Restrictions on Migration Create Gender Inequality:
The Story of China’s Left-Behind Children
Xuwen Gao ∗Wenquan Liang†

Ahmed Mushfiq Mobarak‡

Ran Song§
July 2022
Abstract
About 11% of the Chinese population are rural-urban migrants, and the vast
majority of them (124 million people) possess a rural hukou which severely
restrict their children’s access to urban public schools. As a result, 61 million
children are left behind in rural areas. We use a regression-discontinuity design
based on school enrollment age cutoffs to evaluate the causal effects of hukou
restrictions on children left behind. Migrants are significantly more likely toleave middle-school-aged daughters behind in poor rural areas without either
parent present, compared to middle-school-aged sons. The effect is larger whendaughters have a male sibling. They also send significantly less remittances
back to daughters than sons. We use a shift-share instrumental variables strategy to document that children living in rural areas adjacent to cities with more
restrictive hukou policies are more likely to be left behind as new job opportunities arise in nearby cities due to trade policy changes. We pair this witha longitudinal dataset of children to show that those children are more likely
to not complete middle school, remain in the rural area, and remain poor laterin life. Although China’s hukou mobility restrictions are not gender-specific in
intent, they have larger adverse effects on girls.

Keywords: Migration, hukou, Left-Behind Children, Gender Inequality
JEL Codes: J13, J16, R23∗

Gao: Peking University, Email: gaoxw@phbs.pku.edu.cn.
Liang: Jinan University, Email: liang.wenquan@jnu.edu.cn.
‡
Mobarak: Yale University and NBER, Email: ahmed.mobarak@yale.edu.
§
Song: National University of Singapore, Email: ran.song@yale-nus.edu.sg.
†

1

Introduction

People leaving rural areas to go work in factories located in cities has been an important engine of growth in rapidly developing countries like China. 11% of the Chinese
population in the 2005 census – 145 million people – were rural-urban migrants. The
rapid urbanization generates a complex set of social and economic effects on both thecities migrants move into, and the places they leave behind. Family separation is oneof the most important aspects of the societal disruption that accompanies structuraltransformation and urbanization. As parents move to cities in search of employment,
they often leave their children behind under the care of others. This can have gendered effects if migration, remittance, and leave-behind choices differ between theparents of sons versus daughters.
These choices can hold large consequences for the country’s development pathways, because of the massive scale of this issue. 69 million Chinese children weregrowing up in rural areas without parents in 2015, left behind when their parents
migrated (UNICEF, 2018). This represents 30 percent of all children born in rural
areas (Chen, 2013). The issue is also very policy-relevant, because China imposesinternal mobility restrictions that undermine parents’ ability to migrate with theirchildren. In particular, stringent hukou restrictions in many Chinese cities can makeit prohibitively expensive or even impossible for in-migrants to bring their children
with them and enroll them in urban schools. Of the 145 million rural-urban migrants
in the 2005 census, the vast majority (124 million) were unskilled migrants with arural hukou, which implies that they would have to pay a large fee called zanzhuf ei
to enroll their children in a public school in the city. Zanzhuf ei for junior middle
school enrollment is about 10% of the average migrant’s earnings, which acts as a
big financial deterrent. Such constraints on migrant parents are becoming even moreacute over time as cheaper schools specifically designated for migrant children are
shut down in Beijing and other popular migration destinations (Report, 2016).
We use variation in the stringency of hukou restrictions in cities where migrantparents work to analyze how parents decide whether and when to leave their children
behind in rural areas. Schooling is compulsory, and children must transition fromprimary school to junior middle school around the age of 12 or 13, depending on their1month of birth. Zanzhuf ei for junior middle school is 53% larger than for primaryschool, which changes parents’ incentives and ability to keep their children with themin the city exactly at that age. We employ a regression discontinuity research design
based on the age cutoff for middle school entry using data on the exact date of birthof 173,468 children of migrants, to study whether sons or daughters are treated any
differently when parents make migration choices. We show that parents who had
migrated to cities with stringent hukou restrictions are 3 percentage points (9%)
more likely to leave their daughters behind in the rural area exactly when daughterstransition into middle school age. These daughters are most frequently left behindwithout either parent present. That same discontinuity at that age cutoff does notexist for sons. The discontinuity also does not exist for girls whose parents had
migrated to less-hukou-restrictive cities.1
To further address any selection issues arising from parents’ destination choices, westudy the effects of a 2014 policy in which the central government urged “mega cities”- defined as those with a population of over five million in the city central district area
- to rigidly control the population. This new “migrant population control policy” ledto a tightening of hukou restrictions and shutting down on migrant schools in mega
cities(see Fig. 1). We find that parents who had previously migrated to cities above
the 5-million-population cutoff become 7 percentage points more likely to leave theirmiddle-school-aged daughter behind after 2014, relative to parents who had previously
migrated to cities below the “mega-city” population cutoff. The effect is robust when
we restrict attention to migrants who had made their destination choices before the2014 policy was announced. That same discontinuity does not exist for boys.
Thus, using a different research design and very different variation in the data, weagain find that although China’s policy of mobility restrictions is not gender-specificin its intent or design, it produces a gendered effect in which daughters of a certain
age become more likely to be separated from their parents.
If migrating for work improves parents’ earnings capacity, that could benefit children left behind even if parents are unable to spend time with them. The net effect1

Migrant parents’ destination choices may depend on the importance parents place on their child’s
education. Our triple difference set-up (by hukou policy stringency, by middle school age cutoff,and by gender of child) helps mitigate this endogeneity concern.

2

on children depends whether the parents’ time or money is more important for thechild’s human capital accumulation (Gibson et al., 2011; Zhang et al., 2014). We
therefore add two pieces of analysis to better understand the lives of children left behind. First, we analyze migrant parents’ remittance behavior, and find that migrants
who leave daughters behind remit 10% less than migrants who leave sons behind.
Girls therefore receive less parental time as well as less money compared to boys.
Second, we use a longitudinal survey that tracks rural children from Gansu province
over 15 years to analyze the long run consequences of being left behind on later-life
outcomes. This survey allows us to identify up to 2000 children growing up in ruralarea either with or without their parents. Since the parents’ decision to migrate (leaving their child behind) is not random, we instrument that choice using global importdemand shocks that raises labor demand in cities near each rural area (Khanna etal., 2021), interacted with the hukou policy stringency of those cities. This interaction term identifies the migration-pull to the types of cities where parents find itvery difficult to take their children with them. This analysis shows that growing up
without parents has adverse effects on the child’s human capital accumulation, andon their socioeconomic achievements as adults. Children whose parents migrated andleft them behind complete three fewer years of schooling and are 40 percentage points
more likely to end up with below-average income as adults, compared to children who
parents remain with them in the rural hometown 2 .
Taken together, our results suggest that girls suffer disproportionately when strict
mobility restrictions are imposed on migrant workers in a rapidly developing andurbanizing society. When it is expensive for migrants to keep their children with them,
they are more likely to separate from daughters than sons, and daughters receive lesstime, attention, and money from their parents. This undermines their human capital
accumulation and hurts girls throughout their lives. These gendered effects can betraced back to a conscious policy choice of imposing restrictions on people’s mobility.
Moreover, this issue is not only restricted to China; ‘hokhau’ policy in Vietnam also
makes it similarly difficult for migrant children to be enrolled in public schools at
2

An alternative estimation strategy in which we instrument parents’ decision to migrate with
rainfall shocks in the rural area interacted with historical migration ties due to presence of urban
visitors in that rural area in 1982 (e.g. due to the Mao-era send-down movement) produces very
similar results.

3their parents’ work locations (Cameron, 2012). Rich countries that host cross-bordermigrant workers but discourage those migrants from bringing family members withthem (Mobarak et al., 2021) may also produce such distributional effects.
Other research has examined the effects of migration on children’s educational
outcomes (Zhang et al., 2014), but we are among the first to document the long-run
consequences in adulthood, and the first – to the best of our knowledge – to document
these gendered effects, and connect it to the stringency of mobility restrictions. We
add to the literature on the sources of gender disparities 3 by identifying a newmechanism by which gender disparities might emerge even if the underlying policy(of mobility restrictions) has no direct, explicit gender dimension. We also contributeto the literature on the adverse welfare effects of spatial immobility (Gollin et al.,2014; Bryan et al., 2014; Khanna et al., 2021), and add a gender dimension to the
distributional consequences of migration restrictions.
The remainder of this paper proceeds as follows. Section 2 describes the data
and Section 3 discusses stylized facts about the hukou system and left-behind children in China. Section 4 provides RD estimates of how hukou restrictions result inschool-aged girls being left behind, Section 5 presents the long-term economic consequences associated with leaving children behind and Section 6 discusses the potential
mechanisms driving our empirical pattern. Section 7 concludes.

2

Institutional Background2.1

Hukou Restrictions, Migration, and Children Left behind

In 1958, China formally instituted comprehensive mobility restrictions known as the
hukou system to control internal migration.4 The institution required that each person be classified as rural or urban and be assigned a locality of hukou registration,
which is typically the person’s location of birth. One’s hukou registration determines
3

Blau and Kahn (2017); Goldin (2014); Goldin et al. (2017); Goldin et al. (2021); Barth et al.
(2017); Qian (2008); Bhalotra et al. (2019); Dahl and Moretti (2008); Chetty et al. (2016).
4
See http://www.npc.gov.cn/wxzl/gongbao/2000-12/10/content_5004332.htm for morebackground information.

4

one’s entitlement to pursue many activities and eligibility for state-provided goods
and services in a specific place. All internal migration was subject to approval fromlocal authorities at the destination. Thus, the red hukou book served as an internal
passport that determines a person’s rights to reside and work in specific locations
within China.
These mobility restrictions have been gradually relaxed since 1984. Chinese citizens can now migrate to cities, but without an urban hukou, they have limited accessto many government-provided benefits at the destination. Most importantly, it isextremely difficult for the children of migrant parents to enter local schools in cities.
Economic growth in China triggered a dramatic increase in rural-urban migration.
With an influx of rural migrants, the population of Chinese cities surged from 200
million in 1985 to 900 million in 2020 (Figure 2). Only a subset of those migrants
were classified as urban, so Figure 2 also indicates that the number of urban residents
without urban hukou privileges also increased dramatically during this period. Obtaining an urban hukou requires levels of professional skills or educational attainmentthat are very difficult for the vast majority of rural migrants to attain (Khanna et al.,2021). The schooling restrictions have therefore led to large increases in the numberof children left behind in rural areas. In 2018, approximately thirty percent of allchildren in rural China (69 million children) were growing up without their parents(UNICEF, 2018).
The stringency of hukou regulations varies, with more developed cities with better amenities placing more restrictions on migrants. Figure 3 illustrates that thestringency level of hukou restrictions is positively correlated with the share of rural
migrants who leave their kids behind. Teachers in rural schools have lower educational
attainment than their counterparts in urban schools (Table A.3), urban teachers are
more professionally accomplished (Table A.4), and urban schools provide better education facilities (Table A.5), so there are many clear indications that left-behind ruralchildren also experience worse educational quality.
To keep their school-aged children in urban schools, migrant parents either haveto pay an extra fee called zanzhufei, or send their children to “migrant schools” set up
in cities specifically for poor migrant children without a local hukou. These schools

5are also of poorer quality.5 Many cities closed migrant schools in recent years, making
it even harder for migrant children to receive education in cities (Table A.6). Withlimited availability of migrant schools, migrant parents have to pay zanzhufei, which
can be prohibitive for poor migrant households. The amount of zanzhufei is higher
in cities that have more stringent hukou restrictions (Figure 4), which is why hukou
policy stringency is a useful measure of the difficulty migrant parents face in keeping
their children with them.

2.2

Junior Middle Schools More Restricted than Primary
Schools

Education is compulsory in China. By law, parents must enroll their children in
primary school if they turned six by September 1 in a given year and must enroll themin junior middle school if they turn 12 by that day. Hukou-policy based restrictions area much bigger constraint on migrant families with junior middle school aged children
relative to primary-school-age. Junior middle schools charge a substantially higher
amount of zanzhufei than primary schools (Table A.2). The number of available
school seats is more limited in urban junior middle schools compared to primaryschools.
Figure 5 shows that migrant workers are always more likely to leave middle-schoolaged children behind than primary-school-aged children. They are also more likely
to leave children of all ages behind when they migrate to cities with more stringent
hukou restrictions. Guangzhou – a popular destination for migrant workers – offers
an interesting case study on what happens to migrant children as they transition
from primary to middle school age (Table A.7). In 2008, about 43% of the children inmigrant households studied in primary schools in Guangzhou, but only around 21%of them studied in local junior middle schools. Further, a fraction of the migrantchildren enrolled in junior middle schools are allowed to take the high school entrance
5

The majority of teachers in migrant schools do not have adequate credentials or experience toobtain jobs in local public schools. In addition, migrant schools are often overcrowded and use
second-hand desks, chairs and buildings. Many also have poor lighting, heating, ventilation andsanitation, and do not even provide drinking water, restrooms, and student grounds. Althoughmigrant school fees are much lower than zanzhufei charged by public schools for migrant students,
they are still high for the average migrant family.

6exam.

2.3

The 2014 Migrant Population Control Policy in MegaCities

In July 2014, the State Council of China promulgated “Opinions on Promoting the
Hukou System Reform”, which urged mega-cities - categorized as those with a population of over five million in the city central district area - to “exercise strict control
over the population”. Those mega-cities were required to set a population target by
2020, and local government performance is evaluated against that target. Starting in
2014, local governments in mega cities start strongly restricting the inflow of unskilledmigrants by imposing even more stringent restrictions on school enrollment for migrant children. The same “Opinion” led to a gradual relaxation of hukou restrictions
in small and medium-sized cities. We will examine how the leave-behind decisionsof migrant parents attached to mega-cities changed after 2014, relative to migrants
attached to other cities.

3

Data

3.1

Left-behind Children Data

We use individual-level data on children from the China Migrants Dynamic Survey(CMDS) conducted by the National Health and Welfare Commission. This is thelargest nationally representative survey of China’s migrant population. The samplingframe consists of migrants who have lived in cities for more than one month but have
no local hukou. The survey records socioeconomic information of migrant parents
and their children’s age, gender, education, and residential location. This allows us
to identify whether parents leave their children behind in rural areas at different
stages of their education.
We combine six waves of the survey from 2011 to 2016 and construct individuallevel pooled cross-sectional data for our empirical analysis. We focus on the sample
of children whose parents are in cities where we can measure the stringency of hukou

7restrictions. Our baseline sample contains over 171,859 children (47,121 children at
junior middle school age and 124,738 children at primary school age) whose parents
are rural-urban migrants across 30 provinces.

3.2

Longitudinal Data on Children

We use the Gansu Survey of Children and Families (GSCF) to track long-term socioeconomic outcomes for children. The GSCF is a longitudinal, multi-level study ofrural children conducted by the University of Pennsylvania and the Gansu Bureauof Statistics in five waves in 2000, 2004, 2007, 2009 and 2015. The first wave surveyed a representative sample of 2,000 children aged 9–12 across 100 villages in Gansu
Province. Subsequent waves track these rural children for 15 more years, which allows us to link their long-term socioeconomic outcomes during adulthood, including
educational achievement, earnings, and migration status, with their childhood experience of being left behind by parents or not. We construct individual-level longitudinal
panel data by combining GSCF 2000, 2004 and 2015. As we restrict our data to those
who appear in the 2015 wave, our longitudinal panel data has 1414 individuals.

3.3

Hukou Restrictions Data

We use the hukou index constructed by Khanna et al. (2021) to measure the stringency of hukou regulations across Chinese cities. The main channels for migrants toobtain local urban hukou include tax payment and investment, home purchase, andemployment.6 The requirements of these channels differ by cities, and the composite
hukou index measures the overall difficulty for adult migrants to obtain local hukou
through these main channels.
The hukou system has been used by local government as a policy tool to control
city population and fiscal resource allocation. Internal migrants without a local hukou
have limited access to many government-provided benefits, including local public
education for children. Because China experienced significant changes in the hukou
6

We do not take the channel of family reunion into account, because only a very small fractionof immigrants can obtain local hukou through this channel.

8policy in 2014,7 Zhang et al. (2019) construct city-level hukou index specific for theperiods of 2000–2013 and 2014–2016.

3.4

Data to Construct Instrumental Variables

Estimating the consequences associated with leaving children behind requires us todevelop a few instruments for parents’ decisions to migrate leaving children behind.
One of the instruments uses a labor demand shock in nearby cities due to international trade, which is a pull factor for rural migrant workers. The raw data used
to calculate world import demand are drawn from the International Trade Statistics
Database of UN Comtrade. Second, we leverage rainfall variation during the planting season in rural areas as a push factor, with data from the China Meteorological
Data Service Center. Rainfall is interacted with each rural area’s historical ties tomigration destinations, which is a function of visitors from those destinations in eachrural area. We construct this using the China Population 1982. Appendix Table A.1
reports summary statistics of the key variables used in the analysis.

4

Results on the Propensity to Leave Children Behind

4.1

A Regression Discontinuity (RD) Design Based on School
Enrollment Age

Given the increased difficulty migrant parents face to enroll their children in urban
junior middle schools, we test whether the propensity to leave children behind changes
at the age cutoff for middle school entry. We show the RD result both graphically7

China experienced two rounds of hukou reforms in the past two decades. First, in the early 2000s,
many provinces abolished the hukou quota system for rural to urban hukou transition; also, the stateabolished the grain and oil permit system, thus separating the food supply from hukou registration.
Although the abolition of the hukou quota system lowered the barrier for hukou transition, it was
still very hard for internal migrants to obtain a local hukou in most Chinese cities during that period.
Second, in 2014, following the issuance of “Policies on the Reform of the Household Registration
System”, small and medium-sized cities loosened hukou restrictions, whereas large cities strengthened
hukou restrictions.

9and using the following regression specification:
Lef t behindijt = ψ0 + ψ1 School Ageit × High Hukoujt + ψ2 School Ageit + ψ3 Tj ×
School Ageit + ψ4 Tj + ξjt + ηn + vijt
(1)
where Lef t behindijt is an indicator for whether child i (whose parents work in city
j and do not have a local hukou in their place of residence) are left behind in arural area in year t.8 School Ageit is an indicator for whether child i is above theenrollment age for junior middle school, based on their exact date of birth relative to
the September 1 school entry date.9 High Hukoujt is a binary variable that equals
one if the stringency level of hukou restrictions in city j and year t is above theaverage city level. The running variable Tj is the number of years between school
enrollment age and children’s age. Our primary variable of interest is the interaction between School Ageit and High Hukoujt , which examines whether there is any
differential discontinuous shift in the probability of leaving children behind at theschool enrollment age (Tj = 0) in cities with more restrictive hukou policies. We
combine CMDS 2011-2016 to create an individual-level pooled cross-sectional dataset
to estimate equation (1).
We estimate equation 1 separately for male and female children to examine whether
migrant parents’ decisions vary by the gender of their child. Imbens and Lemieux(2008) and Gelman and Imbens (2019) suggest that a local linear regression using
samples near the RD cutoff is likely to yield the most robust estimates. We use alocal linear control function for the running variable Tj , and select two years as the
bandwidth in our baseline specification. We conduct robustness checks with alternative bandwidths and control functions for Tj .
We add city-by-year fixed effects ξjt to control for city-by-year characteristics suchas industrial structure and economic development plans of local government that may
be correlated with the city’s hukou policies . We control birth cohort fixed effects ηn
8

We exclude rural-urban migrants who migrated from rural to urban areas within the same
prefecture-level region. There are 333 prefecture-level regions in China. A rural and an urban area
located within the same prefecture are close to each other, and thus it is easy for migrant parents
to go back home and be with their children.
9
Our empirical identification strategy is a fuzzy RD design, as some migrant workers may send
their children to a junior middle school later than the compulsory enrollment age.

10

to account for any changes in other policies (e.g. the One Child Policy) pertaining tochild outcomes. Table A.8 examines whether other variables change systematicallyat the RD cutoff. We do not see any discontinuities in the fraction of migrants who
get a local urban hukou, parents’ migration decisions, or incomes.

4.2

Graphical Analysis of the Regression Discontinuity

Figure 6 graphically represents shifts in the fraction of left-behind children at theage cutoff for middle school enrollment . Reflecting our triple difference research
design, we show separate graphs for sons and daughters, and for cities where migrantparents face more or less stringent hukou restrictions. There is a sharp increase in
the share of left-behind girls just at the school enrollment age if their parents arein highly hukou-restricted cities (the left panel of Figure 6a), whereas we do not
observe any discontinuous changes at the enrollment age for boys in those highly
hukou-restricted cities (the right panel of Figure 6a). We also do not observe any
discontinuity for either girls or boys in less hukou-restricted cities (Figures 6b). In
addition, irrespective of child gender, the fraction of children that are left behind
is much lower in less restricted cities than it is in highly restricted cities. Migrantparents appear to leave their daughters rather than their sons in their rural hometown
in response to strict hukou restrictions, whereas there is no obvious gender bias forparents in cities with relaxed hukou policies .

4.3

Regression Analysis

We estimate equation (1) to statistically examine the discontinuity described above.
The dependent variable in Table 1 is a binary indicator for the decision to leave thechild behind, and our independent variable of interest is the interaction between theindicator for the child reaching junior-middle-school enrollment age and an indicatorfor parents in cities with above-average stringency of hukou-restrictions. Our baseline
specifications use two years as the bandwidth around the age cutoff and employ a local
linear control function for the running variable. We perform the analysis separately
for daughters (columns 1-4) and sons (columns 5-8).
We control for city-by-year fixed effects in columns 1,2,5,6. To absorb any dif11

ferences in attitudes towards boys’ versus girls’ education between migrants fromdifferent areas, columns 3,4,7,8 add a triple interaction between city-, city- and hukou
province- fixed effects. Columns 2,4,6,8 add birth cohort fixed effects. All columns
control for household socioeconomic characteristics.
Across all the specifications for daughters (columns 1-4), the interaction of theabove-enrollment-age indicator and the high-hukou-restriction indicator is statistically significant, and the coefficient implies that girls become 3.2-3.5 percentage points
more likely to be left behind exactly when she reaches the legal enrollment age forjunior middle school and her parents work in a city with restrictive hukou policy.10
34% of girls in migrant households in China are left behind in rural areas, so thediscontinuous jump at that age-cutoff represents a 9% increase at the mean. The
coefficient on the above-enrollment-age dummy is close to zero, which suggests thatthe discontinuity does not exist for parents who migrated to cities with relatively
relaxed hukou policies.
Across all specifications for sons (columns 5-9), both the above-enrollment-age
indicator and its interaction with the high-hukou-restriction indicator are statisticallyindistinguishable from zero. The daughter effect is statistically distinguishable fromthe son coefficient (Table A.11). In contrast to daughters, the elevated entry feesfor middle school does not appear to deter migrant parents from keeping their sonswith them in the city, regardless of how stringent the hukou restrictions are. China’s
hukou policies are not formally gender-specific by design, but when that schoolingexpense is imposed on parents, they seem more willing to sacrifice time with theirdaughters. This is reminiscent of Dahl and Moretti (2008)’s findings that parents seem
to prefer spending time with sons. Some pre-existing underlying son preference in
China appears to be interacting with mobility restrictions to produce gender-unequal
outcomes.
Given son preference in China and the availability of sex selection technology,
there is a plausible concern that child gender may reflect parental choices. Existing
evidence suggests that sex selection is more common at higher birth orders, butobserved gender ratio of the first-born child match biological expectations (Almond
10

Table A.9 shows that the results remain similar under RD design variations in which we extend
the bandwidth or use a quadratic control function for the running variable.

12et al., 2019). We therefore re-run our regressions in Table A.10 limiting the sample tofirst-born children only. The empirical patterns remain very similar, where daughtersof parents in hukou-restrictive cities become 3.7-4.2 percentage points more likely tobe left behind when they cross the age threshold for middle-school entry.
Table 2 shows that of the children left behind in rural areas by migrant parents,
the majority are left behind without either parent present. These cases account for
24% of the 34% of rural children that are left behind. Furthermore, the discontinuous
jump in parents’ propensity to leave daughters behind at middle-school-age mostoften leads to those additional daughters being left behind in rural areas without
either parent present. This is relevant because the emotional toll and developmental
burden on children are likely larger when both parents are absent (citation ). Other
descriptive data from China shows that in such cases, grandparents are asked to takecare of children left behind in rural areas.

4.4

Another RD Design Based on 2014 Mega-city Migrant
Population Control Policy

We use the 2014 “migrant population control policy” imposed on mega cities toconstruct a different RD research design to again test for gender biases in migrantparents’ “leave-child-behind” decisions. This new policy forced local governments inmega-cities to impose new restrictions on migrants’ access to local public services.
Since “mega-cities” have a precise definition (population exceeding five million in
the city central district), we construct the following RD specification based on that
population threshold:Lef t behindijt = α0 + α1 School Ageit × I(P op > 5 million)j × I(t > 2014)+
α2 School Ageit × I(P op > 5 million)j + α3 School Ageit × I(t > 2014)+(2)

α4 School Ageit + ξjt + ηn + vijt
where School Ageit is an indicator for children who have reached middle-school enrollment age by year t, I (P op > 5 million)j is an indicator for the mega-cities subjectedto the new policy, and I (t > 2014) is an indicator for the post-treatment period.

13

The running variable in this RD design is the city-specific difference between baseline
city population and 5 million, which is absorbed by city-by-year fixed effects–ξjt . We
restrict the sample to parents who made their migration destination choices before
2014, to mitigate any endogeneity concerns about parents choosing destinations basedon concerns about children’s access to urban schools.
Columns 1 and 2 of Table 4 show that for female children, the RD variable of interest—the triple interaction between having reached the junior middle school enrollment age; the indicator for cities with above-5-million population; and the indicatorfor post-2014—is positive and significantly different from zero. In response to the newpolicy, parents who had migrated to mega-cities prior to 2014 become 7 percentage
points more likely to leave daughters behind. The second row shows that parents
were not exhibiting that behavior before the policy went into effect. Columns 3-4
show that there is no such effect for boys in migrant households. All these coefficients
jointly imply that new migration restrictions that increase the cost of raising children
in the city pushes parents into discriminating against their daughters.

5

Remittance Behavior

Leaving children behind in rural areas reduces the cost of raising children because
parents can avoid paying extra school fees in urban areas. Therefore, migrant parents
can compensate daughters for separating from them by sending remittances back to
the rural area. Both parental time and money are useful for child development, so it’s
possible that this is on net beneficial for daughters. Table 3 examines the patterns ofremittances sent back by migrant parents as a function of child gender. Remittancesent back is actually 9% lower when a daughter is left behind compared to a son being
left behind. In panel C, we see that this gender difference gets even larger when thechild reaches junior-middle-school age. In this sample, remittances are 13-16% lower
for left-behind girls.
In summary, there is no evidence that daughters who (our previous analysis shows)are more likely to be left behind at that age are financially compensated by parents.
Daughters receive less time and less money from their parents.

14

6Long-term Consequences of Leaving Children Behind

We now use longitudinal data to study the longer term consequences of being leftbehind as a child on socio-economic outcomes in adulthood, observed 15 years later.
We estimate the following specification using data from the 2000, 2004, and 2015
rounds of the Gansu Survey of Children and Families (GSCF), which tracks children
born in rural Gansu over a long period:
Yict = β0 + β1 Lef t behindict + ξm + ηt + εit(3)

We use information on the parents’ location to identify children who were either livingwith their parents, or were left behind when they were middle-school-age in 2000 or
2004.11 Socio-economic outcomes Yict are measured in 2015 for individual i born ina rural area in prefecture c in year t.12 In our main specifications, Lef t behindict is
an indicator for whether individual i was separated from parents for more than six
months in a survey year (2000 or 2004) during junior middle school age. We control
for residential township fixed effects ξm , and birth cohorts fixed effects, ηn .
Note an important difference in the structure of this data relative to datasets weused in our earlier analysis in section 4: in this panel dataset, left-behind children arethose whose parents migrated, while parents of the “control group” are non-migrants.
Each parent’s decision about whether to migrate is an endogenous choice, so we needan instrument for the parents’ migration decision to isolate the causal effect of leaving
children behind.
11

Because GSCF 2000 (the initial wave of GSCF) surveyed children aged 9–12, and the school
age for junior middle school is 12-15 for those whose birthday is before September 1 and 13-16 forthose whose birthday is after September, we can observe their experience of being left behind during
middle school age in the 2000 or 2004 wave (the first two waves of GSCF).
12
All children in our sample hold a local rural hukou in the prefecture of birth (a local hukou inrural areas in the birth prefecture) in 2000 and 2004. In China, a prefecture region includes bothrural and urban areas. The GSCF covers rural children in rural areas in 11 prefectures.

15

6.1

Instrument #1: Import Demand Shocks in Nearby Cities

Since the growth in China that induced this large-scale rural-urban migration wasexport-led, we can use global import demand shocks for the products/industries thateach city specializes in as sources of exogenous variation that drive migration choicesfrom nearby rural regions of Gansu. Using UN Comtrade data on imports, we create
an index called W IDct , which measures each rural region’s exposure to a world importdemand shock in each year. The import demand shock experienced by each city isdefined as the 2-year increase in import demand for industry k weighted by theimportance of that industry to destination city d, as measured by that city’s preEXk,d). Every city experiences these
period (1997) export share of that industry ( P EXk,jj
demand shocks, so each rural region’s exposure is determined by their proximity toevery “potential” migration destination. We therefore weight the city-specific demand
shocks by the inverse of the distance from the migrant’s birth location c to every urban
destination d, to create the index for rural region c:
W IDct =Xd1
distdc

 Xk

EX k,dW orld IM k,t−2, t × P
j EX k,j!
(4)This is akin to “shift-share” instruments common in the economics literature. We
assign non-zero weights only to potential destination cities that are located within a
400 km radius of birthplace c. The exact instrument we use in our regressions is theinteraction between W IDct and restrictiveness of hukou regulations in nearby cities,
because we are trying to extract the migrant’s pull to destinations where they cannot
easily take their children. The specification of the first-stage estimation is:
Lef t behindicn,t = γ0 + γ1 W IDct × Des High{Hukou}c + γ2 W IDct + ξc
+ ηn, t × F emale + εicn,t(5)

Des High Hukou c is an indicator for whether migrants from birthplace c would
face stringent hukou restrictions in cities near location c. We first compute the inverse distance-weighted sum of the hukou index across potential destination cities,
P  1
d distdc Hukou Indexd , and consistent with our approach in section 4, the indi
P  1cator Des High Hukou c turns on if d distdc Hukou Indexd is above the average
16level of all cities.
We directly control for W IDct (and Des High{Hukou}c is absorbed by the location fixed effects ξc ) in the first and second stages of this 2SLS strategy, so only
the interaction between WID shocks and hukou restrictions acts as the excluded instrument. The exclusion restriction of this instrument is violated if positive importdemand shocks in nearby cities affect children growing up in rural Gansu throughmechanisms other than being left behind by migrant parents. That’s actually a very
plausible concern: increased world import demand like raises wages for migrant parents (which could benefit children in other ways), and if the shock persists, it could
create future economic opportunities for the children as they enter adulthood, andit could also thereby raise their perceived returns to education. All of that should
improve child education and economic outcomes, while we estimate the opposite, aspreviewed in the introduction: Gansu children are worse off in multiple dimensions
when their parents migrate and leave them behind. Violations of the exclusion restriction therefore lead to an underestimation of the detrimental effects of leaving
children behind. Our estimates, if anything, will be conservative in magnitude.

6.2

Instrument #2: Rainfall and Historical Migration Ties

Our first instrument is created based on shift-share “pull” shocks in cities that attract
rural people to migrate. We next leverage “push” factors in places of origin. In
particular, our second instrument is the interaction of rainfall in original locationinteracted with historical migration ties. The specification of the first-stage estimationis:
Lef t behindicn,t = γ0 + γ1 Rainct × M ig T ierc + γ2 Rainct + ξc(6)
+ ηn, t × F emale + εicn,twhere Rainct is the rainfall in the planting season in birth location c and year t. Decreased rainfall in the planting season can negatively affect agricultural productivity.
A positive income shock from rainfall can either hold migrants back in the rural area,or it could relax liquidity constraints and permit more migration (Bazzi, 2017).
Like Imbert et al. (2022), we combine this rainfall shock with those rural areas’
pre-existing connection to cities in order to predict migration propensity. Internal17

migration was prohibited before 1984, so migration flows prior to 1984 were mainly
driven by government programs like the Sent Down Youth campaign, which resulted
in idiosyncratic variation in each rural region’s connection to cities from which theyouth had visited pre-1984. We use the Population Census 1982 to calculate the shareof in-migrants to rural birth location c to measure such migration network ties. Rural
areas that had hosted in-migrants from a large city may have retained better personalconnections and knowledge about that city, which in turn increases the desirability
or salience of that city as a possible migration destination (Kinnan et al., 2018).
We employ the two instruments discussed above independently as they representvery different sources of variation (driven by “pull” demand shocks in potential destination cities versus “push” weather shocks in places of origin). In Table A.12, weshow the strength of the first-stage relationships between our different instruments
and our (endogenous) independent variable of interest.

6.3

Results on Long-term Socioeconomic Outcomes

Table 5 reports the effects of being left-behind on the educational attainment of children, where we use the world import demand shift-share IV strategy. The estimatedequation 3 includes birth location fixed effects and cohort fixed effects, and (sometimes) controls for household characteristics like whether a grandparent is alive andwhether a grandparent resides in the same village. Parental absence during childhood
have significant negative effects on future educational achievements. Leaving children
in poor rural areas during junior middle school age reduces schooling attainment by
three years. This is a very large effect that represents 0.85 standard deviations of thedependent variable. Columns 3-4 further show that the years of schooling are 28-29
percentage points lower for those who experienced parental absence during school age
than for those who did not.
We next restrict our sample to the subset of children who took high school entrance exams. Separation from parents during junior middle school age reduces theirprobability of passing high school entrance exams by as much as 41-45 percentage
points (columns 5 and 6). This result is especially striking because anecdotally, areason migrants often provide for sending their middle-school-aged-child back is so18that the child can prepare for the high-school entrance exam, for which the curriculum
varies by prefecture.
Table 6 shows that being left behind also significantly negatively affects later-life
socioeconomic outcomes. In columns 1 and 2, we divide the children in our sample
into two groups based on their income in 2015; the low-income group includes those
whose income is below the average level and those who do not have any income.
Parental absence during school age increases the probability of ending up in the lowincome group by up to 40 percentage points. We next look at the persistence of rural
status across generations, in columns 3 and 4. The dependent variable here is anindicator for whether an individual either remains in the village or migrates without
an urban hukou, both of which capture disadvantaged rural status in adulthood. The
experience of being left behind increases the probability of retaining rural status byas much as 35 percentage points, which in turn is expected to produce negative effects
for the next generation (the children of those left-behind), if the results of this paper
are correct. Those “grandchildren” without an urban hukou will also be restrictedfrom accessing higher-quality urban educational systems. This undermines intergenerational mobility. Indeed in the GSCF data, people who had been left behindin villages in childhood are approximately 20% more likely to leave their children
behind in adulthood, compared to those who had not. Left-behind children are alsosignificantly more likely to have an obesity problem later in life (columns 5 and 6).
While these effects are large, they may yet be under-estimates of the true effects(as argued above), because the world import demand shock instrument should improve migrant family’s socioeconomic and educational outcomes through other channels (remittances, future economic opportunities, returns to education, etc.). Table
A.13 shows estimates of the long-term consequences using the (rainfall × historicalmigration ties) instrument. The coefficient estimates are slightly larger in magnitude
and document a similar empirical pattern. Once again, leaving children behind has asignificant negative effect on their educational achievement, health and socioeconomic
status. In Table A.14, we change the RHS measure in equation 3 to ”the amount oftime that parents are away from children when they are school-aged”. We empiricalpatterns remain the same.

19

6.4

Hukou Restrictions and the Gender Wage Gap

Two caveats about these long-term results are that (a) the longitudinal data allow us
to compare children growing up without parents in rural areas to those growing up
with parents in rural areas, not to those growing up in cities, and (b) our instruments
capture the general economic drivers of parental migration, so it cannot separately
identify any differential effect of parental absence on sons versus daughters. In orderto shed light on the gender-differentiated long-term consequences of parents’ greater
propensity to leave daughters behind (as established in section 4), we can return to
the CMDS dataset to examine whether there are larger gender differences in adultlabor market outcomes for individuals who originate in rural areas adjacent to cities
with stricter hukou restrictions (where parents exhibited the bias against daughters).
Figure 7 correlates hukou policy restrictiveness in nearby cities on the horizontal
axis with a “gender wage gap” measure on the vertical axis, which is the differencein wage rankings between male and female workers who have the same rural area oforigin. We divide individual wages into three terciles to measure wage rankings. When
individuals come from a rural origin located near potential migration destinations witha restrictive hukou environment, there is a greater gender wage gap in earnings later inlife for women and men from that origin. This is a natural and sensible implication of
the two sets of results we showed in sections 4 and 6: migrant parents are more likely
to leave daughters behind when they face a restrictive hukou environment, and thechildren left behind fare worse later in life. The joint implication of these two facts isthat we should observe larger gaps in adult economic outcomes in rural areas adjacentto cities with restrictive hukou policies, which is exactly what Figure 7 shows.

7

Mechanisms

In this section, we evaluate the underlying mechanisms through which hukou restrictions lead to female children being left behind. At least three potential mechanisms
may result in our empirical pattern. First, hukou restrictions exacerbate the effectsof the son preference and cause parents to sacrifice their female children. Second,
the rate of returns to education may be lower for females than males. Third, sons20

are potentially more productive than daughters. We empirically examine the threemechanisms and find the most consistency with the first mechanism: the interaction
between hukou restrictions and the son preference.

7.1

The Interaction between Parental Gender Bias and Hukou
Restrictions

We firstly assess whether our empirical pattern is driven by the interplay between
parental son preference and hukou restrictions. Table 7 assigns girls (of migranthouseholds) into two groups, based on whether they have male siblings who willcompete with them for limited educational resources in cities. We find that the effectsof hukou restrictions on the probability of girls being left behind are larger for thosewith male siblings. Thus, the gender bias of parents leads to unequal intra-household
allocation of resources between boys and girls and drives our empirical pattern.
In rural China, the male-female ratio of second births captures the level of son
preference. As documented by the literature, rural parents who have a strong son
preference are likely to make a sex selection for second births (Almond et al., 2019).
Therefore, we create an indicator for whether the male-female ratio of second births
in migrant parents’ hukou provinces (provinces of origin) is above the national median level, to inform us whether those parents come from provinces featuring a strong
parental gender bias. To account for the confounding effects of current economic
factors on gender ratio, we use the China Population Census 1990 (21 years prior to
our sample period) to construct the indicator. Almond et al. (2019) also documentthat the sex ratio of second births measured using China Census 1990 reflects theson preference of parents (rather than differential potential earnings between maleand female children). We thus re-perform our RD estimation and additionally interact our independent variable of interest – the interaction between hukou restrictions
and the above-enrollment-age indicator – with the indicator for male-biased secondbirth sex ratio in migrant parents’ original provinces. Table 8 shows that the tripleinteraction term is significantly positive for female children, indicating that the association between hukou restrictions and girls being left behind is significantly more
pronounced for migrants who come from regions featuring higher gender bias towards

21

sons. The results are in accordance with the literature showing that, when people
migrate, their beliefs and values on gender roles move with them, even though theirexternal environment has changed (Alesina et al., 2013).

7.2

Other Mechanisms

Men and women are likely to have heterogeneous returns to education, and one may
expect that parents leave their female children in villages if females have a lower rateof return to education and therefore should be allocated less educational resources. In
Table A.15, we use individual data to perform Mincer wage regressions and introduce
an interaction between a female indicator and a high school education indicator 13 .
The interaction term is positive and significantly different from zero, which implies
that females have a higher (rather than a lower) rate of return to education. Higher
returns to skill for females are evident for both rural and urban people and also for
migrant workers. Thus, our empirical pattern is unlikely to be driven by differential
returns to education by gender.
Another competing mechanism is the “productive son” mechanism. To consider
the possibility that potential higher productivity and wages are expected from malechildren, we examine whether the effects of hukou restrictions on female children
being left behind are more pronounced in regions with higher baseline male-female
gaps in wages. The results in Table A.16 imply that the association between hukou
restrictions and the probability that female children are left in villages is not affectedby baseline gender gaps in wages in either the origin or destination of migrant parents
14.
One may also expect that migrant workers leave their female children behindbecause separation from parents may have a more detrimental effect on male children.
However, we do not find gender differences in socioeconomic outcomes associated with13

We use individual-level pooled cross-sectional data by combining CLDS 2012, 2014, 2016 and2018 to perform mincer wage regression, because CLDS has a sample period similar to our baseline
analysis and allows us to look at the pattern of gender-specific returns to education for people withdifferent migration status and hukou types (rural or urban hukou).
14
We follow Dahl (2002) and Gao et al. (2022) to run Mincer wage regressions city by city using
the Population Census 2005. We use the coefficient on the female dummy in Mincer wage regressions
to measure city-specific gender gaps in wages.

22leaving children behind.
In sum, the son preference channel does a better job of explaining the observed
relationship between mobility restrictions and rural girls being left behind than doother mechanisms we have discussed 15 . Nevertheless, we acknowledge that there may
be other mechanisms behind the effects of hukou restrictions on left-behind girls that
require additional data collection and analysis.

8Conclusion

Our analysis highlights the unintended consequences of an important new pattern ofmobility on gender inequalities. As economic growth and industrial activities increasedemand for unskilled workers in Chinese cities, adult migrant workers without a local
hukou are authorized to work in urban areas, while their children have only limitedaccess to education in cities. Our RD estimates based on the school age cutoff reveal
that, under hukou restrictions, rural-urban migrants are more likely to leave behind
their daughters than their sons in poor rural areas. We further document that people
who were left behind during their school age tend to drop out of education early andend up with lower socioeconomic status.
Other studies have documented that mobility constraints trigger economic losses
for adult workers and widen economic gaps between rural and urban people. Ourcontribution is to quantify how migration restrictions placed on children can translate into long-term socioeconomic disadvantages and how female children are more
vulnerable to these restrictions. Thus, both the aggregate and the distributional effects of mobility constraints may be larger than development economists previously
thought. Our work proposes a new mechanism whereby placing restrictions on migration can aggravate gender inequities among children, even if the migration policy
does not have an explicit gender dimension.
Although we focus on gender disparities, our analysis sheds light on economic inefficiencies in the developing world. While improved access to economic opportunities
15

We acknowledge the son preference of parents may be affected by historical gaps in earnings andproductivity by gender. Nevertheless, our results demonstrate that our baseline empirical pattern
has nothing to do with current gender disparities in wages and productivity.

23

for females and disadvantaged groups has significantly boosted economic growth in
the U.S. (Duflo, 2012; Hsieh et al., 2019), limited access to education and economic
resources that disproportionally affect girls in migrant households may undermine
long-term economic development in China.

24

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27

Figure 1: 2014 Population Control Policy and Hukou Restrictions

Note: Data come from Zhang et al. (2019).

Figure 2: More and More People Don’t Have Local Urban Hukou as China Urbanizes

Note: The blue line denotes the population in urban areas, and the red line shows the population
holding local urban hukou in urban areas. Data come from the China Statistical Yearbook.

28

Figure 3: Hukou Index and the Share of Migrants Leaving Children Behind

Note: This figure shows the relationship between the share of migrants leaving children behind andthe stringency of hukou regulations in migrants’ destination cities. Cities are grouped into fiftygroups according to the quantile of the hukou index. The vertical axis denotes the mean value ofthe share of migrants leaving children behind and the horizontal axis denotes the mean value of the
hukou index in each quantile. Data on left-behind children come from the China Migrants Dynamic
Survey (CMDS), and data on the hukou index come from Zhang et al. (2019).

29

Figure 4: Hukou Restrictions and Zanzhufei (Extra School Fee) for Migrants’ Children

Note: In China, migrant children without a local hukou have to pay zanzhufei (an extra fee imposed
specifically on them) in order to go to a local school. This figure shows the relationship between theamount of zanzhufei and the stringency of hukou regulations in migrants’ destination cities. Cities
are grouped into fifty groups according to the quantile of the hukou index. The vertical axis denotes
the mean value of the amount of zanzhufei and the horizontal axis denotes the mean value of the
hukou index in each quantile. Data on left-behind children come from the China Migrants Dynamic
Survey (CMDS), and data on the hukou index come from Zhang et al. (2019).

30

Figure 5: Share of Left-behind Children by School Age(a) Highly restrictive cities(b) Less restrictive cities

Note: We divide cities into two groups based on the stringency of hukou restrictions. Highly
restrictive cities are those in which the hukou index is above the national mean, and less restrictive
cities are those in which the hukou index is below the national mean. Hukou index measures thestringency of hukou regulation and the difficulty for migrants to obtain local hukou. Data on leftbehind children come from the China Migrants Dynamic Survey (CMDS), and data on the hukou
index come from Zhang et al. (2019).

31

Figure 6: School Enrollment and Left-behind Children(a) Girls in highly restrictive cities(b) Boys in highly restrictive cities(c) Girls in less restrictive cities(d) Boys in less restrictive cities

Note: The vertical axis shows the share of children left behind in villages, for girls and boys,
repectively. The horizontal axis shows the number of years relative to the junior middle school
enrollment age. We divide cities into two groups based on the stringency of hukou restrictions.
Highly restrictive cities are those in which the hukou index is above the national mean, and lessrestrictive cities are those in which the hukou index is below the national mean. Hukou index
measures the stringency of hukou regulation and the difficulty for migrants to obtain local hukou.
Data on left-behind children come from the China Migrants Dynamic Survey (CMDS), and data on
the hukou index come from Zhang et al. (2019).

32

Figure 7: Hukou Restrictions and Male-Female Wage Gaps

Note: These figures illustrate how hukou restrictions in migrants’ potential destination cities during individuals’ childhood affect the gender gap in wages later in life.
The horizontal axis denotes the inverse distance-weighted hukou index of potential
destination cities (for migrants coming from a particular city of origin) when these
individuals were at junior middle school age. The vertical axis shows differences inwage rankings between male and female workers who have the same city of origin.
We divide individual wages into three tertiles to measure wage rankings. Cities aregrouped into fifty groups according to the quantile of the inverse distance-weighted
hukou index. Wage data come from the China Migrants Dynamic Survey (CLDS)
2016, and data on the hukou index come from Zhang et al. (2019).

33

Table 1: School Enrollment Age and left-behind Children(1)

Above enrollment age × Highly restricted cities (=1) (ψ1 )Above enrollment age (ψ2 )34

P-value of ψ1 + ψ2
Coeff diff pval
Observations
Adjusted R-squared
Mean of Dep. Var.
Household Control
City FE×Year FE
City FE×Year FE×Hukou Province FE
Cohort FE
Age Bandwidth
Control function for the running variable

(2)
(3)
(4)
(5)
(6)
(7)
(8)
Dependent Variable: Indicator for leaving the child in rural hometown
FemaleMale
FemaleMale
FemaleMale
FemaleMale
0.0324** 0.00331 0.0330** 0.00444 0.0349** 0.00871 0.0354** 0.00984(0.0145) (0.0150) (0.0144) (0.0148) (0.0145) (0.0170) (0.0144) (0.0167)-0.00451 0.000905 -0.00545 0.00125 -0.00375 0.000643 -0.00644 0.000597(0.0158) (0.0136) (0.0159) (0.0134) (0.0176) (0.0153) (0.0178) (0.0152)
0.0341
0.679
0.03970.576
0.01490.400
0.0271
0.360
0.000
0.000
0.000
0.000
31,07140,85431,07140,85431,07140,85431,07140,854
0.172
0.146
0.173
0.147
0.206
0.184
0.207
0.184
0.35
0.34
0.35
0.34
0.35
0.34
0.35
0.34
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
No
No
No
No
No
No
No
Yes
Yes
Yes
Yes
No
No
Yes
Yes
No
No
Yes
Yes
2
2
2
2
2
2
2
2
LinearLinearLinearLinearLinearLinearLinearLinearNotes This table shows the results of estimating equation (1). The bandwidth is two years. We use a RD sample of children who are two years older oryounger than the enrollment age of junior middle school. “Coeff diff pval” reports the p-value of a test of equality of (ψ1 ) between the female and male, using
the Fisher’s permutation test. Household controls include father’s age and age-squared, an indicator for whether household income is above the median value
among the migrant population in the city and an indicator for whether household consumption is above the median value among the migrant population in
the city. We use a local linear control function for the running variable. Robust standard errors clustered at the city level are reported in parentheses. ***p<0.01, ** p<0.05, * p<0.1.

Table 2: One Parent Versus Both Parents Are Separated from Children
(1)

(2)

35

(3)
(4)
(5)
(6)
(7)
FemaleMale
Panel A: Dependent Variable: Indicator for leaving the child behind without both parents
Above enrollment age × Highly restricted cities (=1) (ψ1 ) 0.0202*
0.0208*0.0230** 0.0236**
0.006150.00726
0.00912(0.0118) (0.0117) (0.0107) (0.0106) (0.0124) (0.0121)(0.0143)
Above enrollment age (ψ2 )-0.00903-0.0145-0.00770-0.0137-0.00126 -0.00500 -0.00151(0.0133) (0.0132) (0.0137) (0.0136) (0.0129) (0.0129)(0.0143)
Observations
31,071
31,071
31,071
31,07140,85440,85440,854
Adjusted R-squared
0.130
0.131
0.188
0.189
0.142
0.142
0.174
Mean of Dep. Var.
0.24
0.24
0.24
0.24
0.23
0.23
0.23
Panel B: Dependent Variable: Indicator for leaving the child behind with one parent
Above enrollment age × Highly restricted cities (=1) (ψ1 )0.01170.01170.01190.0118-0.00284 -0.00282 -0.000407(0.00733) (0.00747) (0.00778) (0.00793) (0.00595) (0.00589) (0.00643)
Above enrollment age (ψ2 )0.006830.01090.003940.00725
0.002160.006240.00216(0.00831) (0.00847) (0.00881) (0.00915) (0.00749) (0.00744) (0.00705)
Observations
31,071
31,071
31,071
31,07140,85440,85440,854
Adjusted R-squared
0.207
0.208
0.252
0.253
0.179
0.180
0.225
Mean of Dep. Var.
0.10
0.10
0.10
0.10
0.11
0.11
0.11
Household Control
Yes
Yes
Yes
Yes
Yes
Yes
Yes
City FE×Year FE
Yes
Yes
No
No
Yes
Yes
No
City FE×Year FE×Hukou Province FE
No
No
Yes
Yes
No
No
Yes
Cohort FE
No
Yes
No
Yes
No
Yes
No
Age Bandwidth
2
2
2
2
2
2
2
Control function for the running variable
LinearLinearLinearLinearLinearLinearLinear(8)0.0102(0.0138)-0.00559(0.0142)
40,8540.175
0.23-0.000347(0.00634)
0.00619(0.00696)
40,854
0.226
0.11
Yes
No
Yes
Yes
2
LinearNotes The bandwidth is two years. We use a RD sample of children who are two years older or younger than the enrollment age of junior middle school.
Household controls include father’s age and age-squared, an indicator for whether household income is above the median value among the migrant populationin the city and an indicator for whether household consumption is above the median value among the migrant population in the city. We use a local linear
control function for the running variable. Robust standard errors clustered at the city level are reported in parentheses. *** p<0.01, ** p<0.05, * p<0.1.

Table 3: Remittance sent to rural children by gender
(1)
(2)
(3)
(4)
Dependent variable: Log Amount of RemittancePanel A: Full Sample
Female-0.0872*** -0.0890*** -0.0928*** -0.0956***(0.0332)(0.0332)(0.0342)(0.0341)
Observations
39,55639,55639,55639,556
Adjusted R-squared
0.07780.07850.124
0.125
Panel B: Primary School Age
Female-0.0980*-0.0971*-0.0952*-0.0925*(0.0530)(0.0530)(0.0558)(0.0559)
Observations
14,46014,46014,46014,460Adjusted R-squared
0.08100.08140.133
0.133
Panel C: Junior Middle School Age
Female-0.134**-0.135**-0.165**-0.164**(0.0653)(0.0642)(0.0702)(0.0689)
Observations
8,018
8,018
8,018
8,018
Adjusted R-squared
0.08180.0816
0.113
0.112
Household Control
Yes
Yes
Yes
Yes
City FE×Year FE
Yes
Yes
No
No
City FE×Year FE×Hukou Province FE
No
No
Yes
Yes
Cohort FE
No
Yes
No
Yes
Notes Panel A shows results for all children aged below 16, and panels B and C, respectively, show results for children
at primary school age and junior middle school age. We use the CMDS 2011 and 2012 to perform estimation as only
the two waves of CMDS contain information about remittance. Robust standard errors clustered at the city level arereported in parentheses. *** p<0.01, ** p<0.05, * p<0.1.

36

Table 4: An Alternative RD Design based on Population Controls in Mega Cities
(1)
(2)
(3)
(4)
Dependent Variable: Indicator for leaving the child in rural hometown
FemaleMale
FemaleMaleAbove enrollment age ×I(Population>5 million) × 0.0700*** -0.0429 0.0772** -0.0314
I(Year>2014)(0.0220) (0.0363) (0.0306) (0.0267)
Above enrollment age ×I(Population>5 million)-0.00355
0.0186 -0.00946 0.00909(0.0222) (0.0139) (0.0197) (0.0153)
Above enrollment age (ψ2 ) × I(Year>2014)-0.0495** 0.0342-0.0491
0.0434(0.0214) (0.0262) (0.0291) (0.0277)
Above enrollment age (ψ2 )0.0314*-0.0240 0.0453** -0.0200(0.0173) (0.0166) (0.0172) (0.0186)
Coeff diff pval
0.000
0.000
Observations
10,296
13,812
10,296
13,812Adjusted R-squared
0.163
0.137
0.192
0.169
Household Control
Yes
Yes
Yes
Yes
City FE×Year FE
Yes
Yes
No
No
City FE×Year FE×Hukou Province FE
No
No
Yes
Yes
Cohort FE
Yes
Yes
Yes
Yes
Age Bandwidth2222City Size Bandwidth3333Notes The age bandwidth is two years. We use a RD sample of children who are two years older or younger than theenrollment age of junior middle school. “Coeff diff pval” reports the p-value of a test of equality of “Above enrollment
age ×I(Population>5 million) ×I(Year>2014)” between the female and male, using the Fisher’s permutation test. The
city size bandwidth is 3 million, and thus we only include cities with population between 2 and 8 million. Household
controls include father’s age and age-squared, an indicator for whether household income is above the median value
among the migrant population in the city and an indicator for whether household consumption is above the medianvalue among the migrant population in the city. Robust standard errors clustered at the city level are reported inparentheses. *** p<0.01, ** p<0.05, * p<0.1.

37

Table 5: The Effects of Leaving Children Behind on Education Outcomes
(1)

(2)

Years of Schooling
Indicator for leaving thechild behind
F statObservations
Mean of Dep. Var.
SD of Dep. Var.
Household Controls
Township FE
Year FE-2.863***(0.561)
50.97
1,335
11.37
3.510
No
Yes
Yes

-3.005***(0.697)
43.33
1,335
11.37
3.510
Yes
Yes
Yes

(3)
(4)
(5)
(6)
IHS of Years
Pass High Schoolof Schooling
Entrance Exams (=1)-0.277*** -0.290** -0.411*-0.446*(0.0769) (0.0980) (0.194)(0.232)
50.97
43.33
37.28
36.29
1,335
1,335
946
946
3.07
3.07
0.67
0.67
0.381
0.381
0.469
0.469
No
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

Notes Instrumental variables specification using the interaction of World Import Demand (WID) and hukou restrictions. We drop observations with missing values in the dependent variables. Household controls include an indicator
for whether a grandparent was alive and an indicator for whether a grandparent was living in the same place. Like
Khanna et al. (2020), we control for import tariffs which may affect firm productivity. The Inverse Hyperbolic Sine
(IHS) transformation is applied to years of schooling (columns 3 and 4). We restrict our sample to those who hadtaken high school entrance exams in columns 5 and 6. Robust standard errors clustered at the prefecture of birthlevel are reported in parentheses. *** p<0.01, ** p<0.05, * p<0.1.

Table 6: The Effects of Leaving Children Behind on Health and Labor Outcomes

Indicator for leaving thechild behind
F statObservations
Mean of Dep. Var.
SD of Dep. Var.
Household Controls
Township FE
Year FE(1)(2)
Low Income
Group (=1)
0.397** 0.397**(0.153) (0.152)
47.51
37.67
1,379
1,379
0.71
0.71
0.452
0.452
No
Yes
Yes
Yes
Yes
Yes

(3)
(4)
(5)
(6)
Disadvantaged
Obesity (BMI>30)
Rural Status (=1)
0.347*** 0.352*** 0.109** 0.108**(0.0590) (0.0694) (0.0345) (0.0358)
47.51
37.67
47.51
37.67
1,379
1,379
1,379
1,379
0.91
0.91
0.026
0.026
0.291
0.291
0.160
0.160
No
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

Notes Instrumental variables specification using the interaction of World Import Demand (WID) and hukou restrictions. We drop observations with missing values in the dependent variables. Household controls include an indicator
for whether a grandparent was alive and an indicator for whether a grandparent was living in the same place. Like
Khanna et al. (2020), we control for import tariffs which may affect firm productivity. We divide the children in our
sample into two groups based on their income in 2015; the low-income group includes those whose income is below theaverage level and those who do not have any income (columns 1 and 2). Disadvantaged rural status is an indicator forwhether an individual either remains in the village or migrates without an urban hukou in 2015 (columns 3 and 4).
Robust standard errors clustered at the prefecture of birth level are reported in parentheses. *** p<0.01, ** p<0.05,* p<0.1.

38

Table 7: Heterogeneity by Whether Having Male Siblings
(1)

39

(2)
(3)
(4)
(5)
(6)
(7)
(8)
Dependent Variable: Indicator for leaving the child in rural hometown
Have male siblings
Don’t have male siblings
Above enrollment age × Highly restricted cities (=1) (ψ1 ) 0.0317* 0.0324*
0.0317*0.0324*0.01920.01940.01920.0194(0.0191) (0.0192) (0.0191)(0.0192) (0.0198) (0.0197) (0.0198)(0.0197)
Above enrollment age (ψ2 )0.01340.01370.009480.0109-0.0227 -0.0238 -0.0421** -0.0443***(0.0251) (0.0252) (0.0234)(0.0234) (0.0175) (0.0172) (0.0166)(0.0167)
P-value of ψ1 + ψ2
0.01980.01790.01800.0124
0.840
0.800
0.154
0.125
Observations
13,591
13,591
13,591
13,591
14,395
14,395
14,395
14,395Adjusted R-squared
0.184
0.185
0.184
0.185
0.161
0.161
0.161
0.161
Mean of Dep. Var.
0.405
0.405
0.405
0.405
0.336
0.336
0.336
0.336
Household Control
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
City FE×Year FE
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Cohort FE
No
Yes
No
Yes
No
Yes
No
Yes
Age Bandwidth
2
2
2
2
2
2
2
2
Control function for the running variable
LinearLinear Quadratic Quadratic Linear
Linear Quadratic Quadratic
Notes We use the sample of female children to estimate equation (1). Columns 1-4 show RD estimates for girls without male siblings, and columns 5-6
show RD estimates for girls with male siblings. The bandwidth is two years. We use a RD sample of children who are two years older or younger than theenrollment age of junior middle school. Household controls include father’s age and age-squared, an indicator for whether household income is above themedian value among the migrant population in the city and an indicator for whether household consumption is above the median value among the migrant
population in the city. We use a local linear control function for the running variable. Robust standard errors clustered at the city level are reported inparentheses. *** p<0.01, ** p<0.05, * p<0.1.

Table 8: Heterogeneity by Baseline Sex Ratio in Original Provinces

Above enrollment age×Highly restricted cities (=1) ×High Baseline Sex Ratio (=1)
Observations
Adjusted R-squaredHousehold Control
City FE×Year FE
City FE×Year FE×Hukou Province FE
Cohort FE
Age Bandwidth
Control function for the running variable

(1)
(2)
(3)
(4)
Dependent variable: Indicator for leaving thechild in rural hometown
0.0680*** 0.0664*** 0.0820*** 0.0812***(0.0222)(0.0222)(0.0169)(0.0168)
31,066
31,066
31,066
31,066
0.101
0.102
0.206
0.207
Yes
Yes
Yes
Yes
Yes
Yes
No
No
No
No
Yes
Yes
No
Yes
No
Yes
2
2
2
2
LinearLinearLinearLinear40

Notes The bandwidth is two years. We use RD sample that are two years older or younger than the enrollment age of junior middle school. Household
controls include father’s age and age-squared, an indicator for whether household income is above the median value among the migrant population in thecity and an indicator for whether household consumption is above the median value among the migrant population in the city. We use a local linear control
function for the running variable. High baseline sex ratio is an indicator for whether the male-female ratio of second births in migrant parents’ hukou
provinces is above the national mean level. Robust standard errors clustered at the city level are reported in parentheses. *** p<0.01, ** p<0.05, * p<0.1.

Online Appendix
A.1 Summary Statistics of Key Variables
Table A.1: Summary Statistics of Key Variables
Variable name

Mean

Std. dev

0.343
4755.343
73629
36775
36.52

0.475
7131.414
45040
21380
5.300

11.34
0.675
0.715
0.907
0.0262
0.786
0.938

3.496
0.469
0.452
0.291
0.160
0.410
0.242

Panel A
Leave children behind (=1)
Amount of Remittance
Household Income
Household Consumption
Age of Father
Panel B
Years of Schooling
Pass High School Entrance Exams
Low Income Group (=1)
Disadvantaged Rural Status (=1)
Obesity (BMI>30)
A grandparent was alive (=1)
A grandparent was living in the same place (=1)

Notes Table shows summary statistics for most outcomes, independent variables and control variables. Data on thevariables in panel A come from the China Migrants Dynamic Survey (CMDS), and data on the variables in panel B
come from the Gansu Survey of Children and Families (GSCF). We divide the children in our GSCF sample into twogroups based on their income in 2015; the low-income group includes those whose income is below the average level
and those who do not have any income. Disadvantaged rural status is an indicator for whether an individual either
remains in the village or migrates without an urban hukou in 2015

I

A.2 Important Facts about the Educational System
in China
Table A.2: Migrant Households’ Spending on Education
Zanzhufei specific for
migrant children
Total education expenditure(excluding zanzhufei )Primary school

Junior middle school

1432.005

2198.481444.093

2339.375

Notes In China, migrant children without a local hukou have to pay zanzhuf ei (an extra fee specifically imposed onthem) in order to go to a local school. Data come from the Chinese Household Income Project Survey (CHIPS) 2007
and 2008.

Table A.3: The Share of Teachers by Education Levels
Master or above
Urban
Rural

0.031
0.004

Urban
Rural

0.010
0.001

College Pre-college High school
Panel A: Junior middle school
0.830
0.135
0.003
0.657
0.328
0.011
Panel B: Primary school
0.570
0.374
0.045
0.249
0.552
0.195

Notes Data come from the EducationalStatisticsY earbookof China2013.

II

Below high school
0.000
0.000
0.000
0.003

Table A.4: The Share of Teachers by Professional Titles

Special Grade (Excellent) Level-1 Level-2
Panel A: Junior middle school
Urban
0.218
0.436
0.270
Rural
0.114
0.405
0.372
Panel B: Primary school
Urban
0.578
0.302
0.022
Rural
0.508
0.360
0.041

Level-3

No title

0.009
0.026

0.068
0.083

0.003
0.002

0.095
0.089

NotesProfessional titles are designated to teachers based on their professionalism and progressive nature. The special
grade teacher is the highest professional title, followed by Level-1 teacher, and then by Level-2 and Level-3 teacher.
Data come from the EducationalStatisticsY earbookof China2013.

Table A.5: Education Facilities per Student

Num of multi-media classrooms Asset value of education equipment
Panel A: Junior Middle School
Urban
0.053
0.511
Rural
0.036
0.358
Panel B: Primary School
Urban
0.081
0.653
Rural
0.036
0.293
NotesData come from the EducationalStatisticsY earbookof China2013.

Table A.6: Beijing Closed Migrant Schools in Recent Years

Year
2006
2007
2008
2010
2011
2012
2013
2014

Number of migrant children
in Beijing (10,000)
37.5
40.0
40.0
43.4
47.8
41.9
52.9
51.1

Share of migrant children
in migrant schools
34.7
36.5
34.0
—
27.2
—
24.2
18.2

Number ofMigrant Schools
300
268
228
—
176
158
130
127

NotesData come from the AnnualReportonEducationf ortheChina′ sM igrantChildren(2016).

III

Table A.7: Migrant Children in Guangzhou Disappear as They Enter Junior Middle
SchoolPrimary school
Junior middle school
High school
Entrance Exam

2008
2012
2015
Num of migrant children 376963 434473 458216
Share of migrant children 43.69% 52.82% 48.86%
Num of migrant children 86089 121426 127815
Share of migrant children 21.09% 32.51% 37.97%
Num of migrant children
—
23762
31969
Share of migrant children—
20.06% 28.87%

NotesOnly a small fraction of migrant children without a local hukou are eligible to take local high-school entrance
exams. Every year, the Guangzhou government sets a quota for the number of migrant children who can take local
high-school entrance exams. Additionally, the threshold for them to be enrolled in local high schools is higher thantheir local counterparts. Data come from the AnnualReportonEducationf orChina′ sM igrantChildren(2016).

IV

Table A.8: Summary Statistics of Observables for Below and Above the School Age
CutoffHousehold hukou transfer (=1)
Father migrates (=1)
Mother migrates (=1)
Father income (=1)
Mother income (=1)

Household hukou transfer (=1)
Father migrates (=1)
Mother migrates (=1)
Father income (=1)
Mother income (=1)(1)(2)
Below age cutoff Above age cutoff
Panel A: Boys
0.006
0.003
(0.078)(0.054)0.014
0.009(0.117)(0.092)0.018
0.018(0.135)(0.133)37,288.474
30,975.676(23,504.601)(23,217.771)
21,312.289
21,306.623(14,738.911)(17,566.470)
Panel B: Girls
0.003
0.002
(0.052)(0.041)0.009
0.010(0.096)(0.101)0.023
0.031(0.149)(0.173)35,217.738
35,613.582(22,727.107)(23,917.980)
21,669.966
19,778.509(15,597.513)(15,566.202)(3)
Diff. in means(4)
RD Estimates-0.003[0.003]-0.005[0.009]-0.000[0.010]-6,312.798*[3,253.024]-5.666[2,327.219]-0.010[0.007]-0.027[0.035]-0.008[0.039]-6,720.214[13,079.839]
8,199.975[10,131.891]-0.001[0.002]0.001[0.008]0.008[0.013]395.844[3,333.514]-1,891.457[2,430.097]

0.006[0.008]0.000[0.032]-0.037[0.052]-7,051.000[11,393.291]-9,579.064[8,001.999]

Notes Household hukou transfer is an indicator for whether a particular household transfers their hukou location.
Father migrates and Mother migrates are indicators for whether father and mother, respectively, move away from their
hukou city. Columns 1 and 2 report the sample mean and standard deviation for children whose ages are above andbelow the age cutoff, respectively. Column 3 reports the raw difference between these sample means. Note that thisstatistic shows a simple difference between all children aged 6-15, which is not necessarily a discontinuous differenceat the RD cutoff. In column 4, we use our RD sample to investigate whether there is such a discontinuous difference.
We use local linear regression to obtain RD estimates for the observables and report the standard errors in brackets.
In columns 1 and 2, standard deviations are reported in parentheses. In columns 3 and 4, standard errors are reported
in brackets. *** p<0.01, ** p<0.05, * p<0.1.

VA.3 Additional Results of RD Estimates
Table A.9: Alternative RD Control and Different Bandwidth

VI

(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
Dependent Variable: Indicator for leaving the child in rural hometown
FemaleMale
Panel A: Quadratic Control+2-year Bandwidth
Above enrollment age × Highly restricted cities (=1) (ψ1 ) 0.0324** 0.0330** 0.0349** 0.0354** 0.00331 0.00444 0.00871 0.00984(0.0145) (0.0144) (0.0145) (0.0144) (0.0150) (0.0148) (0.0170) (0.0167)
Observations
31,071
31,071
31,071
31,07140,85440,85440,85440,854
Adjusted R-squared
0.172
0.173
0.206
0.207
0.146
0.147
0.184
0.184
Panel B: Quadratic Control+3-year Bandwidth
Above enrollment age × Highly restricted cities (=1) (ψ1 ) 0.0261* 0.0269* 0.0268* 0.0274*
0.01610.01670.01870.0193(0.0146) (0.0144) (0.0144) (0.0142) (0.0148) (0.0145) (0.0159) (0.0154)
Observations
47,04047,04047,04047,04061,572
61,572
61,572
61,572Adjusted R-squared
0.176
0.177
0.208
0.209
0.152
0.152
0.187
0.188
Panel C: Local Linear Control+3-year Bandwidth
Above enrollment age × Highly restricted cities (=1) (ψ1 ) 0.0261* 0.0269* 0.0268* 0.0274*
0.01620.01680.01880.0193(0.0146) (0.0144) (0.0144) (0.0142) (0.0149) (0.0145) (0.0159) (0.0154)
Observations
47,04047,04047,04047,04061,572
61,572
61,572
61,572Adjusted R-squared
0.176
0.177
0.208
0.209
0.152
0.152
0.187
0.188
Household Control
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
City FE×Year FE
Yes
Yes
No
No
Yes
Yes
No
No
City FE×Year FE×Hukou Province FE
No
No
Yes
Yes
No
No
Yes
Yes
Cohort FE
No
Yes
No
Yes
No
Yes
No
Yes
Notes This table shows the results of estimating equation (1). We use a RD sample of children who are two years older or younger than the enrollment
age of junior middle school. Household controls include father’s age and age-squared, an indicator for whether household income is above the median value
among the migrant population in the city and an indicator for whether household consumption is above the median value among the migrant population in
the city. Robust standard errors clustered at the city level are reported in parentheses. *** p<0.01, ** p<0.05, * p<0.1.

Table A.10: Estimates using the Sample of First-born Children(1)

Above enrollment age × Highly restricted cities (=1)

VII

Observations
Adjusted R-squared
Mean of Dep. Var.
Household Control
City FE×Year FE
City FE×Year FE×Hukou Province FE
Cohort FE
Age Bandwidth
Control function for the running variable

(2)
(3)
(4)
(5)
(6)
(7)
(8)
Dependent Variable: Indicator for leaving the child in rural hometown
FemaleMale
0.0366** 0.0374** 0.0413** 0.0418** 0.00864 0.00974
0.01310.0141(0.0155) (0.0154) (0.0170) (0.0170) (0.0159) (0.0158) (0.0188) (0.0185)
27,37027,37027,37027,37034,234
34,234
34,234
34,234
0.172
0.173
0.203
0.203
0.141
0.142
0.175
0.176
0.36
0.36
0.36
0.36
0.35
0.35
0.35
0.35
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
No
Yes
Yes
No
No
No
No
Yes
Yes
No
No
Yes
Yes
No
Yes
No
Yes
No
Yes
No
Yes
2
2
2
2
2
2
2
2
LinearLinearLinearLinearLinearLinearLinearLinearNotes This table shows the results of estimating equation (1) using the sample of first-born children. The bandwidth is two years. We use a RD sample
of children who are two years older or younger than the enrollment age of junior middle school. Household controls include father’s age and age-squared,
an indicator for whether household income is above the median value among the migrant population in the city and an indicator for whether household
consumption is above the median value among the migrant population in the city. We use a local linear control function for the running variable. Robust
standard errors clustered at the city level are reported in parentheses. *** p<0.01, ** p<0.05, * p<0.1.

Table A.11: Triple Difference Regressions

Female × Above Enrollment Age × Highly
restricted cities (=1)
Observations
Adjusted R-squaredHousehold Control
City FE × Year FE
Cohort FE
Age Bandwidth
Control function for the running variable

(1)
(2)
(3)
(4)
Dependent variable: Indicator for
leaving the child in rural hometown
0.0282* 0.0279*
0.0282*0.0279*(0.0152) (0.0151) (0.0152)(0.0151)
71,92571,92571,92571,925
0.157
0.158
0.157
0.158
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
No
Yes
No
Yes
2
2
2
2
LinearLinear Quadratic Quadratic

Notes The bandwidth is two years. We use a RD sample of children who are two years older or younger than theenrollment age of junior middle school. Household controls include father’s age and age-squared, an indicator forwhether household income is above the median value among the migrant population in the city and an indicator
for whether household consumption is above the median value among the migrant population in the city. Robust
standard errors clustered at the city level are reported in parentheses. *** p<0.01, ** p<0.05, * p<0.1.

VIIIA.4 Additional Results of Long-term Consequences
Table A.12: First-Stage Estimation

WID
WID × High hukou restrictions
Log rainfall
Log rainfall × Migration ties

IX

Observations
Adjusted R-squared
F statHousehold Controls
Township FE
Year FE

(1)
(2)
(3)
(4)
Indicator for leaving the child in rural hometown-0.141-0.152(0.319)(0.321)
1.053*** 1.048***(0.153)(0.171)0.384***
0.376***(0.0698)(0.0692)-3.588***-3.518***(0.332)(0.408)
1,379
1,379
1,414
1,414
0.126
0.125
0.126
0.125
47.55
37.70
116.8
74.26
No
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

(5)
(6)
(7)
(8)
IHS of the amount of time that parents are away
-0.482-0.537(1.218)(1.236)1.906*** 1.891***(0.528)(0.581)
0.698**
0.669**(0.225)(0.224)-3.389***-3.140***(0.649)(0.944)
1,379
1,379
1,414
1,414
0.146
0.146
0.149
0.149
13.02
10.61
27.29
11.06
No
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

Notes Household controls include the number of children, an indicator for whether a grandparent was alive, and an indicator for whether a grandparent wasliving in the same place. The Inverse Hyperbolic Sine (IHS) transformation is applied to the amount of time that parents are away (columns 5-8). Robust
standard errors clustered at the prefecture of birth level are reported in parentheses. *** p<0.01, ** p<0.05, * p<0.1.

Table A.13: Alternative Instrumental Variables
(1)

(2)

Years of Schooling
Indicator for leaving the child behindX

F statObservations
Mean of Dep. Var.
SD of Dep. Var.
Household Controls
Township FE
Year FE-3.603**(1.273)
102.6
1,366
11.34
3.496
No
Yes
Yes

-4.034**(1.494)
74.55
1,366
11.34
3.496
Yes
Yes
Yes

(3)
(4)
IHS of Yearsof Schooling-0.332** -0.370**(0.127)(0.159)
102.6
74.55
1,366
1,366
3.065
3.065
0.380
0.380
No
Yes
Yes
Yes
Yes
Yes

(5)
(6)
(7)
(8)
Low Income
Disadvantaged
Group (=1)
Rural Status (=1)
0.508* 0.512* 0.375*** 0.389***(0.238) (0.243) (0.112)(0.112)
116.7
74.21
116.7
74.21
1,414
1,414
1,414
1,414
0.715
0.715
0.907
0.907
0.452
0.452
0.291
0.291
No
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

Notes Instrumental variable specification using the interaction of rainfall with historical migration ties. We drop observations with missing values in thedependent variables. We divide the children in our sample into two groups based on their income in 2015; the low-income group includes those whose income
is below the average level and those who do not have any income (columns 5 and 6). Disadvantaged rural status is an indicator for whether an individual
either remains in the village or migrates without an urban hukou in 2015 (columns 7 and 8). We control for other weather conditions, including sunshine,
temperature, and humidity. Household controls include an indicator for whether a grandparent was alive and an indicator for whether a grandparent wasliving in the same place. The Inverse Hyperbolic Sine (IHS) transformation is applied to years of schooling (columns 3 and 4). Robust standard errors
clustered at the prefecture of birth level are reported in parentheses. *** p<0.01, ** p<0.05, * p<0.1.

Table A.14: Alternative Measure of Leaving Children Behind
(1)

(2)

Years of Schooling
Indicator for leaving the child behind

XI

F statObservations
Mean of Dep. Var.
SD of Dep. Var.
Household Controls
Township FE
Year FE-1.640***(0.463)
17.37
1,335
11.37
3.510
No
Yes
Yes

-1.727**(0.594)
14.68
1,335
11.37
3.510
Yes
Yes
Yes

(3)
(4)
IHS of Yearsof Schooling-0.159** -0.167*(0.0598) (0.0748)
17.37
14.68
1,335
1,335
3.067
3.067
0.381
0.381
No
Yes
Yes
Yes
Yes
Yes

(5)
(6)
(7)
(8)
Low Income
Disadvantaged
Group (=1)
Rural Status (=1)
0.219** 0.220** 0.191*** 0.195**(0.0828) (0.0841) (0.0557) (0.0645)
13.01
10.60
13.01
10.60
1,379
1,379
1,379
1,379
0.714
0.714
0.906
0.906
0.452
0.452
0.291
0.291
No
Yes
No
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes

Notes Instrumental variables specification using the interaction of World Import Demand (WID) and hukou restrictions. We drop observations with missing
values in the dependent variables. We divide the children in our sample into two groups based on their income in 2015; the low-income group includes those
whose income is below the average level and those who do not have any income (columns 5 and 6). Disadvantaged rural status is an indicator for whether
an individual either remains in the village or migrates without an urban hukou in 2015 (columns 7 and 8). Household controls include an indicator forwhether a grandparent was alive and an indicator for whether a grandparent was living in the same place. Like Khanna et al. (2020), we control for importtariffs which may affect firm productivity. The Inverse Hyperbolic Sine (IHS) transformation is applied to the amount of time that parents are away (theindependent variable of interest) and years of schooling (the dependent variable in columns 3 and 4). Robust standard errors clustered at the prefecture ofbirth level are reported in parentheses. *** p<0.01, ** p<0.05, * p<0.1.

A.5 Results of Competing Mechanisms
Table A.15: Differential Returns to Education by Gender
(1)

(2)

(3)
Log income
Rural hukou Urban hukou
Full Sample
holders
holders
High school (=1)
0.167***
0.143***
0.323***(0.0148)(0.0184)(0.0295)
High school (=1) × Female (=1)
0.178***
0.106***
0.110***(0.0197)(0.0268)(0.0400)
Observations
30,01821,855
8,123
Adjusted R-squared
0.364
0.331
0.278
City FE
Yes
Yes
Yes
Year FE
Yes
Yes
Yes

(4)

(5)

Migrants

Locals

0.289***(0.0243)-0.548***(0.0231)0.150***(0.0329)
Yes
Yes

0.207***(0.0177)-0.579***(0.0168)0.203***(0.0251)
Yes
Yes

Notes We control for an indicator for female, an indicator for rural hukou, age and age-squared. Robust standard
errors clustered at the city level are reported in parentheses. *** p<0.01, ** p<0.05, * p<0.1.

XIITable A.16: Heterogeneity by Gender Wage Gaps
(1)

XIII

(2)
(3)
(4)
(5)
(6)
(7)
(8)
Destination Regions
Original Regions
Dependent variable: Indicator for leaving the child in rural hometown
Above enrollment age × Highly restricted cities (=1) × Gender wage gaps -0.00663 -0.00492 -0.0489 -0.0443 -0.0336 -0.0327 -0.00619 -0.00262(0.0745) (0.0735) (0.0675) (0.0660) (0.107) (0.107) (0.102)(0.102)
Observations
31,02631,02631,02631,02631,021 31,021
31,021
31,021
Adjusted R-squared
0.172
0.173
0.206
0.206
0.101
0.102
0.206
0.206
Household Control
Yes
Yes
Yes
Yes
Yes
Yes
Yes
Yes
City FE×Year FE
Yes
Yes
No
No
Yes
Yes
No
No
City FE×Year FE×Hukou Province FE
No
No
Yes
Yes
No
No
Yes
Yes
Cohort FE
No
Yes
No
Yes
No
Yes
No
Yes
Age Bandwidth
2
2
2
2
2
2
2
2
Control function for the running variable
LinearLinearLinearLinearLinear Linear
LinearLinearNotes The bandwidth is two years. We use baseline gender wage gaps in destination cities in columns 1-4 and in original provinces in columns 5-8. We use
a RD sample of children who are two years older or younger than the enrollment age of junior middle school. Household controls include father’s age andage-squared, an indicator for whether household income is above the median value among the migrant population in the city and an indicator for whether
household consumption is above the median value among the migrant population in the city. We use a local linear control function for the running variable.
Robust standard errors clustered at the city level are reported in parentheses. *** p<0.01, ** p<0.05, * p<0.1.