a child’s cognitive achievement. These coe¢ cients are qualitatively
consistent with the …ndings of the di¤erence-in-indi¤erences analysis reported in the last
column of Table 2. That is, the absence of both parents is associated with signi…cantly
lower achievement progress relative to both the presence of a single parent and that of
both parents, whereas the di¤erence in the test score changes of the latter two cases is
small and insigni…cant. However, our GMM estimates in Table 3 are consistently larger in
magnitude than the observed di¤erences in test score changes shown in Table 2, suggesting
that the absence of both parents is positively correlated with the omitted time-varying
determinants of a child’s cognitive achievement. There are at least two possible reasons
that might explain the existence of such a positive correlation. First, parents may choose to
migrate and leave their child behind when a suitable guardian becomes available, such as the
retirement of a grandparent, the return migration of a sibling to the home township/village,
etc. Second, the return of parents may be induced by some family-level shocks, which
demand a lot of their time and attention after returning. Examples for such shocks include
the worsening of the health condition of a grandparent, the pregnancy of the mother, the
birth of a younger sibling, etc. In either case, the observed relationship between a child’s
14

15. contemporaneous achievement progress and his/her parental absence status is mitigated
because of the existence of unobserved confounding factors that a¤ect both parental absence
status and achievement progress. The advantage of the dynamic panel approach adopted
here is that it can address the contamination of these unobserved confounding factors through
the employment of lagged parental absence status as instruments.
As our estimates of the coe¢ cient on single parent absence are indistinguishable from 0,
for simplicity, we drop the dummy for single parent absence (sit) and adopt a dichotomous
classi…cation of parental absence status, i.e., the absence of both parents (bit = 1) and the
presence of at least one parent (bit = 0). This simpli…ed version of the achievement function
takes the following form
yit = yit 1 + bit + i + 'it (5)
where the coe¢ cient measures the impact of the absence of both parents on a child’s
contemporary achievement relative to having at least one parent at home. Columns 2 and
5 of Table 3 report our estimates of Equation (5) that pools the presence of one and both
parents together as the default category. The coe¢ cient estimates on the dummy indicator
bit are only reduced slightly in magnitude compared to those in columns 1 and 4 and remain
negative and signi…cant, indicating that the absence of both parents lowers their children’s
score in math and Chinese by 4.2 and 3.7 percentile points, respectively, relative to having
at least one parent at home.
Note that our baseline achievement function assumes that parental absences a¤ect student
achievement through only the current status but not any of the historical values. However,
in practice, the e¤ect of parental absence may be path dependent. For example, the absence
of both parents for the …rst time may have a larger adverse e¤ect than their continuing
absence if children in the latter case better adjust themselves to a family environment with
no parents. Also, the return of one or both parents may generate a larger positive e¤ect than
their continuing presence if the availability of parental inputs upon their return can generate
some short-run catch-up e¤ects. To address these possibilities, we consider an extension of
our baseline achievement function in which we allow a child’s learning progress to depend on
the interactions between his/her parental absence status in the current period (t) and that
in the previous period (t 1). For simplicity, we still adopt a dichotomous classi…cation of
15

16. parental absence status into the absence of both parents and the presence of at least one
parent. This extended achievement speci…cation takes the following form
yit = yit 1 + 1bit(1 bit 1) + 2bitbit 1 + 3(1 bit)bit 1 + i + 'it (6)
Here the coe¢ cients 1, 2, and 3 correspond, respectively, to the transition (bit = 1; bit 1 =
0), continuation (bit = 1; bit 1 = 1), and termination (bit = 0; bit 1 = 1) e¤ects of the absence
of both parents on a child’s cognitive achievements relative to the default category of having
at least one parent at home in both periods (bit = 0; bit 1 = 0). The coe¢ cients of this
extended achievement speci…cation, as reported in columns 3 and 6 in Table 3, are much
less precisely estimated than those in columns 2 and 5 because there are fewer numbers of
observations falling into each category. Nevertheless, the point estimates ^1 and ^2 are quite
similar to each other and both are very close to the corresponding point estimate ^ and ^3 is
also indistinguishable from 0. As our estimates of the extended achievement function suggest
no evidence that past parental absence status matters for a child’s contemporary learning
progress, we thus focus only on the baseline achievement function in which parental absence
status works only through its current value in the rest of the paper.
Finally, we consider estimates of the persistence coe¢ cient, which range from 0.54 to 0.59
for math and from 0.43 to 0.47 for Chinese. Although the point estimate is higher for math
than Chinese in all speci…cations, the di¤erence is never signi…cant. It is important to note
that the parameters on the parental absence dummies we estimate above correspond to the
immediate impact of parental absence on a child’s contemporaneous achievement. According
to our value-added achievement function, the e¤ect of the permanent or persistent absence
of both parents on a child’s ultimate achievement is =(1 ). Given our point estimates
^ and ^ in columns 2 and 5, the permanent absence of both parents can lower a child’s
score by 10.3 and 7.1 percentile points for math and Chinese, respectively. With an average
class size of 40, these estimates indicate that the permanent absence of both parents lowers
a student’s within-class rank by about 3-4 positions, which are notable though still modest
long-run e¤ects.
16

17. 5 Discussion
5.1 Regression Diagnosis
The consistency of our estimates hinges upon the assumption of no serial correlation in the
unobserved individual-level, time-varying determinants it. Arellano and Bond (1991) pro-
pose a test for the autocorrelation in it based on the residuals from the …rst-di¤erenced equa-
tion. In the standard dynamic panel estimation without measurement errors, the Arellano-
Bond test is performed by examining the existence of second-order serial correlation in the
error term 4'it in the …rst-di¤erenced transformation, Equation (4). However, because 4'it
further contains eit, eit 1 , and eit 2 due to measurement error in test scores in our context,
it is serially correlated in both the …rst and second orders even if it itself is serially uncorre-
lated. Therefore, we implement the Arellano-Bond test by performing a test of third-order
serial correlation in 4'it. The p-values of the Arellano-Bond AR(3) test, reported in the
bottom of each column in Table 3, are larger than 0.20 for math and 0.45 for Chinese in all
of the speci…cations, showing little evidence for the existence of serial correlation in it.
We next consider the Hansen’s J test of overidenti…cation, also reported in the bottom
of each column in Table 3. The Hansen’s J statistics never reject the over-identifying re-
strictions implied by the model for math. However, the same over-identifying restrictions
fail for Chinese, suggesting that at least some of the local parameters identi…ed by di¤erent
instruments are signi…cantly di¤erent from each other for Chinese. However, as we have
employed lagged variables as instruments to identify both the persistence parameter and the
coe¢ cient(s) on the parental absence status, the failure of the over-identifying restrictions
can come from deviations in the local estimates of either of them. As the main purpose
of this paper is to identify the impact of parental absence, we are particularly concerned
if the rejection of the over-identifying restrictions were caused by di¤erences in the local
estimates of the coe¢ cients on parental absence status. To identify the source of the failure
of the over-identifying restrictions, we conduct in the next subsection a robustness analysis
in which we restrict to a set of constant values and estimate the coe¢ cients on the parental
absence status only.
17

18. 5.2 Robustness
A key for the success of applying the value-added speci…cation is to properly account for the
learning dynamics, i.e., how past achievement contributes to cumulative learning in the fu-
ture. In our model, we assume a linear relationship between lagged and current achievement
and use the persistence parameter to account for depreciation, if any. Another commonly
used speci…cation of the value-added function assumes that lagged achievement contributes
cumulatively to future achievement without loss, i.e., restricting to be 1.17
An advantage
of this restrictive value-added model is that the dependent variable can be speci…ed as the
di¤erence between current period and previous period test scores (4yit), thus circumventing
the empirical estimation of . As a robustness check, we adopt this restrictive model in
columns 1 and 5 of Table 4 to estimate the e¤ect of the absence of one and both parents
on student achievements in math and Chinese, respectively. The results are qualitatively
the same and quantitatively very similar to those in Table 3: the absence of both parents
has signi…cant adverse e¤ects on a child’s immediate achievement scores, lowering scores in
math and Chinese by 6.4 and 4.7 percentile points, respectively, whereas the absence of a
single parent has only very small and insigni…cant e¤ects for both subjects. However, the
assumption of perfect persistence of lagged achievement is likely to be too restrictive in our
context, particularly because these exams, aimed to assess students’learning outcomes in a
particular school term, di¤er substantially in test content. Moreover, a large number of em-
pirical studies suggest that the test score e¤ects of educational inputs fade out very rapidly.18
Thus, we further allow the persistence parameter to vary from 0.8 to 0.4 with decrements
of 0.2 to examine whether the estimated parental absence e¤ects are sensitive to the choice
of persistence parameter value. The results, reported in the remaining columns in Table
4, again lead to the same conclusion that only the absence of both parents has signi…cant
adverse e¤ects on children’s test scores. Taken together, the exercises in Table 4 show that
the persistence parameter makes little di¤erence in estimating the parental absence e¤ects.
Moreover, the over-identifying restrictions hold in all speci…cations where the persistence
parameter is determined exogenously: the p-values of the Hansen’s J statistics increase
17
See, for example, Hanushek (2003) and Hanushek, Kain, Markman, and Rivkin (2003).
18
For example, Jacob, Lefgren, and Sims (2010) and Rothstein (2010) …nd low persistence of teacher
e¤ects over time, and Currie and Tomas (1995) and Banerjee, Cole, Du‡o, and Linden (2007) show that the
impacts of the Head Start program in the United States and of a remedial education program in India fade
out rapidly after the intervention.
18

19. substantially and always exceed 0.57 in Table 4. These results suggest that the failure of
the over-identifying restrictions for Chinese in Table 3 is likely to be caused by di¤erences in
the local estimates of the persistence parameter rather than in the coe¢ cients on parental
absence status.
To examine the possible heterogeneity in parental absence e¤ect by child gender, we
further conduct in Table 5 separate estimates for boys and girls. The speci…cations are the
same as columns 1 and 4 in Table 3, in which parental absence status is summarized by two
dummy indicators for the absence of a single parent (sit) and both parents (bit), respectively.
The results for boys are the same as those for the combined sample: the absence of both
parents has signi…cant and adverse e¤ects on their son’s achievements in both subjects while
the absence of a single parent does not. The point estimates of the coe¢ cients on the both-
parents-absent dummy (4.9 for math and 5.2 for Chinese) are signi…cant at the 10 percent
level for both subjects and are also very close to those of the combined sample (5.0 for math
and 4.7 for Chinese) reported in Table 3. For girls, only the coe¢ cient on the both-parents-
absent dummy for math (-5.5) is signi…cant at the 10 percent level. However, despite the
insigni…cant estimate of that coe¢ cient for Chinese (-2.3), we cannot reject the equality
of the coe¢ cients on the both-parent-absence dummy across genders for Chinese. Taken
together, the results in Table 5 show little evidence for heterogeneous e¤ects of parental
absence between genders.
5.3 Survey Evidence on After-school Study Hours, Family Inputs
and Relationship with Others
As mentioned in Section 2.2, we conducted student surveys to collect information on time
allocations after school, tutoring help from parents and others, and satisfaction levels on rela-
tionships with parents, other adult family members, and teachers and classmates. However,
because all these measures are contemporary rather than longitudinal, we cannot apply the
same dynamic panel methods to identify the e¤ects of parental absence on them. Nonethe-
less, we still present the cross-sectional relations between parental absence status and each
of these variables in Table 6. To the extent that these cross-sectional relationships partly
re‡ect the impacts of parental absence, they may be informative and shed light on the pos-
sible channels through which parental absence a¤ects student achievements. Panel A shows
19

20. little di¤erence in the average after-school study hours across students with di¤erent parental
absence status. Students of all three groups spent on average about 70 minutes each day
in study after school, of which about 37 minutes were for homework. However, Panel B
indicates large disadvantages of students left-behind by both parents on family inputs in
after-school tutoring relative to those with one and both parents at home, with the latter
two groups having similar statistics in all measures of tutoring inputs. Because we de…ne
parental absence status as a parent/parents away from home for more than half of the time
during a school term, some students classi…ed as being left-behind by both parents happened
to have their parent(s) at home in the week prior to our survey and thus 19.1 percent of them
still reported tutoring help from parents, although the number is substantially lower than
that of those having one (64.9 percent) and both parents (67.1 percent) at home (for more
than half of the time in the current school term). In terms of parental tutoring time, students
with both parents absent from home (for more than half of the time) on average received 4.2
minutes’tutoring help from their parents per day in the past week, compared to 14.3 and
14.5 minutes for those with one and both parents at home, respectively. Nonetheless, de-
spite the large discrepancies in parental tutoring inputs between students with and without
parent(s) at home, the proportion of students reported having tutoring help from others19
(about 40 percent) and the average tutoring minutes from others (about 11 minutes per day)
are almost the same across students with di¤erent parental absence status. The fact that
students left-behind by both parents did not receive more tutoring help from others suggests
that there is little compensation of others’inputs for the loss of parental inputs in tutoring.
If after-school tutoring is highly complementary to both school inputs and students’e¤orts,
the lack of parental tutoring inputs may be a main reason for the adverse e¤ects of the
absence of both parents on student achievements. Our results in Panels A and B of Table
6 seem to suggest that students with parent(s) at home are able to make more e¤ective
progress in learning holding constant the school inputs and their after-school study hours
because of the crucial role of family tutoring inputs, which has a large shortfall for those
with no parent at home. However, the absence of a single parent seems to have little e¤ect
on parental tutoring inputs, implying a very high degree of substitution between paternal
and maternal inputs in tutoring, which can also explain our …nding of lack of evidence for
adverse e¤ects of the absence of one parent.
19
Most often, such tutoring was provided by older siblings and grandparents.
20

21. Panel C presents students’ self-reported satisfaction levels on their relationships with
parents, other adult family members, and teachers and classmates. We classify a student as
satis…ed with a relationship if he/she gave it a rating of 4 or more out of a scale of 5. The
results suggest that the absence of either a single or both parents has signi…cant adverse
e¤ects on their family relationships. The absence of one and both parents increases the
probability that a student reports being unsatis…ed with his/her relationships to parents
by 4.4 percentage points (or 29.7 percent) and 2.5 percentage points (or 16.9 percent),
respectively. Students with one or both parents absent from home are also more likely to
be unhappy with their relationships with other adult family members. However, we …nd
no di¤erence in students’satisfaction with their relationships to teachers and classmates by
parental absence status. These …ndings suggest that the migration of parents, even that of
a single one, is likely to have other adverse e¤ects on child development beyond test scores,
such as their psychological well-beings. Unfortunately, the lack of longitudinal data on these
aspects precludes us from substantiating the suggestive evidence presented here, which leaves
room for future investigations.
6 Summary and Conclusions
Parental migration with children left-behind is a world-side phenomenon, but with the largest
absolute numbers of children a¤ected in rural China –an estimated 60 million plus such chil-
dren. The implications of this phenomenon have created considerable interest and concern.
But the systematic evidence of the implications of this phenomenon for children have been
limited and have focused on impacts on time use inputs into learning such as school atten-
dance and time studying. The previous literature generally has not considered the impacts
of parental migration on learning itself as measured by children’s cognitive achievements. A
priori the impacts on learning may be positive or negative, depending on whether, for ex-
ample, the income e¤ect due to increased parental income outweighs the impacts of reduced
parental time inputs into child learning and reduced parental direct supervision related to
learning. Therefore it is not surprising that some previous studies have found positive and
others have found negative or no signi…cant e¤ects on children’s time use related to learn-
ing. And, of course, even if children’s time use related to learning increases, learning may
decrease or not be a¤ected if parental presence has large e¤ects on child learning.
21

22. We investigate how primary-school-aged children’s cognitive achievements are a¤ected
by the absence of their parents from home. Based on a cumulative educational production
function, we derive a value-added speci…cation that relates a child’s contemporary learning
to his/her lagged achievement, family inputs, and individual heterogeneity in learning speed.
We then estimate this model using a retrospective panel data set that we collected for third
to …fth graders in a very poor rural county in China with a considerable proportion of left-
behind children, and proxy for family inputs by children’s parental absence status. Our
GMM estimates of the dynamic panel model show signi…cant adverse e¤ects of the absence
of both parents on the cognitive achievements of their children left-behind. In contrast we
…nd that the absence of a single parent has estimates that are much smaller in magnitude
and are not signi…cant.
If, as would seem to be the case based on other estimates for other contexts, primary-
school level cognitive achievements have cumulative impacts on upper-school level cognitive
achievements and post-school cognitive achievements, which in turn a¤ect life-time produc-
tivities, there may be considerable long-run costs of the reduced primary-school cognitive
achievements that we estimate results from absences of both parents. Given that a large
proportion of children are left-behind by both parents in rural China, our …ndings here may
have major policy implications. There is a de…nite value in investigating possible compen-
satory programs for ameliorating these negative learning e¤ects of absence of both parents
or for lessening or eliminating the restrictions that cause absence of both parents.
22

23. References
All-China Women’s Federation, 2013. A Study of the Situation of Left-behind Children in
Rural China.
Alcaraz, Carlo, Chiquiar, Daniel, Salcedo, Alejandrina, 2012. Remittances, schooling, and
child labor in Mexico. Journal of Development Economics 97(1): 156-165.
Andrabi, Tahir, Das, Jishnu, Khwaja, Asim Ijaz, Zajonc, Tristan, 2001. Do value-added
estimates add value? Accounting for learning dynamics. American Economic Journal:
Applied Economics 3(3): 29-54.
Arellano, Manuel, Bond, Stephen, 1991. Some tests of speci…cations of panel data: Monte
Carlo evidence and an application to employment equations. Review of Economic Studies
58(2): 277-297.
Antman, Francisca, 2011. The intergenerational e¤ects of paternal migration on schooling
and work: What can we learn from children’s time allocations? Journal of Development
Economics 96(2): 200-208.
Antman, Francisca, 2012. Gender, educational attainment, and the impact of parental
migration on children left behind. Journal of Population Economics 25(4): 1187-1214.
Antman, Francisca, 2013. The impact of migration on family left behind. In Klaus F.
Zimmerman and Amelie F. Constant (eds.) International Handbook on the Economics of
Migration, United Kingdom: Edward Elgar.
Banerjee, Abhijit V., Cole, Shawn, Du‡o, Esther, Linden, Leigh. 2007. Remedying ed-
ucation: Evidence from two randomized experiments in India. Quarterly Journal of
Economics 122(3): 1235-1264.
Beine, Michel, Docquier, Frederic, Rapoport, Hillel, 2008. Brain drain and human capital
formation in developing countries: Winners and losers. Economic Journal 118(528):
631-652.
Boardman, Anthony E. , Murnane, Richard J., 1979. Using panel data to improve estimates
of the determinants of educational achievement. Sociology of Education 52(2): 113-121.
Chang, Hongqin, Dong, Xiao-Yuan, Macphail. Fiona, 2011. Labor migration and time
use patterns of the left-behind children and elderly in rural China. World Development
39(12): 2199-2210.
Chen, Joyce J., 2013. Identifying non-cooperative behavior among spouses: Child outcomes
23

24. in migrant-sending households. Journal of Development Economics 100(1): 1-18.
Chen, Yuanyuan, Feng, Shuaizhang, 2013. Access to public schools and the education of
migrant children in China. China Economic Review 26(75): 75-88.
Currie, Janet, Thomas, Duncan. 1995. Does Head Start make a di¤erence? American
Economic Review 85(3): 341-364.
Dustmann, Christian, Glitz, Albrecht, 2011. Migration and education. In Eric A. Hanushek,
Stephen Machin and Ludger Woessmann (ed.) Handbook of the Economics of Education
Volume 4, pp. 327-441, New York: Elsevier.
Edwards, Alejandra Cox, Ureta, Manuelita, 2003. International Migration, Remittances,
and Schooling: Evidence from El Salvador. Journal of Development Economics 72(2):
429-461.
Gibson, John, McKenzie, David, Stillman, Steven, 2011. The impacts of international mi-
gration on remaining household members: Omnibus results from a migration lottery
program. Review of Economics and Statistics 93(4): 1297-1318.
Hanushek, Eric A., 2003. The falure of input-based schooling policies. Economic Journal
113(485): F64-98.
Hanushek, Eric A., Kain, John F., Markman, Jacob M., Rivkin, Steven G., 2003. Does peer
ability a¤ect student achievement? Journal of Applied Econometrics 18(5): 527-544.
Haveman, Robert, Wolfe, Barbara, 1995. The determinants of children’s attainments: A
review of methods and …ndings. Journal of Economic Literature 33(4): 1829-1878.
Jacob, Brian A., Lefgren, Lars, Sims, David P., 2010. The persistence of teacher-induced
learning. Journal of Human Resources 45(4): 915-943.
Kuhn, Randll, 2007. The e¤ect of fathers’ and siblings’ migration on children’s pace of
schooling in rural Bangladesh. Asian Population Studies 2(1): 69-92.
Lyle, David S., 2006. Using Military Deployments and Job Assignments to Estimate the
E¤ect of Parental Absences and Household Relocations on Children’s Academic Achieve-
ment. Journal of Labor Economics 24(2): 319-350.
Mani, Subha, Hoddinott, John, Strauss, John, 2012. Long-term Impact of Investment in
Early Schooling – Empirical Evidence from Rural Ethiopia. Journal of Development
Economics 99 (2): 292-299.
Mckenzie, David, Rapoport, Hillel, 2011. Can migration reduce educational attainment?
Evidence from Mexico. Journal of Population Economics 24 (4): 1331-1358.
24

25. National Bureau of Statistics, 2012. Tabulations on the 2010 Population Census of People’s
Republic of China. Beijing, China: China Statistical Press.
Rapoport, Hillel and Fredeirc Docquier. 2006. The economics of migrants’ remittances.
In S. Kolm and J. Yithier (eds.) Handbook of the Economics of Giving, Altruism and
Reciprocity Volume 2, Amsterdam: North Holland.
Roberts, Kenneth, Connelley, Rachel, Xie, Zheming, and Zheng, Zhenzhen. 2004. Patterns
of temporary labor migration of rural women from Anhui and Sichuan. The China
Journal 52: 49-70.
Rothstein, Jesse. 2010. Teacher quality in educational production: Tracking, decay, and
student achievement. Quarterly Journal of Economics 125(1): 175-214.
Stark, Oded, 1993. The Migration of Labor. Cambridge, MA: B. Blackwell.
Todd, Petra E., Wolpin, Kenneth I., 2003. On the speci…cation and estimation of the
production function for cognitive achievement. Economic Journal 113: F3-F33.
Yang, Dean, 2008. International migration, remittances and household investment: Evidence
from Philippine migrants’exchange rate shocks. Economic Journal 118(528): 591-630.
Yang, Dean, 2011. Migrant remittances. Journal of Economic Perspectives 25(3): 129-152.
25

26. 26
Both parents at home Only mother at home Only father at home Both parents absent
Percentage share of the full sample 28.0% 27.3% 4.9% 39.1%
Primary caregivers when both parents were absent
Paternal grandparents - - - 65.9%
Maternal grandparents - - - 15.9%
Old siblings - - - 2.0%
Other close relatives (uncles, anties, cousins, etc.) - - - 6.4%
Others (friends, neighbors, etc.) - - - 9.7%
Average math percentile score in class in the latest exam 49.88 51.08 45.76 49.87
Average Chinese percentile score in the latest exam 50.12 50.10 44.60 50.52
Average years of schooling of fathers 9.31 8.98 8.49 8.81
Average years of schooling of mothers 8.39 8.08 8.02 8.15
Median family income in the previous year (RMB) 26,000 30,000 29,000 40,000
Number of students 1,335 1,270 228 1,820
Notes : The number of observations used to calculate the median family income is smaller than what is reported in the bottom row due to missing data. Specifically, the
numbers of observations used to calculate the median family income are 1,177 in column (1), 1,122 in column (2), 202 in column (3), and 1,643 in column (4).
Table 1 Summary Statistics by Current Parental Absence Status

27. 27
Change in number of
parents at home from t-
1 to t
Number of
observations
Mean test score
change in t-1
Mean test score
change in t
Difference in test
score changes
between t-1 and t
Difference in test score changes by
number of parents at home
nt-1 → nt Δyt-1 Δyt Δyt-Δyt-1
(1) (2) (3) (4) (5) (6)
Panel A. Math
(1a) 2 → 0 292 1.203 -1.876 -3.078
(1.026) (1.153) (1.895) Δy(n=0)-Δy(n=2)
(1b) 0 → 2 255 -2.408** -0.189 2.220 -2.648**
(1.198) (1.113) (1.889) (1.344)
(2a) 1 → 0 402 0.631 -0.362 -0.993
(0.810) (0.888) (1.360) Δy(n=0)-Δy(n=1)
(2b) 0 → 1 423 -1.069 1.376* 2.444* -1.719*
(0.814) (0.816) (1.326) (0.950)
(3a) 2 → 1 508 0.299 0.014 -0.286
(0.762) (0.748) (1.246) Δy(n=1)-Δy(n=2)
(3b) 1 → 2 400 0.851 0.961 0.109 -0.198
(0.781) (0.795) (1.238) (0.891)
Panel B. Chinese
(1a) 2 → 0 292 0.466 -2.025* -2.492
(1.086) (1.044) (1.745) Δy(n=0)-Δy(n=2)
(1b) 0 → 2 255 -3.100 -0.156 2.944 -2.718**
(1.020) (1.153) (1.764) (1.245)
(2a) 1 → 0 402 0.994 -0.429 -1.423
(0.827) (0.872) (1.410) Δy(n=0)-Δy(n=1)
(2b) 0 → 1 423 -1.731 2.067** 3.797*** -2.610***
(0.818) (0.863) (1.385) (0.988)
(3a) 2 → 1 508 0.212 -0.958 -1.170
(0.710) (0.754) (1.197) Δy(n=1)-Δy(n=2)
(3b) 1 → 2 400 -0.161 1.042 1.203 -1.186
(0.731) (0.796) (1.293) (0.885)
Notes : Cells contain the mean test score changes in columns (3) and (4), the differences in the test score changes from t-1 to t in column (5), and the differences
in test score changes by the number of parents at home in column (6). Standard errors are in parentheses.
*** p<0.01, ** p<0.05, * p<0.1
Table 2 Means and Differences in Test Score Changes for Children Whose Parental Absence Status Varied

28. 28
(1) (2) (3) (4) (5) (6)
Lagged achievement 0.559*** 0.594*** 0.544*** 0.433*** 0.472*** 0.452***
(0.063) (0.064) (0.061) (0.055) (0.058) (0.057)
Only one parent absent from home (sit=1) -1.564 -1.775
(2.097) (2.081)
Both parents absent from home (bit=1) -5.012** -4.190** -4.706** -3.728**
(2.017) (1.787) (2.094) (1.807)
Beginning of the absence of both parents (bit-1=0, bit=1) -3.355 -4.449
(5.316) (5.342)
Continuation of the absence of both parents (bit-1=1, bit=1) -3.711 -4.353*
(2.401) (2.494)
Termination of the absence of both parents (bit-1=1, bit=0) 0.514 -1.131
(4.765) (5.001)
p-value of the Arrelano-Bond test for AR(3) in the first-differenced
equation
0.200 0.202 0.211 0.456 0.483 0.466
p-value of the Hansen J test of overidentification 0.405 0.145 0.104 0.047 0.014 0.027
Number of observations 22,595 22,595 22,595 22,595 22,595 22,595
Number of students 4,653 4,653 4,653 4,653 4,653 4,653
Math Chinese
Notes : The table reports the differenced-GMM estimates of a dynamic panel model of a student's contemporary achievement on his/her lagged
achievement and contemporary parental absence status. Each column corresponds to a different classification of parental absence status.The default
categories are the presence of both parents in columns (1) and (4), the presence of at least one parent in columns (2) and (5), and the presence of at least
one parent in both the current and previous periods in columns (3) and (6). All regressions include school term fixed effects. Robust standard errors are
reported in parentheses.
*** p<0.01, ** p<0.05, * p<0.1
Table 3 GMM Estimates of the Value-added Achievement Function with Estimated Persistent Parameter

29. 29
(1) (2) (3) (4) (5) (6) (7) (8)
Persistent parameter (exogenously assigned ) 1 0.8 0.6 0.4 1 0.8 0.6 0.4
Only one parent absent from home (sit=1) -0.332 -0.611 -0.890 -1.169 -1.966 -1.663 -1.361 -1.059
(2.419) (2.212) (2.098) (2.091) (2.382) (2.182) (2.081) (2.093)
Both parents absent from home (bit=1) -6.369*** -5.736*** -5.102** -4.469** -4.693** -4.607** -4.521** -4.435**
(2.337) (2.130) (2.027) (2.044) (2.354) (2.158) (2.070) (2.104)
p-value of the Arrelano-Bond test for AR(3) in the first-differenced
equation
0.174 0.182 0.205 0.260 0.803 0.736 0.614 0.425
p-value of the Hansen J test of overidentification 0.906 0.880 0.831 0.750 0.575 0.612 0.650 0.698
Number of observations 22,595 22,595 22,595 22,595 22,595 22,595 22,595 22,595
Number of students 4,653 4,653 4,653 4,653 4,653 4,653 4,653 4,653
*** p<0.01, ** p<0.05, * p<0.1
Table 4 GMM Estimates of the Value-added Achievement Function with Exogenously Assigned Persistent Parameter
Math Chinese
Notes : The table reports the differenced-GMM estimates of a dynamic panel model of a student's contemporary achievement progress ( ) on his/her
contemporary parental absence status. Each column uses a different persistent parameter as indicated in the first row. All regressions have the presence of both
parents as the default category for parental absence status and include school term fixed effects. Robust standard errors are reported in parentheses.
𝑦𝑖𝑖 − 𝜆𝑦𝑖𝑖−1

30. 30
Math Chinese Math Chinese
(1) (2) (3) (4)
Lagged achievement 0.454*** 0.406*** 0.394*** 0.338***
(0.076) (0.068) (0.086) (0.077)
Only one parent absent from home (sit=1) -1.120 -2.812 -4.438 0.478
(2.853) (2.971) (3.070) (3.041)
Both parents absent from home (bit=1) -4.886* -5.230* -5.520* -2.279
(2.678) (2.896) (2.970) (2.994)
p-value of the Arrelano-Bond test for AR(3) in the first-
differenced equation
0.756 0.837 0.175 0.301
p-value of the Hansen J test of overidentification 0.053 0.001 0.293 0.055
Number of observations 12,777 12,777 9,244 9,244
Number of students 2,613 2,613 1,916 1,916
*** p<0.01, ** p<0.05, * p<0.1
Boys Girls
Table 5 Gender-specific Estimates of the Value-added Achievement Function
Notes : The table reports separate GMM estimates of the value-added achievement function by student
gender and subject. All regressions have the presence of both parents as the default category for parental
absence status and include school term fixed effects. Robust standard errors are reported in parentheses.

31. 31
Both parents at home
Mean Mean Difference Mean Difference
(1) (2) (3) (4) (5)
Panel A. After-school study hours
Minutes spent in learning after school per day 70.438 69.773 -0.665 70.945 0.506
(52.681) (52.978) (1.988) (52.985) (1.904)
Minutes spent in home work after schools per day 38.303 36.809 -1.494 37.763 -0.539
(29.762) (29.319) (1.111) (29.228) (1.061)
Minutes spent in after-school learning activities other than home work per day 32.134 32.963 0.829 33.181 1.046
(30.554) (31.187) (1.162) (30.942) (1.109)
Panel B. Family inputs in tutoring
Ever received tutoring help from someone in the past week 0.769 0.744 -0.024 0.478 -0.291***
(0.421) (0.436) (0.016) (0.499) (0.016)
Ever received tutoring help from parents in the past week 0.671 0.649 -0.021 0.191 -0.481
(0.469) (0.477) (0.017) (0.392) (0.015)
Ever received tutoring help from someone other than parents in the past week 0.423 0.395 -0.028 0.409 -0.013
(0.494) (0.489) (0.018) (0.491) (0.017)
Total tutoring minutes per day 25.949 25.373 -0.575 15.259 -10.689***
(35.798) (37.502) (1.381) (28.357) (1.143)
Tutoring minutes from parents per day 14.505 14.264 -0.241 4.232 -10.273***
(24.302) (25.152) (0.931) (15.474) (0.709)
Tutoring minutes from others per day 11.443 11.109 -0.334 11.027 -0.416
(21.468) (22.432) (0.827) (21.255) (0.769)
Panel C. Relationship with others
Satisfied w/ relationship with parents 0.852 0.827 -0.025* 0.808 -0.044***
(0.354) (0.378) (0.013) (0.393) (0.013)
Satisfied w/ relationship with other adults in family 0.634 0.576 -0.057*** 0.576 -0.058***
(0.481) (0.494) (0.018) (0.494) (0.017)
Satisfied w/ relationship with teachers and clsssmates in school 0.839 0.849 0.010 0.845 0.006
(0.367) (0.357) (0.013) (0.361) (0.013)
Number of students 1335 1498 2833 1820 3155
Table 6 Survey Evidence on After-school Study Hours, Family Inputs and Relationship with Others
One parent absent Both parents absent

32. 32
*** p<0.01, ** p<0.05, * p<0.1
Notes : For each variable indicated by the row heading, columns (1), (2) and (4) report the means and standard deviations (in parentheses) for the subsample with both
parents at home, the subsample with only one parent absent from home, and the subsample with both parents absent from home, respectively; columns (3) and (5) report
the difference in variable means and its standard error (in parentheses) between columns (2) and (1) and between columns (4) and (1), respectively.