Does being “left–behind” in childhood lead to
criminality in adulthood? Evidence from data on
rural-urban migrants and prison inmates in China∗
Lisa Cameron†

Xin Meng‡

Dandan Zhang§

October 7, 2021

Abstract
Large scale rural-to-urban migration and China’s household registration system have
resulted in about 61 million children being left-behind in rural villages when their
parents migrate to the cities. This paper uses survey and experimental data from
male rural-urban migrants – prison inmates and comparable non-inmates – to examine whether parental absence in childhood as a result of migration is associated with
increased criminality in adulthood. Control functions and sibling fixed effects are
used to identify causal impacts. Parental absence due to migration is found to increase the propensity of adult males to commit crimes. Being left-behind decreases
educational attainment and increases risk-loving behavior, both of which increase
criminality.
Keywords: Migration, Crime, China.
JEL Classification Code: O12, O15, J12.

∗

We would like to thank seminar and conference participants at the Australian National University,
University of Melbourne, Fudan University, Jinan University, the 2016 NBER-CCER Conference, the 2019
CCER Summer Institute and the 2019 Asian and Australasian Society of Labour Economics (AASLE)
Conference for their helpful suggestions and comments. We also thank Guochang Zhao for his technical
guidance and Matthew Notowidigdo for his advice. Funding for the data collection was provided by
the Australian Research Council Linkage Grant Scheme (Projects LP0669728 and LP140100514). Ethics
approval was obtained from the Australian National University (2013/494).
†
Melbourne Institute of Applied Economic and Social Research, University of Melbourne; Email:
lisa.cameron@unimelb.edu.au
‡
Research School of Economics, CBE, Australian National University; Email: xin.meng@anu.edu.au
§
China Center for Economic Research, National School of Development, Peking University; Email:
ddzhang@nsd.pku.edu.cn.

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1

Introduction

The unprecedented economic growth in China in the past few decades has led to large
scale rural-urban migration. Between 1997 and 2019 the number of rural workers working
in Chinese cities increased from 38 to 174 million (World Bank, 2009; NBS, 2020). Institutional restrictions on rural workers’ access to social services and social welfare in cities
- China’s household registration system (hukou) – has resulted in a large proportion of
migrants leaving their families, especially their children, behind in rural areas and coming
to cities alone to work, Meng and Yamauchi (2017). This has induced dramatic changes
in family structure in rural China. A large cohort of migrant children have been leftbehind in rural villages where they are often looked after by one parent, grandparents, or
other relatives, with a small proportion live in boarding schools. According to the 2010
Population Census, there were 61 million left-behind children, accounting for 38% of all
rural children and 22% of all children nationwide. There are yet another 9 million children
left–behind in one city by parents working in another. This makes 70 million in total,
almost equal to the total number of children in the United States (All-Women Federation
in China, 2013; Economist, 2015).
This phenomenon of “Left-behind Children” in China has given rise to concerns about
the potential consequences for society as parents play an important role in guiding their
children’s development and modelling socially-acceptable behavior, (Maccoby and Martin,
1983; Zinn et al., 2016; Wright and Wright, 1993; Bornstein, 2002; McLanahan and Percheski, 2008). Family structure is thought to affect the propensity for adolescent delinquency
(which is associated with criminality in adulthood) via its effects on parental control, supervision and the emotional attachment of child to parent, (Nye, 1958; Van Voorhis et al.,
1988)). Nye (1958)’s social control theory maintains that children’s delinquency is influenced through direct control of behavior through parental supervision, restrictions and
punishment; internalized control through the influence on the child’s conscience; and indirect control through the affectionate attachment between the child and parent. Hirschi
(1969)’s social bond theory argues that the bond of attachment (Nye’s indirect and internalized controls) is likely the most important family factor in determining delinquency,
with empirical support, (for example, see Demuth and Brown, 2004). All of these forms
of parental influence and control are potentially disrupted for China’s “left-behind children” as parental migration results in the parent being physically absent, which not only
limits his or her ability to supervise, monitor and punish, but also may lead to emotional
absence and weakened attachment. Parental absence could also lead to the child feeling
rejected which has been shown to be one of the most significant predictors of delinquency,
Wright and Wright (1993).
Empirical research on the impacts of family dissolution, mostly in developed countries,
has found parental divorce or separation to be associated with negative outcomes in terms

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of children’s education and health, behavioral problems, delinquency, and crime (See,
for example, Geismar and Wood, 1986; Brady et al., 1986; Wright and Wright, 1993;
McLanahan and Sandefur, 1994; Amato and Keith, 1991; Demuth and Brown, 2004).
These associations have been corroborated by studies that seek to identify causal impacts.
Manski et al. (1992) generate a range of estimates of the effect of family structure on high
school graduation obtained under differing assumptions about the process generating these
variables. Their results strengthen the evidence that living in an intact family increases
the probability of high school graduation. Gruber (2004) exploits variation across states
and over time in changes in divorce regulations in the US and 40 years of census data
to show that adults who were exposed to unilateral divorce laws as children experienced
higher rates of parental divorce, were less well educated, had lower family incomes, married
earlier but separated more often, and were at higher risk of suicide. Grogger and Ronan
(1995) and Sandefur et al. (1997) use sibling fixed effects estimation which identifies the
impact of fatherlessness off a comparison of siblings with different exposure to it due
to their different ages. They find that each additional year of fatherlessness in the US
reduces children’s educational attainment and entry wages when they grow up.1
Almost all of the literature on the impact of parents leaving children behind in China
has focused on the impacts in childhood. Zhang et al. (2014) finds that parental absence,
especially of both parents, reduces children’s cognitive achievements. Meng and Yamauchi
(2017) found a sizeable adverse impact of exposure to being left-behind due to parental
migration on children’s health and education outcomes. Shi et al. (2016) and Zhao et al.
(2017) found that parental out-migration has a significant negative impact on the mental
health and psychosocial well-being of “left-behind” children, as they tended to exhibit
higher levels of anxiety and lower levels of self-esteem, emotional difficulties and difficulties
in conduct, peer relationships and pro-social behaviors. Wang (2019) reveals that being
left-behind reduces children’s probability of being enrolled at school, while Hong and
Fuller (2019) identified adverse impacts on children’s educational aspirations.
A few empirical attempts have also been made to link parents’ out-migration to children’s wellbeing indicated by education and health attainments in other developing countries. For example, Yang (2008), in the context of the Philippines, and Hanson and
Woodruff (2003), in the context of Mexico, found that out-migration could generate a
“positive income effect” which might mitigate the “negative impact” arising from the lack
of parental care. A recent Lancet study combines data from many developing countries
to conduct a meta-analysis of the impact of parental migration on left-behind children’s
1

Lang and Zagorsky (2001), however, find that the impact of the number of years lived with one’s
biological mother and father before age 18 is less strongly associated with some outcomes after controlling
for a suite of family background variables. Using parental death as a “natural experiment” they found
little evidence that parental absence during childhood affects economic wellbeing in adulthood. Finlay
and Neumark (2010) used an instrumental variables approach to quantify the effect of never-married
motherhood (i.e., paternal absence) on high school dropout rates of black and Hispanic children and
found no negative effect.
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health outcomes. The study concludes that left-behind children and adolescents have
substantial unmet mental health and nutritional needs and as labour migration increases
globally, many children are at risk (Fellmeth et al., 2018).2
Few studies, if any, have addressed long-term effects of being left-behind during childhood by parents who migrated. It is, however, well-established that childhood experiences
often have life-long impacts. Even “relatively mild shocks in early life can have substantial
negative impacts”, Almond et al. (2018).
The large numbers of “left-behind” children in China who were born in the 1990s
and early 2000s have now grown up and have started migrating to cities themselves.
They now account for a sizeable share of the Chinese urban labor force.3 The parental
absence they experienced during their childhoods not only potentially affects their own
wellbeing and human capital accumulation, but also the Chinese economy and society.
Policy makers have been particularly concerned as to whether, and how, the experience
of being “left-behind” in childhood affects adult social and economic outcomes.
In the same period that many left-behind children are reaching adulthood, crime rates
in China are increasing dramatically - from 7.4 per 10,000 in 1982 to 47.8 per 10,000 in
2014 (Zhang et al. (2011b) and Law Yearbook of China 2010-2015). Previous studies have
highlighted several factors that could contribute to increased crime rates, including large
scale rural-urban migration with a high proportion of migrants being crime-prone young
males (Zhang et al., 2014), significant increases in the sex ratio (ratio of males to females)
due to the introduction of the One Child Policy which generated fierce marriage market
competition and the need for financial advancement (Edlund et al., 2013; Cameron et al.,
2019) and significant increases in income inequality (Zhang et al., 2011a).
In this paper we investigate another potential contributing factor to the increase in
crime: being “left-behind” in childhood and its effects on subsequent adult criminal behavior. Despite media attention on a possible link between being left-behind and increases
in crime rates, we are aware of no studies which have investigated such a link. This is
largely due to a lack of data. In 2013 we implemented a survey and conducted economic
experiments with inmates in a prison for male offenders in Shenzhen, China. Over 85%
of the inmates in the prison were rural-to-urban migrants. In the same year we conducted the same experiments and survey with a randomly selected sample of non-inmate
rural-urban migrants in Shenzhen. Using these unique survey and experimental data on
rural-urban migrants this paper examines whether parental absence in childhood (prior
to age 16) due to parents migrating from rural areas to urban areas for jobs is associated
with increased criminality in adulthood. We examine the extent to which educational at2

The study combines data from 111 studies, 91 of which were studies of left-behind children in China.
The remainder include studies of Thailand, the Philippines, Indonesia, India, Mexico, Guatemala, Peru,
Ethiopia, Kenya, Malawi, Trinidad, Tobago, Jamaica, Romania, and Moldova.
3
The 2014 Rural-Urban Migration in China (RUMiC) survey shows that 18% of those in the labor market
(who were born since 1990) were left-behind in childhood due to parental migration.
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tainment, behavioral preferences and personality traits are affected by being left-behind
and drive increases in crime.
The behavioral preferences we focus on are risk-attitudes and time preferences as
these are known to be associated with criminality (Wood et al., 1993). Risk-taking may
be affected by parental absence as the presence of parents has been observed to buffer adolescents from the risk-taking influence of their peers, see van Hoorn et al. (2018). Parental
presence has similarly been associated with more future-oriented time preferences, Lersch
and Baxter (2021).
Unlike much of the previous research which compares left-behind children in rural
areas with rural children whose parents did not migrate, e.g. Zhang et al. (2014),Meng
and Yamauchi (2017) and Shi et al. (2016), we compare the outcomes for left-behind individuals with an additional comparison group - children who migrated to cities with their
parents. Our main focus is on this latter comparison as our aim is to inform government
policy which currently actively discourages parents from migrating with their children.
To do so we need to compare the outcomes of children who did and did not migrate with
their parents.
The potential endogeneity of being left-behind and the migration decision are addressed using a control function approach. This involves two-stage estimation. The first
stage models the endogenous variables. The (generalized) residuals from the first stage
(the control functions) capture the endogenous component of these variables and are
included in the second stage regressions which renders the endogenous variables appropriately exogenous, Wooldridge (2015). We use control functions rather than the more
oft-used instrumental variables (IV) estimation as IV estimation produces biased estimates
in models such as ours with non-linear endogenous explanatory variables (the binary variables reflecting whether one’s parents migrated and whether one was left-behind). We
also estimate sibling fixed effects models.
Our results show that being left behind in childhood by one or both rural-urban migrant parents increases the propensity of males to commit crimes in adulthood. Being
‘left-behind’ results in lower educational attainment and also in more risk-loving preferences. Lower educational attainment and risk-loving behavior are both significant determinants of being in prison in adulthood. Together these factors account for over half of
the total impact of being left-behind on criminality, with education accounting for the
lion’s share.
The paper is organised as follows. Our data sources are discussed in Section 2. Empirical methods are presented in Section 3, which is followed by the discussion of the
main results and an investigation of the channels through which parental absence affects
left-behind children’s outcomes in Section 4. Concluding remarks and policy implications
are presented in Section 5.

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2

Data

In 2013 we conducted two sets of surveys and experiments - one with a random sample
of the male rural-urban migrant population in Shenzhen, and one with inmates in a male
prison in the same city. Shenzhen is at the heart of China’s manufacturing boom and
has been a magnet for migrant workers since the early 1990s. In 2013 50% of Shenzhen’s
population were rural-urban migrants, while in the city’s male prison, 85% of its inmates
were rural-urban migrants.
The data set used in this study is obtained by combining these two sources of information. We surveyed a random sample of 959 rural-urban migrants in the prison. Of
these, 735 prisoners were randomly chosen to participate in experimental sessions.4 Our
non-inmate sample consists of 299 male rural-urban migrant workers in Shenzhen. We
oversampled inmates as they constitute only a very small percentage of the population
and account for this in our estimation strategy, as is discussed in detail below.5
The non-inmate sample was constructed using the sampling frame of a representative
sample of rural-urban migrants - the 2012 wave of the Rural-Urban Migration in China
(RUMiC) survey. The prison takes inmates arrested in both Shenzhen and the neighboring
city of Dongguan so our migrant sample is selected to be representative (in terms of age,
education and industry of employment) of the male migrant population in these two cities,
weighted by the relative size of the migrant populations in Shenzhen and Dongguan.
From this combined sample of 1034 individuals, we exclude observations with missing
values for key variables (28 observations) and, in order to focus on the phenomenon of
being left-behind due to parental migration, 38 individuals who experienced parental
absence due to other reasons (e.g. divorce, death of a parent). Our final analysis sample
size is 968, comprised of 678 inmate migrants and 290 non-inmate migrants.

2.1

The Experiments

Both the inmate and non-inmate samples participated in a series of economics experiments. The sessions were conducted by one of the authors of this paper (Zhang) who
worked with a team of 20 student research assistants from Peking University. The experiments were all conducted in Mandarin with pen and paper. Each participant received
a printed copy of the experimental instructions which were also read to the group as a
whole. There were opportunities to ask questions and test questions were embedded to
4

Fewer prisoners were selected to participate in the experiment for budgetary reasons and because of the
limited time we were given to access the inmate subjects. The experiments were conducted in September
2013. We first randomly selected 1200 prisoners to be survey respondents. From these we then randomly
selected 1000 to participate in the experimental sessions. We then drop inmates in our sample who are
not rural-urban migrants.
5
The ratio of inmate to non-inmate observations also reflects survey budget constraints and the greater
cost associated with implementing the non-inmate sample.
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enable us to discern whether participants understood the instructions.6
The participant information sheet and experimental instructions are included in Appendix A.1. The experimental protocols were kept as similar as possible for the inmates
and non-inmates. This includes using the same script, same procedures, same researcher
conducting the session, spacing between desks and prohibition on communication across
participants during the session. In the prison the experiments were conducted a week before the survey. For non-inmate participants the experiments and surveys were conducted
in the same session, with the experiments being conducted first.
In the prison, the randomly selected inmates were told that they had been selected
to participate in an experiment in which there would be the chance to earn some money.
The experiments were conducted during the Thursday afternoon and Saturday free time
periods in a large conference room. At the conclusion of the games participants received
a deposit receipt for the money which was paid into their savings accounts.7
Migrant participants were told that there was an opportunity to take part in some
activities in which they could earn some money. If they agree to participate, they were
invited to go to a meeting room in a hotel in downtown Shenzhen, close to public transport,
where the experiments and exit survey were conducted.8 A show-up fee of RMB100
(USD14) was paid to offset transport and opportunity costs and so to ensure that we
were able to attract a representative sample of migrants.9 A total of 10 sessions were
conducted with each session lasting between 2.5 and 3 hours. At the end of each session,
and after the completion of the survey, the participants were paid in cash according to
their experimental choices and outcomes, plus the show-up fee.
The risk experiments implemented were standard multiple price list format experiments which involve a series of eleven choices between lotteries, similar to that used in
Murnighan et al. (1988). Each decision involves choosing between receiving an amount
with certainty or a lottery with a 50% chance of receiving a larger amount and a 50%
chance of receiving nothing. The specific choices faced by the inmate participants are
shown in Appendix A.2.10 The “winning” amount increases as one works one’s way
6

Participants were also read statements assuring data confidentiality and lack of identifiability and were
invited to leave if they no longer felt like participating, before commencing or at any point during the
sessions. They were informed that if they decided not to participate at any point, any data they provided
to that point would be destroyed. Verbal consent was sought prior to commencing the experiments.
7
Each prisoner has a prison savings account in which they receive payment for any work they do while
in prison, for example, working in the prison factory. These funds can be used to buy items in prison,
can be transferred to people outside the prison and can be withdrawn when the inmate leaves prison.
8
The migrant sample appears to be relatively representative. For example, the distribution of place of
birth in our migrant sample is very similar to the distribution in the representative sample of migrants
in the RUMiC survey data. The rate of unemployment in our migrant sample (9.3%) is also very similar
to that amongst rural migrants in Shenzhen and Dongguan (8.9%) in the RUMiC data.
9
We paid a show-up fee and used higher stakes for the migrant sample to reflect their higher opportunity
cost of time. This is the protocol typically used when conducting games across different cultural settings
so as to keep the real value of the stakes as close as possible to constant across groups, Cameron et al.
(2009).
10
The choice of stakes was complicated by the fact that prisoners’ earnings in jail are very low (less than
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through the choices. Relatively risk-loving individuals will prefer the lottery even if they
stand to gain only a small amount, while more risk-averse individuals will switch to choosing the lottery only when the “prize” becomes sufficiently large. Participants were allowed
to switch from choosing the certain sum to choosing the lottery only once. Once all participants had made their choices a participant was asked to draw a ball from a bag in
which there were eleven balls numbered from 1 to 11. The chosen ball determined which
choices the participants were to be paid for. Then a different participant was asked to
roll a dice which determined the outcome for those who had selected a lottery.11

2.2

Survey and Administrative Data

The survey collected a wide array of information including demographic information,
place of birth, migration history, labour market history, criminal history, and conducted
personality tests.12 In addition, a simple Raven’s test was implemented to elicit a measure
of individuals’ cognitive ability.
A series of unincentivized time preference questions were also asked during the survey
which are used to construct our measures of patience. The respondent is asked to choose
between getting a certain amount of money in a month’s time (1000 RMB or approximately USD160) and a series of higher amounts of money in seven months’ time. More
patient people will choose to defer payment even for a relatively small increase in the
amount received, whereas less patient people will only choose to defer payment if the
10% of that of the non-prison migrant sample) and not representative of their earnings outside prison.
For this reason we chose stakes for prisoners which were lower in absolute value than those for migrants
but a significantly greater percentage of their current daily earnings. The lottery choices for the inmate
(non-inmate) sample involved a choice between receiving RMB45 (RMB67) with certainty and a lottery
with a 50% chance of receiving nothing and a 50% chance of receiving a sum which ranged from RMB60
to RMB 210 (RMB 90 to RMB 315) The average experimental earnings received by non-inmates was
RMB100 (excluding the show-up fee), while for prisoners it was RMB64. Non-inmates received on
average 175% of their daily income. Prisoners received approximately 18 times their average daily
earnings but only 6% of the average amount held in their prison savings account. Importantly, we have
since conducted the same risk games, using the same protocols, with a sample of female prisoners in
China. In these games we varied the stakes used. We find that increasing or decreasing the stakes by
50% does not affect their behavioral choices (p=0.63). Results are available on request.
11
The actual payoff method was slightly more complicated than this as each participant played four games
in the following order: 1) ultimatum game; 2) risk game; 3) trust game; 4) half of the sample played
a dishonesty game based on Mazar et al. (2008) and Friesen and Gangadharan (2013) and half played
a compliance game based on (Friesen, 2012). Participants were aware that payments would be made
for only one of these games, which was selected randomly by drawing balls with number 1 to 4 from a
bag. The method described above was followed if the risk game was randomly selected for payment.
We focus on risk attitudes and time preferences in this paper because, as discussed above, risk-taking
and short time horizons are known to be related to criminality. Further, being left-behind and parental
migration are not strong determinants of behavior in the trust and ultimatum games (see Appendix
Table C4). The other games are quite different in nature and were included for another paper.
12
The same survey and experiments were conducted across the two groups, with some small changes
necessitated by the different contexts. For questions about job status and living conditions we asked
migrants about their current situation whereas we asked the prisoners about their situation prior to
being imprisoned. These particular questions are not used in this paper.
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amount received increases by a substantial amount. The choices in these time preference
questions are presented in the Appendix A.3.
The survey also collects information about the respondents’ parents and their siblings (birth year, gender, education, current employment, migration history, and whether
he/she ever committed a crime).
The prison also granted us permission to access the prisoners’ administrative records
and we merge these onto the survey and experimental data. The administrative data
include demographic information such as age and ethnicity and hukou (residency status).
These allow us to confirm information provided directly by the inmate respondents.

2.3

Other Data

We also make use of a characteristics of migrants’ sending prefectures/counties as control
variables and instrumental variables in the control function estimation. At the prefecture
level these include GDP per capita, Gini coefficients of individual income, the proportion
of the population who come from an ethnic minority group, and the sex ratio. At the
county level we have the teacher-student ratio, out-migration rate, and the proportion of
children aged 0-15 who were left-behind. The latter two variables are used as instrumental
variables. The majority of these variables were calculated using China’s 2000 Population
Census, with the exception of per capita GDP which is from the China City Statistical
Yearbooks (various years) and the county level teacher-student ratio which is from the
Ministry of Education’s National Statistical Report on Education Finance: 1993-2013.

2.4

Descriptive statistics

Table 1 shows what percentage of our samples were left–behind and whether they were
left-behind by their mother, father or both parents. Table 2 presents summary statistics
by left-behind and inmate status. Note that as our sample over-represents the prisoner
population and under-represents the migrant population, summary statistics presented in
both tables are weighted by the population weight.13 Table 1 shows that on average, about
16 per cent of prisoners were left-behind by one or both parents during their childhood
(before the age of 16). This is about twice the rate experienced by non-inmate migrants
(8.3 per cent). The predominant form of parental absence in our sample, for both prison
inmates and non-inmates, is both parents having been absent. Very few respondents
(0.7%) were left behind by their mother to live with their father, with only slightly more
(1.75%) being left behind by their father to live with their mother.14
13
14

The data and assumptions used to generate the weight are detailed in Appendix B.
These small sample sizes preclude us from separately examining the impact of being left-behind by both
parents and the impact of being left behind by one parent. The point estimates obtained if one tries
to do this suggest slightly smaller effects of one parent being absent than both parents being absent.
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The average age of men in our sample is 29 years. Forty-three percent are married.
On average they have 11 years of education. Most of our sample was born after the
introduction of the One Child Policy but as they were born in rural areas where couples
were allowed to have two children if the first born was a girl and where the policy was
also often not strictly enforced, ninety per cent have siblings, with the majority having
more than one sibling. Those who were left-behind because of parental migration are five
years younger on average (reflecting the increase in migration over time), less likely to be
married, more likely to be an only child and have slightly better-educated mothers and
fathers. The raw data show that those who were left-behind also have higher cognitive
ability, are more risk-loving and less patient, and are more likely to be in jail at the time of
the survey. They are more likely to have been born in counties where a greater proportion
of children were left-behind.
The inmates in our sample are a similar age to their non-inmate counterparts, but are
less likely to be married, have lower cognitive scores, less educated parents, less education
themselves and are less likely to be ethnically Han Chinese (the predominant ethnic group
in China). They are also more likely to make the most risky and least patient choices in
the experimental tasks.

3

Estimation Strategy

To examine whether being left-behind before age 16 because of parental migration increases individuals’ probability of committing crime and affects other adult outcomes, we
estimate the following equation:
Yi = α0 + α1 LBi + α2 M igiP + α3 Xi + α4 WiP + α5 SiS + δp + i ,

(1)

where Yi is a vector of outcome variables. Our main interest is in examining the effect of being left-behind due to parental migration on the probability of being in prison,
P risoneri , a dummy variable indicating whether individual i is in prison or not. In addition, we examine whether being left-behind in childhood affects behavioral preferences,
personality traits, and education outcomes. LBi is a variable indicating whether the individual was left-behind when under the age of 16 due to one or both parents having
migrated (in some specifications we alternatively use the number of years the child was
left-behind); M igiP is a dummy variable indicating whether one or both parents migrated
to a city; Xi is a vector of individual level control variables including age, cognitive test
score, whether the individual is married or not, whether the individual is a single child, the
number of siblings he has, and Han ethnicity; WiP is a vector of parental controls which
includes mothers’ and fathers’ years of schooling and whether either parent has ever committed a crime; and SiS is a vector of sending region (s) controls, including prefecture
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level log per capita GDP, Gini coefficients of individual income, the share of minority
groups in the prefecture population, and the prefecture’s sex ratio. We include the sex
ratio because previous studies have found that sex ratio imbalance and the consequent
increase in marriage market competition is an important driving force for increases in the
crime rate (see, for example, Edlund et al., 2013; Cameron et al., 2019).15 A county level
control variable, the teacher-student ratio, is included to absorb differences across sending
counties in investment in public education. δp are sending province fixed effects.16
Our sample is comprised of three groups of individuals: 1) those who were left-behind
due to parental migration when they were under 16 years of age; 2) those whose parents
migrated but were not left-behind, and 3) those whose parents did not migrate. α1
captures differences in outcomes between groups 1 and 2 and is our key parameter of
interest in Equation 1. It measures the effect of being left-behind, relative to someone
whose parents migrated and who was not left-behind, i.e. who migrated to the city with
their parents.17 α1 + α2 captures differences between groups 1 and 3 and is also of interest
as it measures the sum of the effects of being left-behind and parental migration, and so
captures the impact of being left-behind relative to someone whose parents stayed living
with them in the village through childhood. We focus primarily on α1 as it captures the
effect of being left-behind, abstracting from the migration decision, and it is the policy
lever over which the government has some control. That is, given the level of rural-urban
migration – which is widely viewed as being essential to economic development (Lewis,
1954) and so is not something a government would normally wish to inhibit – α1 identifies
what would be gained by making it easier for parents to bring their children to the cities.
15

We calculate the sex ratio for those aged 18 to 27 at the time of our survey (2013) as this captures
the crime-prone years for men. The variable is calculated using data on those aged 5 to 14 in the 2000
population census.
16
We have elected to examine the impact of being left-behind on educational attainment, rather than
including it as a control variable in the vector of individual characteristics Xi when examining the
causes of criminality. We make this decision acknowledging that education is a known determinant of
criminality (Lochner and Moreffi, 2004; Machin et al., 2011) but as the existing literature has identified
a causal link between being left-behind and child school performance (see, for example Zhang et al.,
2014; Meng and Yamauchi, 2017) take the view that it is important to treat education as a channel
through which being left-behind can lead to crime. One could argue that whether a child is left-behind
is potentially a function of the child’s abilities as reflected in educational status. For example, parents
may be more likely to leave a more able child behind or vice-versa. If so, the omission of education
could give rise to omitted variable bias. To mitigate against this we directly control for individuals’
Ravens test scores as a non-verbal measure of cognitive ability.
Marital status could similarly be modelled as a mediating variable, however, it is unclear why being leftbehind would affect marriageability. Further, once one controls for education and age, any difference in
marital status between those who were left-behind and those who were not is statistically insignificant.
17
The majority of the individuals in group 2 accompanied their parents to the cities, with a small number
not being “left-behind” because their parents either migrated before their birth, or after they turned
16. We are unable to define this group to be exclusively those who migrated with their parents as the
date of parental migration is missing for some observations. For observations which are missing the
date of parental migration we only know that they report not being left-behind before the age of 16
and that their parents migrated. However, for those who reported a date of migration and were not
left-behind, 72% had a parent who migrated when they were aged between 0 and 15.
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In addition to capturing the effect of being left-behind, α1 also captures the impact of
growing up in the city as opposed to a rural area. We are unable to separately identify
these impacts. From a policy perspective, however, the inability to separately identify
these two effects is unimportant as a policy that supports parents to migrate with their
children will lead to both impacts being experienced. It is important to understand,
however, that migration in China, as a result of the hukou system which does not grant
urban residency rights to those who were born in rural areas, is largely a temporary
phenomenon, and is commonly characterized by “movements back and forth from rural
to urban areas”, Dustmann et al. (2021). Hence those parents (and children) who migrate
to cities normally return to their home village from where they may embark on another
migration, often to another city. Only 37% of our sample of rural-urban migrants report
having lived in only one city. Hence, those children who accompanied their parents who
moved to the city for work are unlikely to have stayed permanently.18
There are two main issues we need to address when estimating equation 1. The first
is that we have a choice-based sample. When estimating equation 1 (and all subsequent
specifications with Prisoner i as the dependent variable) we need to account for the way in
which our sampling frame was constructed. Incarceration is a rare event. To understand
factors related to incarceration we cannot use a random sample of the population as that
would provide a very small sample of prison inmates. To overcome this problem we oversampled prison inmates. We then use a case-control approach to account for this choicebased sampling. Case-control approaches have been widely used to study criminality
and other relatively rare events such as maternal mortality and infant mortality (Ganatra
et al., 1998; Blair et al., 1996; Dobrin, 2001). In this paper when modelling the probability
of being incarcerated we present results from weighted probit estimation where the weights
reflect the share of the sampled groups in the population.19
The second issue needing to be addressed is the potential endogeneity of both LBi and
M igiP . Not everybody’s parents choose to migrate. The migration decision may depend
18

An additional possible benefit accrues to those who migrate with their parents and stay in the city –
that of having lived in the city for a longer time and so having more extensive networks and a greater
familiarity with the city systems. It is also possible that as our sample consists of people who are ruralurban migrants in the Shenzhen region, some of the “left-behind” individuals in our sample may have
rejoined their parents when they migrated to the cities (if their parents’ migration was to Shenzhen and
they remained there). However, due to the circular nature of rural-urban migration in China, these are
very rare events as explained above. To the extent this happened and there were benefits to migrants
reuniting with their parents in the city, our estimates will be underestimates of the impact of being
left-behind.
19
An alternative approach is to estimate logistic regressions with a correction for the oversampling of
the rare event. This approach relies on the assumption that the errors follow a logistic distribution,
King and Zeng (2001) which can be tested by comparing the results with those obtained from weighted
logit estimation, Xie and Manski (2010). If the errors follow a logistic distribution the results of the
weighted regressions should be very similar to the results obtained by the corrected logistic regression.
Table C1 in the appendix conducts this comparison and as the results differ substantially, we proceed
using weighting to address the sample design. See Appendix B for a detailed discussion of how the
weights are constructed.
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on unobservable characteristics of the parents and their children, which in turn could
also be related to whether the child later commits a crime or not. Also, once parents
decide to migrate to a city, whether they take the child with them potentially reflects the
household’s and child’s unobservable characteristics. These two potential selection biases
could result in the estimates of α1 and α2 in Equation (1) being inconsistent.
We employ two methods to handle the potential endogeneity: a control function approach and sibling fixed effects estimation.

3.1

Control Functions

We are unable to use standard instrumental variables estimation to deal with the endogeneity because it produces biased estimates in a non-linear setting such as ours. Instead
we use a control function approach as our main estimation method. This is closely related
but parsimoniously handles fairly complicated models that are non-linear in endogenous
explanatory variables, Wooldridge (2015).20 This approach involves adding variables (the
control functions) to the regression to control for the endogenous components of LBi and
M igiP and which then renders these variables appropriately exogenous. The control functions utilized are the generalized residuals from first stage regressions of the endogenous
independent variables on all exogenous regressors in the system of equations. That is,
we estimate probit models with the endogenous variables from the structural model as
the dependent variables and the exogenous variables as the explanatory variables. So as
to not be relying on functional form for identification we include instruments (zi ) which
affect the dependent variable in the second stage only through their effect on LBi and
M igiP . We estimate:
LBi = γ1 Zi + 1i

(2)

M igiP = η1 Zi + 2i

(3)

where Zi = (Xi , WiP , Sis , zi , δp ).
The exogenous variation induced by the instruments provides separate variation in the
residuals obtained from the reduced form, and these residuals act as the control function.
The instruments we use are: 1) the proportion of children aged 0-15 in five year age groups
who were left-behind in one’s own sending county (calculated from the 2000 Population
Census data);21 and 2) the share of individuals aged 20-44 who had migrated out of the
20

The non-linear functional form involves an assumption that the model is correctly specified in the first
stage, which is not necessary in standard instrumental variables.
21
For individuals who were under the age of 16 in 2000 we set this instrument equal to the proportion of
children of the same gender and age (five year age group) in their sending county who were left-behind
in 2000. For those who were aged 16 and above in 2000 we set the instrument to zero as we assume
they were not left behind which is reasonable because migration in those years (prior to the late 1990s)
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county at the time of the 2000 Population Census.
The share of people migrating and the share of children being left behind in the
county-birth cohort will mainly be driven by the county’s geographic, economic, and cultural environment and so are likely to be independent of individuals’ family and personal
situations. To further mitigate against the possibility that these variables are directly
related to the probability of an individual committing a crime we also include the vector
of prefecture and county level controls, SiS , and sending province fixed effects, δp , in all
estimations.
We then calculate the generalized residuals from each equation:
r1 (LBi , δ1 Zi ) = LBi λ(δ1 Z) − (1 − LBi )λ(−δ1 Z)

(4)

r2 (M igiP , η1 Zi ) = M igiP λ(η1 Z) − (1 − M igip )λ(−η1 Z)

(5)

where λ is the inverse Mills ratio, φ(.)/Φ(.), and include them (and higher powers of these
when they are statistically significant) in the second stage regression:
P risoneri = β0 + β1 LBi + β2 M igiP + β3 xi + β4 r1i + β5 r2i + 3i

3.2

(6)

Sibling Fixed Effects

An advantage of our survey is that it provides information not only on the respondents’
characteristics and how long their parents were away due to migration before they turned
16 years of age, but also information on their siblings’ characteristics, how long the siblings
were left behind by one or more parents, and whether their siblings ever committed a
crime. Equipped with these data we are able to estimate a model with family fixed effects
as follows:
P risonerij = θ + γ1 LBij + γ2 Xij + Fj + εij ,
(7)
where LBij is the number of years either parent was away from individual i in family j
before he turned age 16; Xij is a vector of individual characteristics, including years of
schooling, age, gender, and birth order;22 Fj are family fixed effects; and εij is the random
error term.
Equation (7) identifies the effect of being left behind on crime from within family
variation in the length of time children were left behind. It examines whether variation in
the length of time siblings were left-behind during childhood is associated with different
22

was a rare event.
Survey respondents were directly asked the question as to how many years they were left-behind,
whereas for their siblings we calculate this number from their birth year and the years of parental
migration. To control for this discrepancy and potential measurement errors in other sibling variables
due to recall errors, we also include a dummy variable indicating whether the observation is for a survey
respondent or a sibling of a respondent. The results are also robust to including an interaction of this
dummy variable with the parental absence variables.
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probabilities of the siblings committing crimes when they become adults. The fixed effects model thus removes any effect of unobserved parental and household characteristics,
e.g. variations in parental preferences and upbringing style, on the probability of children
committing a crime later in life. It is an alternative to the control function approach.
Although it brings us closer to identifying a true causal impact than estimates from equation 1 it does not completely solve the issue as child-specific unobservable characteristics
may affect the probability of an individual child in the household being left-behind for a
longer period than his or her sibling. For example, parents may elect to take unruly children with them which would bias the results. We judge that children’s characteristics are
likely to play a lesser role in determining parent’s decisions than parental and household
characteristics in the decision whether to leave a child behind. Regardless, a comparison
of these results with estimates from equation 1 (which does not account for the potential
endogeneity of the parental migration decision and the decision whether to leave a child
behind) and the estimates from equation 6 (control function estimates) is instructive as
an examination of the extent and direction of endogeneity bias in the original estimates.

4
4.1

The Empirical Results
Parental Absence and Its Impact on Migrant Criminality

We first examine whether parental absence in childhood due to migration, LBi , is associated with a higher probability of migrants committing crimes (and hence being incarcerated).23 Panel A in Table 3 presents marginal effects from weighted probits with the
dependent variable defined to equal 1 if the individual is in prison and 0 otherwise (without the inclusion of generalized residuals as control functions). We start by regressing
this variable, P risoneri , on LBi , a dummy variable indicating whether the individual was
left-behind between age 0 and 15 due to parental migration, M igiP , whether one or both
parents ever migrated to an urban area, and a set of provincial fixed effects. Column 1 of
Table 3 shows that migration of parents is significantly associated with a reduced likelihood of incarceration in adulthood (at the time of the survey) – a 0.7 percentage point
decrease – but that being left behind in the rural area by migrant parents significantly
increases the probability of incarceration by 2.5 percentage points relative to children
who were not left behind (significant at the 1% level). Left-behind children are thus 2.8
percentage points more likely (α1 + α2 ) to be incarcerated in adulthood than children
whose parents never migrated and 2.5 percentage points more likely than children who
23

Note that our dependent variable reflects incarceration, and not criminality per se. It thus reflects the
probability of committing a crime and the probability of being caught and jailed. The widely cited
crime statistics that show crime increasing in China similarly reflect criminal convictions, rather than
the number of crimes actually committed. As not everyone who commits a crime is imprisoned, our
estimates are likely to be an underestimate of the effect on criminality.
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were either older than 15 when parents migrated or taken to the cities with their parents.
Column 2 presents results when household, individual and regional (prefecture and
county) controls are added. The addition of the controls leaves the size of the association
of being left-behind with incarceration largely unchanged such that being left-behind is
associated with a 2.5 percentage point increase in the probability of incarceration relative
to children whose parents didn’t migrate (and to children whose parents migrated when
they were older than 15 or were took them to cities with them, as the coefficient on parents
migrating is now insignificant and close to zero). 8.5 percent of the weighted sample were
left-behind, so the predicted increase in the incarceration rate is 0.025 x 0.085 = 0.21
percentage points. This is a large effect - a 8.5 % increase - as the incarceration rate for
males in Shenzhen is 2.5%.
Column 3 shows results when we control for the length of parental absence, instead of
just whether the child was left-behind or not.24 Every additional year of parental absence
is associated with a 0.2 percentage point increase in the probability of being incarcerated
as an adult. (The average years of absence in our sample is 8 years.)
Being married reduces the probability of being in prison. As does having a better
educated mother and higher cognitive ability. Coming from a prefecture with a higher
GDP/capita is associated with an increased incarceration probability, possibly at odds
with expectations. Higher inequality is positively associated with a higher probability of
being in prison, as is a higher sex-ratio (more males to females), consistent with Cameron
et al. (2019) and Edlund et al. (2013). Being Han Chinese significantly decreases the
probability of being in prison and the proportion of the prefecture population who are
non-Han Chinese, i.e., from ethnic minority groups, is strongly associated with increased
likelihood of incarceration. A higher teacher-student ratio reduces the probability of being
incarcerated as an adult.
As discussed above, the estimates presented in Panel A of Table 3 are potentially
contaminated by selection bias as the decisions whether to migrate and whether to leave
the child behind are likely to be a function of unobservable household and/or child characteristics. Panel B of Table 3 presents the control function results which correct for
this potential endogeneity. The instruments are strongly statistically significant determinants of being left-behind, and marginally significant in the parental migration first
stage (Columns 1 to 3 of Table C2).25 The test of joint significance of the generalized
24

The length of absence is calculated as the total number of years the individual was left-behind between
age 0 and 15 by one or both parents. If the mother and father were absent for different number of years
we use the maximum of these two figures.
25
Jack-knifed standard errors are reported for these specifications. The control function approach involves including a control for the endogenous component of the potentially endogenous variables. The
endogenous component falls in to the (generalized) residuals from the first stage and for identification (other than that achieved off nonlinearities) at least one instrument with a non-zero coefficient is
needed, Wooldridge (2015). Our first stages for the left-behind variables are strong. The first stages
for parental migration are less strong but have one variable either statistically significant or close to
it. (The county left-behind rate is not statistically significant in the parental migration regression.
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residuals in the second stage indicates that they are statistically significant in the specification using the left-behind dummy variable (Column 2 of Table 3) and when we focus on
the length of time left-behind (Column 3 of Table 3), p=0.018 and p=0.066 respectively.
This suggests that being left-behind and parental migration are likely to be endogenous to
criminality. Being left-behind remains statistically significant in the second stages. The
magnitude of the effect is now larger. Being left-behind by either/both parent increases
the probability of being incarcerated as an adult by 12.2 percentage points relative to
otherwise similar children who were not left–behind (statistically significant at the 5%
level). The coefficient on parental migration is now also larger but remains statistically
insignificant. Column 3 shows that an additional year of absence is associated with a
0.5 percentage point increase of the probability of incarceration (significant at the 10%
level). The parental migration dummy in this specification is also positive and statistically significant, adding to the disadvantage of left-behind children compared to children
whose parents never migrated. Having one or both parents migrate is associated with a
10 percentage point increase in the probability of being incarcerated.
The results of our second method of accounting for the potential endogeneity of the
decision whether to leave a child behind – estimation with sibling fixed effects - are shown
in Table 4. Column 1 of Table 4 presents results analogous to those in Table 3 and
examines the effect of the length of parental absence (defined as the absence of the father
or the mother, whichever is longer). Column 2 examines paternal absences, column 3
maternal absences, and column 4 includes the length of both maternal and paternal
absences. We control for years of schooling, age, gender (although our sample comprises
only male individuals, many have female siblings) and birth order.
The fixed effects results are largely consistent with the control function results in that
every additional year of absence of either parent when the individuals were less than 16
years of age increases the probability of being incarcerated as an adult. The estimated
magnitude of the effect is however larger (1.4 percentage points per year of absence versus
0.5 percentage points, and now significant at the 1% level). How the length of parental
absence is measured does not seem to matter, there is a slightly larger effect detected for
mothers’ absences than fathers’ absences.26
This is anticipated as it was only intended to predict the county left-behind rate.) Nevertheless, to
examine the sensitivity of the results to the ability to instrument for parental migration, we estimated
models where we exclude observations where parents did not migrate and so only estimate one first
stage equation - for being left-behind. The point estimates are of a similar magnitude. Due to the
significantly smaller sample (412 observations) the estimates are imprecisely estimated. These results
are presented in Appendix C3.
26
The sibling fixed effects results could be larger than the control function results for several reasons. The
control function approach attempts to correct for the potential endogeneity of being left-behind that
is a result of unobserved family and child characteristics. The sibling fixed effects model controls for
unobservable family factors which affect how long each child is left-behind, but not for unobservable child
characteristics. The larger effect in the sibling fixed effects estimation could reflect that children who
are left behind are those who behaviorally are more likely to end up in prison. The differences between
the sets of estimates however also reflect the different sample in the sibling fixed effects estimation as
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The within family estimations also show that less-educated individuals are more likely
to be incarcerated and younger siblings are less likely to be in prison. Males are much more
likely to commit crime. These results are intuitive and consistent with the criminality
literature.

4.2

Identifying the channels via which parental absence affects
criminality

The previous discussion provides empirical evidence that parental absence due to migration increases the probability of an individual committing crime. However, it does not tell
us how being left-behind results in greater criminality. Sociologists have long discussed the
importance of complete family structure as a form of ‘social capital’ in inducing children’s
aspiration to achieve educational and other social advantages (see, for example, Bourdieu,
1977; Coleman, 1988). And, as discussed above, psychologists and economists have shown
that family structure can affect children’s behavior. Thus, possible mechanisms via which
being left-behind may affect the probability of committing a crime in adulthood include
lower educational attainment (leading to disadvantage and fewer viable income-earning
options), and impacts on children’s behavioral traits such as risk and time preferences,
and personality traits.
We examine the relative importance of each of the above channels through which
parental absence may affect criminality below. We start by examining educational attainment and then go on to examine the role of behavioral preferences and personality
traits.
4.2.1

Education

Studies of educational outcomes of left-behind children in China are abundant. Most find
that being left-behind has a negative correlation with schooling outcomes whether relative
to children whose parents did not migrate or children who migrated with parents to urban
cities (see, for example, Zhang et al., 2014; Meng and Yamauchi, 2017; Wang, 2019; Chen,
2018). The existing studies examine left-behind children’s school performance when they
were still at school, while here we examine their final educational outcome as measured
by years of schooling in adulthood.
The results for education are presented in Table 5. Columns 1 and 2 present results
of ordinary least squares estimations which show that being left behind in childhood due
to parental migration is associated with lower educational attainment, controlling for
individual’s innate cognitive ability. Individuals who were left-behind due to parental
there is one observation for each sibling pair (with many of those with siblings have more than one)
and those without siblings are excluded. Table 2 shows that only children are less likely to be in prison.
It would be interesting to examine whether parental absence is particularly problematic in some age
ranges. Our sample is however not large enough to allow such an examination.
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migration attain on average about 0.8 years less education and each additional year they
are left-behind reduces education by around 0.07 of a year. Columns 3 and 4 present
the control function results. The coefficient on being left-behind becomes slightly larger
and on the length of being left-behind remains about the same size but both are not
precisely estimated. The coefficients on parental migration, however, now become large
and statistically significant. Thus, left-behind children obtain less education relative to
children whose parents migrated but were not left-behind, and even less again compared
to children of parents who never migrated. The tests of joint significance of the generalized
residuals are not significant which suggests that the specifications in Columns 1 and 2
may be preferred.27
4.2.2

Behavioral Preferences and Personality Traits

Table 6 presents the results of regressing measures of risk-aversion and time preferences
(patience) on the indicator of being left-behind, LBi , the indicator of parental migration
and the same individual and household control variables included previously. We examine
two measures of both risk and time preferences. The first set of measures of risk and time
preference measures are continuous variables. Risk-aversion takes on greater values the
later the individual switches from the certain payment to the risky gamble, i.e., when the
amount to be won in the gamble is higher. Patience reflects the number of times the
individual chose to wait longer in order to receive the larger sum of money. The higher
the value of this variable, the more patient is the individual. The second set of measures
indicate that the respondent selected the riskiest or least patient choice. Riskiest equals 1
if the respondent always chose the gamble instead of the certain payment in the risk game,
and zero otherwise. The time preferences variable, Least Patient is defined analogously
and reflects whether the respondent always chose to get the money in the time preferences
task in one month’s time rather than after seven months. We examine the effect of being
left-behind on these extreme behaviors as extreme risk-taking and lack of patience are
likely to be more strongly associated with criminality.
Columns 1 to 4 of Table 6 present results of tobit estimation for the continuous variables (which are censored as they lie on a twelve point scale) and probit estimation (for
the riskiest and least patient indicators). They show that being left-behind has a negative,
but insignificant, effect on risk-aversion. It however is strongly associated with a greater
probability of making the riskiest decisions (it increases the probability of doing so by 8.7
percentage points). The coefficients on being left-behind are insignificant in both time
preference equations.
It is possible that parents take into account the behavioral traits of their children
27

When using sibling fixed effects we also observe a reduction in education with each year of being leftbehind, around 0.06 of a year of schooling, but due to small within family variation in education, this
result is not statistically significant. Results available on request.
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when deciding whether to leave them behind when they migrate. To remove the potential
for endogeneity bias, Columns 5 to 8 present the analogous results when we include the
control function to correct for endogeneity. Being left-behind now has a larger and more
strongly significant effect on both the probability of making the riskiest choice and the
continuous measure of risk-aversion. Being left-behind is associated with a 0.35 decrease
in the switching point on a 12 point scale and increases the probability of making the
riskiest choice by 64 percentage points. This is a very large effect. (Only 19% of those who
weren’t left-behind chose this option.) The 95% confidence interval for this variable lies
between 0.16 and 1.11 so the true impact, while large, may not be of this magnitude. The
result for time preferences is again negative and insignificant, although those who were
left-behind are significantly (p=0.08) more likely to make the least patient choices than
those whose parents stayed with them in the rural areas. The test of joint significance
of the generalized residuals strongly suggests endogeneity for the risk measures and for
making the least patient choices. The difference between the control function results and
the results in Columns 1 to 4 suggests that parents are less likely to leave risk-loving and
impatient children behind. This could reflect a fear that risk-loving, impatient children
might be more likely to get up to mischief in their parents’ absence.
Table 7 presents a similar analysis except in this case for personality traits. There are
no robust findings in relation to personality traits. The OLS results suggest a significant
negative relationship between being left-behind and extroversion, which becomes insignificant in the control function results. The control function results suggest that being
left-behind may result in lower levels of conscientiousness. However, the tests of the joint
significance of the generalized residuals do not find strong evidence of the endogeneity of
being left-behind with respect to these traits, except in relation to neuroticism.

4.3

Do lower educational attainment and risk-loving preferences
explain the left-behind effect?

In this sub–section we examine whether the potential mechanisms we have identified
explain the effect of being left-behind on criminality. We do this by including these
variables as additional explanatory variables in the criminality regression, alongside being
left-behind.28 Tables 8 present the results (estimated using the control function). Column
1 presents the original results from Panel B of Table 3 which show that being left-behind
is strongly associated with an increased probability of being incarcerated.29
28

The first stage estimation results are shown in Appendix Table C2. Columns 4 and 5 of Table C2 are
the first stages for Column 2 of Table 8 and Columns 6 and 7, and 8 and 9 of Table C2 are first stages
results for Columns 3 and 4 of Table 8. In all cases the instruments have predictive power over being
left-behind but not parental migration.
29
A possible concern with these results is that being in prison may affect preferences and so we may
be picking up the effect of being incarcerated on preferences rather than the effect of preferences on
criminality. This is less of a concern for the Big-5 personality traits which are thought to be relatively
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We start by adding controls for years of schooling in Column 2. This reduces the
magnitude of the effect of being left-behind by more than half (relative to those who went
to the city with their parents) from 0.122 to 0.052 and the effect becomes insignificant.
Those who were left-behind in rural areas however still remain more likely to be in prison
than those whose parents did not migrate (by 12.3 percentage points, p=0.07).
Next we add behavioral preferences (risk-aversion and patience), in addition to years
of schooling. We include a square of risk aversion as the data suggest the relationship is
non-linear.30 The coefficient on risk aversion is negative and significant at the 5% level
and the squared term is small, positive and significant at the 1% level. A reduction in
risk aversion associated with being left-behind is associated with a small increase in the
probability of being incarcerated.31 Adding our measures of risk aversion and patience
further reduces the coefficient on being left-behind from 0.052 to 0.046. The difference
between those who were left-behind and those who lived with their parents in rural areas
now also becomes statistically insignificant (p=0.104).
Finally we add the Big-5 personality traits (Column 4 of Table 8). Agreeableness and
extroversion are significantly negatively associated with criminality. The coefficient on
being left-behind remains statistically insignificant as does the difference between those
in rural areas who were left-behind and those who were not.
To quantify the relative importance of the estimates in Table 8 we conduct a mediation
analysis (following, for example, Heckman et al. (2013) and Heckman and Pinto (2015)).
The mediation analysis identifies the share of the impact of being left-behind (and parental
migration) on criminality that is attributable to the direct effect of being left-behind
and the share attributable to indirect effects operating through the mediating factors,
i.e., education and behavioral preferences. We also decompose the indirect effect into
components attributable to each of the individual mediating variables. Section D in the
appendix explains the methodology in more detail.32
stable over time but is a greater concern for the questions on time preferences and risk attitudes.
If incarceration does affect behaviour then one would expect that the length of time spent in prison
would be associated with behavioural differences. In another paper which uses the same data, Cameron
et al. (2019), we test this by adding the time spent in prison and sentence length as additional control
variables. Doing so shows that they are not significant determinants of these behavioural preferences.
30
We also ran a specification which included a square of patience but it was insignificant.
31
Calculated from the mean level of risk-aversion of those who were not left-behind and using the estimate
of the effect of being left-behind in Column 6 in Table 6.
32
The decomposition method makes assumptions similar to many mechanical decompositions e.g. Oaxaca
decomposition. It assumes away the impacts of unobserved mediators that are correlated with the
observed mediators and control variables (so we can attribute the component calculated to accrue to
the observed mediators and the control variables to these variables, and not unobserved mediators
that are correlated with them) and that treatment (being left-behind) does not affect the impact
of the mediator variables or the control variables on the outcome variable (the probability of being
incarcerated). That is, the model is correctly specified without interactions between treatment and
these variables (as is suggested when tested in the OLS model and which cannot be tested in the
control function model owing to a lack of suitably strong instruments for the interaction terms). As we
do not find a systematic effect of being left-behind on big-5 personality traits, we do not treat them as
mediating variables. Doing so, however, does not substantively affect the results.
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The mediation analysis finds that 64% of the effect of being left-behind on criminality
operates via a direct effect, with the remaining 36% being due to the effect of being leftbehind on mediating variables. Education is by far the most important mediating factor
accounting for 94% of the indirect effect, or 34% of the total impact of being left-behind
on criminality. Risk-preferences account for 6% of the indirect effect (2.1% of the total
impact). Time preferences have no impact.
To summarize, our analysis suggests that being left-behind in childhood due to parental
migration has adverse impacts on several human capital related attributes. We examined
the impact on educational attainment, personality traits, and risk and time preference.
We did not find any robust relationship with personality traits. However, being leftbehind makes people more risk-loving and less likely to stay in school. These attributes
partially explain why being left-behind increases the probability of committing crimes in
adulthood. The most important channel is through being left-behind reducing educational
attainment.

5

Conclusions

Industrialization, and its accompanying large scale rural-to-urban migration, coupled with
the hukou residency system has induced dramatic changes in Chinese family structure over
the past three decades. A large cohort of children of rural-urban migrants have been leftbehind in rural villages. The lack of parental care during childhood has been shown to have
important social consequences in the short run. This has aroused concern among public
policy makers and society in general in relation to the possible long-term consequences
for anti-social behavior. Although there are many studies that have examined the impact
in childhood of being “left-behind” on education and health (including mental health),
little is known about the impacts of parental absence on behavior in adulthood.
This paper uses unique survey and experimental data on rural-urban migrants – prison
inmates and comparable non-inmates – in China to examine whether parental absence in
childhood is associated with increased criminality in adulthood. We find that parental
absence in childhood due to migration increases the propensity for men to commit crimes.
Being left-behind reduces educational attainment and increases risk-loving behaviors, both
of which are associated with increased criminality in adulthood. However, the decrease
in educational attainment plays the more important role in increasing criminality. These
findings provide useful insights for policy-making aimed at alleviating the social costs
arising from rural-to-urban migration. While the generalizability of our results may be
limited by our focus on people who were rural-urban migrants at the time of our surveys,
our findings suggest that policies that support migrants to migrate with their families
and, failing that, policies that support children who are left-behind to stay in school, are

21

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likely to provide significant benefits to Chinese society.

22

Electronic copy available at: https://ssrn.com/abstract=3938639

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Table 1: Left–Behind Status
Full
Sample
8.46

At least one parent absent (%)
of which:
Both parents absent
Only father absent
Only mother absent
Neither parent absent
N

Prison Non-inmate
Inmates
Migrants
15.93
8.28

6.01
1.75
0.71

11.80
2.65
1.47

5.86
1.72
0.69

91.54

84.07

91.72

968

678

290

Note: We present weighted means of variables.

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Table 2: Descriptive Statistics

All
(1)

By Left-behind Status
LeftNot leftbehind
behind
(2)
(3)

By Prisoner Status
NonPrisoners prisoners
(4)
(5)

Individual Characteristics:
Age
Married
Siblings
Only Child
Paternal education
Maternal education
Cognitive ability score
Han Ethnicity
Parents had been in jail

29.4
0.43
1.74
0.10
8.01
6.70
6.92
0.97
0.01

24.5
0.20
1.35
0.24
8.65
8.02
7.79
1.00
0.00

29.7
0.44
1.77
0.08
7.96
6.60
6.85
0.96
0.01

29.8
0.32
2.00
0.06
6.92
4.94
5.93
0.86
0.02

29.3
0.43
1.74
0.10
8.04
6.74
6.94
0.97
0.01

Outcome Variables:
Prisoner inmate
Years of education
Risk aversion
Riskiest
Patience
Least Patient
Conscientious
Extroverted
Agreeable
Neurotic
Openness

0.024
11.12
5.97
0.13
5.51
0.22
3.63
3.33
3.77
2.66
3.37

0.045
12.09
4.95
0.20
3.62
0.44
3.59
3.37
3.71
2.75
3.39

0.023
11.04
6.05
0.13
5.66
0.20
3.64
3.33
3.77
2.66
3.37

7.95
6.82
0.23
5.26
0.32
3.42
3.02
3.54
2.89
3.16

11.19
5.95
0.13
5.52
0.22
3.64
3.34
3.78
2.66
3.38

Home Prefecture Variables:
ln(GDP/capita)
Gini coefficient
Ethnic minority share
Sex-ratio

9.46
0.35
0.05
1.12

9.52
0.35
0.02
1.13

9.46
0.35
0.05
1.12

9.38
0.35
0.13
1.15

9.47
0.35
0.04
1.12

0.05

0.05

0.05

0.05

0.05

0.05
0.12
968

0.05
0.24
109

0.05
0.11
859

0.07
0.12
678

0.05
0.12
290

Home County Variables:
County teacher/student ratio
Instruments:
County outmigration rate
County left-behind rate
No. of obs.

Note:
1. Columns (1) to (3) present weighted means.

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Table 3: Marginal Effects from Weighted Probit Estimation
Dependent Variable:
Prisoner (0/1)
A. Not allowing for Endogeneity
Left-behind

(1)

(2)

0.025∗∗∗
(0.007)

0.025∗∗∗
(0.008)

Length of parental absence
-0.007∗
(0.004)

Parent(s) migrated
Age
Married
Cognitive ability score
Siblings
Only child
Paternal education
Maternal education
Han ethnicity
Parent had been in jail
Regional control variables:
Ln(Prefecture GDP/capita)
Prefecture gini coefficient
Ethnic minority share
Prefecture sex ratio
County teacher-student ratio
Test of α1 + α2 = 0 (p-value):
B. Control Function Results
Left-behind

0.007

0.003
(0.004)
0.001
(0.000)
-0.018∗∗∗
(0.005)
-0.004∗∗∗
(0.001)
0.000
(0.002)
-0.002
(0.008)
-0.001
(0.001)
-0.003∗∗∗
(0.001)
-0.021∗
(0.012)
0.014
(0.019)
0.013∗∗
(0.005)
0.093∗
(0.054)
0.079∗∗∗
(0.022)
0.141∗∗∗
(0.042)
-1.250∗∗∗
(0.330)
0.0003

(3)

0.002∗∗∗
(0.001)
0.004
(0.004)
0.001
(0.000)
-0.019∗∗∗
(0.006)
-0.005∗∗∗
(0.001)
0.000
(0.002)
-0.003
(0.008)
-0.001
(0.001)
-0.003∗∗∗
(0.001)
-0.021∗
(0.012)
0.014
(0.019)
0.013∗∗
(0.005)
0.102∗
(0.054)
0.078∗∗∗
(0.022)
0.150∗∗∗
(0.042)
-1.217∗∗∗
(0.330)

0.122∗∗
(0.056)

Length of parental absence
Parent(s) migrated
Test of α1 + α2 = 0 (p-value):
Test of jt sig. of the generalized residuals (p-value):
N

0.066
(0.056)
0.009
0.018
968

0.005∗
(0.003)
0.101∗
(0.053)
0.066
968

Note:
1. We present marginal effects from weighted probits where we weight by the ratio of the population size
(of migrants/inmates) to the sample size (of migrants/inmates). All specifications also include province
fixed effects. The specifications in Panel B also include the full set of control variables shown in Panel A.
2. Robust standard errors are shown in parentheses. Panel B reports jackknifed standard errors.
3. Column 1 in Panel B uses generalized residuals calculated from the specifications in Columns 1 and 3
in Table C2 and Column 2 in Panel B above uses generalized residuals calculated from the specifications
in Columns 2 and 3 in Table C2.

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Table 4: Sibling Fixed Effects Results
Dependent Variable: Prisoner (0/1)
Length of parental absence

(1)
0.014∗∗∗
(0.004)

(2)

Male
Birth order
Constant

Observations
Within R2

0.008
(0.006)
0.010
(0.006)
-0.012∗∗∗
(0.002)
-0.004∗
(0.002)
0.048∗∗∗
(0.012)
-0.023∗∗∗
(0.009)
0.256∗∗∗
(0.092)
3061
0.666

-0.012∗∗∗
(0.002)
-0.004
(0.002)
0.048∗∗∗
(0.012)
-0.023∗∗∗
(0.009)
0.250∗∗∗
(0.091)

-0.012∗∗∗
(0.002)
-0.004∗
(0.002)
0.048∗∗∗
(0.012)
-0.023∗∗
(0.009)
0.253∗∗∗
(0.091)

0.015∗∗∗
(0.004)
-0.012∗∗∗
(0.002)
-0.004∗
(0.002)
0.048∗∗∗
(0.012)
-0.023∗∗∗
(0.009)
0.263∗∗∗
(0.093)

3061
0.665

3061
0.665

3061
0.666

Years mother absent

Age

(4)

0.014∗∗∗
(0.004)

Years father absent

Years of education

(3)

Note:
1. Results presented here are from fixed effects estimation. We also control for whether the
observation is an individual in our survey sample, or a sibling of such a person.
2. Standard errors are clustered at the household level and shown in parentheses.
3. *, **, and *** denote statistical significance at the 10%, 5%, and 1% levels, respectively.

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Table 5: Effect of Being Left-Behind on Educational Attainment
OLS

Left-behind

(1)
-0.796∗∗∗
(0.294)

Length of parental absence
Parent(s) migrated
Age
Married
Cognitive ability score
Siblings
Only child
Paternal education
Maternal education
Han ethnicity
Parent had been in jail

-0.033
(0.200)
-0.023
(0.015)
0.529∗∗
(0.206)
0.363∗∗∗
(0.037)
-0.132
(0.084)
-0.374
(0.369)
0.065∗∗
(0.029)
0.159∗∗∗
(0.027)
0.428
(0.368)
-0.750
(0.473)

Regional control variables:
Ln(GDP/capita)

Control Function
(2)

-0.069∗∗
(0.029)
-0.071
(0.197)
-0.023
(0.015)
0.540∗∗∗
(0.206)
0.363∗∗∗
(0.037)
-0.129
(0.084)
-0.373
(0.370)
0.066∗∗
(0.029)
0.158∗∗∗
(0.027)
0.428
(0.369)
-0.834∗
(0.453)

0.187
0.199
(0.198)
(0.198)
Gini coefficient
-0.454
-0.613
(2.310)
(2.300)
Ethnic minority share
-0.883
-0.853
(0.564)
(0.565)
Sex ratio
-2.598∗
-2.721∗
(1.540)
(1.543)
Teacher-Student Ratio
1.198
0.716
(13.240)
(13.255)
Test of joint significance of the generalized residuals (p-value):
Test of α1 + α2 = 0 (p-value):
0.005
Observations
968
968

(3)
-0.949
(1.432)

-3.082∗
(1.735)
-0.087∗∗
(0.037)
0.420∗
(0.222)
0.390∗∗∗
(0.041)
-0.222∗∗
(0.099)
-0.231
(0.405)
0.088∗∗∗
(0.032)
0.187∗∗∗
(0.031)
0.426
(0.379)
-0.022
(0.757)
0.104
(0.203)
2.138
(2.765)
-1.598∗∗
(0.688)
-2.557
(1.559)
-0.463
(13.669)
0.37
0.038
968

(4)

-0.063
(0.061)
-3.198∗∗
(1.569)
-0.087∗∗
(0.036)
0.424∗
(0.219)
0.391∗∗∗
(0.040)
-0.222∗∗
(0.099)
-0.227
(0.393)
0.088∗∗∗
(0.031)
0.188∗∗∗
(0.032)
0.432
(0.378)
-0.117
(0.644)
0.113
(0.203)
2.035
(2.703)
-1.564∗∗
(0.689)
-2.657∗
(1.557)
-1.036
(13.712)
0.35
968

Note: We present coefficients from ordinary least squares estimation. Robust standard errors for
OLS and Jackknifed standard errors for control function estimations are shown in parentheses.
The specifications reported in Column 2 also includes generalized residuals calculated from the
specifications in Columns 1 and 3 in Table C2. The specifications reported in Column 4 also
includes generalized residuals calculated from the specifications in Columns 4 and 5 in Table C2.
All specifications also include province fixed effects.

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Table 6: Effect of Being Left-Behind on Behavioral Preferences
(1)

(2)
(3)
(4)
Assuming exogeneity of being left-behind
probit
tobit
probit
tobit

Estimation type:
Dependent variable:

Riskiest

Left-behind
Parent(s) migrated
Age
Married
Cognitive ability score
Siblings
Only child
Paternal education
Maternal education
Han ethnicity
Parent had been in jail
Regional control variables:
Ln(GDP/capita)
Gini coefficient
Ethnic minority share
Sex ratio
Teacher-Student Ratio

(5)

(6)
(7)
Control Function Results
probit
tobit
probit

Least
patient
0.069
(0.051)
-0.033
(0.034)
-0.004
(0.003)
-0.012
(0.035)
-0.001
(0.006)
-0.002
(0.014)
-0.096
(0.065)
-0.005
(0.005)
0.002
(0.005)
0.150∗∗
(0.069)
-0.243∗
(0.139)

Patience

Riskiest

0.087∗∗
(0.043)
0.022
(0.030)
-0.004
(0.002)
0.042
(0.032)
-0.010∗∗
(0.005)
0.015
(0.011)
-0.009
(0.056)
-0.005
(0.004)
-0.000
(0.004)
0.038
(0.060)
-0.069
(0.105)

Risk
aversion
-0.032
(0.031)
-0.015
(0.019)
0.004∗∗
(0.002)
-0.029
(0.022)
-0.003
(0.004)
0.003
(0.009)
0.031
(0.036)
0.001
(0.003)
-0.002
(0.003)
-0.037
(0.044)
-0.001
(0.060)

-0.021
(0.042)
0.006
(0.026)
0.003
(0.002)
0.018
(0.028)
-0.011∗∗
(0.005)
-0.009
(0.011)
0.049
(0.050)
-0.002
(0.004)
0.002
(0.004)
-0.137∗∗
(0.059)
0.092
(0.071)

0.048
(0.030)
0.224
(0.321)
0.159∗
(0.091)
0.545∗∗
(0.240)
-0.316
(1.828)

-0.015
(0.020)
-0.024
(0.221)
-0.045
(0.073)
-0.425∗∗
(0.185)
-0.250
(1.314)

0.018
(0.034)
0.269
(0.360)
0.384∗∗∗
(0.108)
0.836∗∗∗
(0.287)
4.463∗∗
(2.087)
0.47
968

Test of joint significance of the generalized residuals (p-value):
Test of α1 + α2 = 0 (p-value):
0.01
0.13
Observations
968
968

(8)
tobit

Least
patient
0.208
(0.384)
0.542
(0.380)
0.010
(0.007)
0.019
(0.038)
-0.007
(0.007)
0.017
(0.016)
-0.145∗∗
(0.073)
-0.009∗
(0.005)
-0.004
(0.006)
0.144∗
(0.075)
-0.461∗
(0.256)

Patience

0.638∗∗∗
(0.242)
-0.108
(0.256)
-0.001
(0.005)
0.065∗
(0.035)
-0.010∗
(0.006)
0.017
(0.014)
-0.072
(0.065)
-0.006
(0.004)
-0.001
(0.005)
0.016
(0.063)
-0.304∗∗
(0.149)

Risk
aversion
-0.349∗∗
(0.176)
0.164
(0.185)
0.004
(0.004)
-0.039∗
(0.023)
-0.004
(0.004)
0.005
(0.010)
0.060
(0.039)
0.000
(0.003)
-0.003
(0.003)
-0.024
(0.045)
0.100
(0.088)

-0.019
(0.027)
-0.406
(0.291)
-0.279∗∗∗
(0.101)
-0.623∗∗
(0.243)
-4.604∗∗∗
(1.694)

0.064∗∗
(0.032)
-0.169
(0.384)
0.197∗
(0.107)
0.424∗
(0.255)
-0.431
(1.929)

-0.022
(0.022)
0.108
(0.270)
-0.042
(0.086)
-0.346∗
(0.192)
-0.057
(1.350)

0.041
(0.036)
-0.386
(0.428)
0.540∗∗∗
(0.131)
0.768∗∗
(0.299)
4.623∗∗
(2.169)

-0.032
(0.028)
-0.044
(0.351)
-0.374∗∗∗
(0.118)
-0.596∗∗
(0.253)
-4.772∗∗∗
(1.741)

0.73
968

0.007
0.06
968

0.038
0.37
968

0.038
0.08
968

0.338
0.13
968

-0.074
(0.251)
-0.363
(0.246)
-0.005
(0.005)
0.001
(0.030)
-0.008
(0.005)
-0.021
(0.013)
0.074
(0.055)
0.001
(0.004)
0.006
(0.004)
-0.136∗∗
(0.062)
0.206∗
(0.112)

Note:
1. We present marginal effects from probits and tobit estimation.
2. Robust standard errors are shown in parentheses. Columns 5 to 8 report jackknifed standard errors.
3. Columns 5 to 8 also include generalized residuals calculated from the specifications in Columns 1 and 3 in Table C2. All specifications
also include province fixed effects.

32

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Table 7: Effect of Being Left-Behind on Big Five Personality Traits
(1)
Extroverted
Left-behind
Parent(s) migrated
Age
Married
Cognitive ability score
Siblings
Only child
Paternal education
Maternal education
Han ethnicity
Parent had been in jail
Regional control variables:
Ln(GDP/capita)
Gini coefficient
Ethnic minority share
Sex ratio
Teacher-Student Ratio
Test of α1 + α2 = 0 (p-value):
Left-behind
Parent(s) migrated
Test of joint sig. of
gen’d residuals (p-value):
Test of α1 + α2 = 0 (p-value):
N

-0.096∗
(0.050)
0.057∗
(0.032)
-0.000
(0.002)
0.093∗∗∗
(0.032)
0.013∗∗
(0.005)
-0.014
(0.012)
0.064
(0.060)
-0.005
(0.005)
0.009∗∗
(0.004)
0.090
(0.058)
-0.085
(0.110)
-0.008
(0.030)
-0.090
(0.349)
-0.113
(0.088)
-0.075
(0.243)
-0.626
(1.942)
0.44
-0.186
(0.262)
-0.304
(0.255)

(2)
(3)
(4)
(5)
Open
Neurotic Agreeable Conscientious
A. No correction for endogenity
-0.045
0.069
-0.060
-0.054
(0.050)
(0.061)
(0.046)
(0.048)
0.017
-0.037
0.043
0.006
(0.030)
(0.037)
(0.031)
(0.033)
0.003
0.003
0.001
0.003
(0.002)
(0.003)
(0.003)
(0.003)
0.069∗∗
-0.085∗∗
0.052
0.127∗∗∗
(0.031)
(0.037)
(0.032)
(0.032)
0.021∗∗∗ -0.016∗∗∗
0.021∗∗∗
0.022∗∗∗
(0.005)
(0.006)
(0.005)
(0.006)
0.023∗
-0.007
0.012
-0.011
(0.012)
(0.014)
(0.012)
(0.013)
0.082
-0.054
0.036
-0.038
(0.059)
(0.072)
(0.051)
(0.059)
0.008∗∗
-0.007
0.006
-0.003
(0.004)
(0.005)
(0.004)
(0.005)
0.010∗∗∗
0.004
0.001
0.005
(0.004)
(0.005)
(0.004)
(0.004)
0.000
-0.063
0.044
0.120∗
(0.061)
(0.060)
(0.065)
(0.063)
-0.082
0.234
-0.084
-0.149
(0.074)
(0.145)
(0.067)
(0.091)
-0.048∗
0.093∗∗∗
-0.060∗∗
(0.028)
(0.036)
(0.030)
0.187
0.061
0.282
(0.323)
(0.379)
(0.325)
-0.114
0.102
-0.158
(0.093)
(0.096)
(0.106)
-0.048
0.194
-0.057
(0.217)
(0.317)
(0.243)
2.815
-0.908
0.548
(1.882)
(2.363)
(1.881)
0.58
0.59
0.71
B. Control Function Results
-0.010
-0.158
-0.073
(0.263)
(0.305)
(0.243)
-0.272
-0.142
0.821∗∗∗
(0.290)
(0.287)
(0.307)

0.45
0.10
968

0.98
0.63
968

0.0002
0.04
968

0.63
0.29
968

-0.107∗∗∗
(0.032)
0.568∗
(0.337)
-0.141
(0.097)
0.046
(0.280)
4.099∗∗
(1.940)
0.32
-0.499∗∗
(0.245)
-0.088
(0.334)
0.11
0.11
968

Note: We present coefficients from ordinary least squares estimation. Robust standard errors for OLS and
jackknifed standard errors for control function estimations are shown in parentheses. The specifications reported
in Panel B also include the full set of controls shown in Panel A and generalized residuals calculated from the
specifications in Columns 1 and 3 in Table C2. All specifications also include province fixed effects.

33

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Table 8: Criminality, Education and Behavioral Preferences - Control Function Results
Dependent variable: Prisoner
Left-behind
Parent(s) migrated

(1)

(2)

(3)

(4)

0.122∗∗
(0.056)
0.066
(0.056)

0.052
(0.050)
0.071
(0.055)
-0.016∗∗∗
(0.002)

0.046
(0.050)
0.068
(0.055)
-0.015∗∗∗
(0.002)
-0.007∗∗
(0.003)
0.0007∗∗∗
(0.000)
0.000
(0.001)

0.049
(0.052)
0.057
(0.057)
-0.012∗∗∗
(0.002)
-0.007∗∗
(0.003)
0.0006∗∗
(0.000)
-0.000
(0.001)
0.006
(0.008)
-0.010
(0.008)
-0.025∗∗
(0.010)
-0.024∗∗
(0.010)
0.006
(0.008)

0.183
0.104
968

0.298
0.154
968

Years of education
Risk-aversion
Risk-aversion squared
Patience
Neurotic
Open
Agreeable
Extroverted
Conscientious

Test of joint significance of the generalized residuals:
0.027
0.154
Test of α1 + α2 = 0 (p-value):
0.009
0.072
Observations
968
968

Notes:
1. We present marginal effects from weighted probit estimation where we weight
by the ratio of the population size (of migrants/inmates) to the sample size (of migrants/inmates).
2. Jackknifed standard errors are shown in parentheses.
3. All specifications also include the full set of controls shown in Table 3 and generalized residuals. Column 1 uses generalized residuals calculated from the specification
in Columns 1 and 3 in Table C2. Column 2 uses generalized residuals calculated from
Columns 4 and 5 in Table C2. Column 3 uses generalized residuals calculated from
Columns 6 and 7 in Table C2. Column 4 uses generalized residuals calculated from
Columns 8 and 9 in Table C2. All specifications also include province fixed effects.

34

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A
A.1

Appendix: Experiments
Information Sheet
Participant Information Sheet
Researcher:
My name is Dandan Zhang and I am a lecturer at Peking University. I work with Prof. Xin Meng from the
Australian National University and Prof. Lisa Cameron at Monash University on this project.

Project Title: Migration and Crime

General Outline of the Project:
The current project is an extension of the Rural-Urban Migration in China and Indonesia project. During
our previous five years of research in this area, one important issue stands out: many migrant workers
are arrested for criminal activities. This sub-project will collect behavioral information to help us to
understand the reasons for this.

Participant Involvement:
The project is voluntary and you can at any point, without any penalty, decline to take part or
withdraw from the activities.
In this study we will conduct interviews and economic experiments. Each participant will spend
approximately one and half hours in a meeting room environment and participate in a number of
experiments in the form of group games. The tasks you are required to perform are simple and
undemanding activities. In addition, the participants will fill in a survey questionnaire, which will take
around one hour, and an IQ test, which will last for 15 minutes.
All participants will receive a payment for participating in the economic experiments. Precisely how
much you will receive depends on the decisions you made, the decisions your partner made as well as
some random elements. In particular, you will be askedto perform some activities, and one of the
activities will be paid. Exactly which one will be determined by rolling a dice. The amount you received
from the game will be directly transferred into individuals’ personal accounts.
If any individual decides to withdraw from the project, any information provided prior to the time of
withdrawal will be destroyed.
Confidentiality: The information you provide will be kept confidential as far as the law allows. The
research outcome will be reported in the form of group averages and no individual information will be
identified or reported. The names of the participants will only appear on the first page of your answer
sheet and they will later be removed and replaced with an assigned ID number.

Data Storage:
Any identifying information will be stored separately from the questionnaires and kept in a locked file
cabinet at the Research School of Economics at the Australian National University, to which only the
principal investigators have access. The data sets used for analysis will contain only the ID numbers and no
identifying information. The data will be stored for 5 or more years from the date of the research
publication.

Queries and Concerns:
Dr. Dandan Zhang
China Center for Economic Research
National School of Development
Peking University Beijing, 100871, China
Email: ddzhang@nsd.edu.cn
Office: (+86)10-6275-9779

Ethics Committee Clearance:
The ethical aspects of this research have been approved by the ANU Human Research Ethics Committee.If
you have any concerns or complaints about how this research has been conducted, please contact:

Ethics Manager, The ANU Human Research Ethics Committee, ,The Australian National University
Telephone: +612 6125 3427; Email:
Human.Ethics.Officer@anu.edu.au

35

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A.2

Instruction for Experiment

General Explanations for Participants
Thank you for taking part in this study.
As part of today’s experiment, we will be performing some tasks. The funding for this research
has been provided by the Peking University and the Australian National University and any
money that you end up with will be yours to keep. You will be paid for one of the tasks. The
different parts are independent in the sense that the decisions you make in one will have no
impact on your outcome in the other. At the end of all the tasks I will throw a dice in front of you
to determine which task you will be paid for. We will give you a receipt for this money and it will
be paid into your savings account.
We are about to begin the first task. Please listen carefully. It is important that you understand
the rules of the task properly. If you do not understand, you will not be able to participate
effectively. A clear understanding of the instructions will help you make better decisions and
increase your earnings. We will explain the task and go through some examples together. There
is to be no talking or discussion of the task amongst you. There will be opportunities to ask
questions to be sure that you understand how to perform each task. At any time whilst you are
waiting during this experiment, please wait at your seat and do not do anything unless instructed
by the experimenter. Also do not look at others responses at any time during this experiment. If
at any time you decide that you are not happy with the task you have been invited to perform,
you can decide not to participate.
After we have completed all the tasks, I would like you to answer some questions about yourself.
Please take your time and answer honestly and as accurately as possible. You will not be identified
and your survey answers will only be used for this experiment and will only be used by the
researcher(s) involved in this project.
Finally, stapled behind this page is a slip of paper with your ID# on it. Please keep this page with
the stapled ID# with you at all times. Do not show this ID# to anyone or allow it to be visible to
anyone during or after this experiment. You will need to present this page with the stapled ID# to
the cashier at the end of the experiment in order to receive your payment information.
If you are ready, then we will proceed. Please turn the page and follow along with the
experimenter.

All decisions that you make today are recorded only by an anonymous subject number
and will only be used for research purposes. Your decisions will remain completely
anonymous.

36

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TASK #1 Instructions
This task is played by pairs of individuals. Each pair is made up of a Player 1 and a Player 2. Each
of you will play this task with someone. However, none of you will know exactly with whom you
are playing. You will never find this out.
Each Player 1 has 100 yuan. No money will be given at this point. All actual payments will be
decided at the end of the experiment if this task is chosen as the one that you will be paid for.
Player 1 must decide how to divide this money between himself and Player 2. Player 1 must
allocate between 0 yuan and the total 100 yuan to Player 2. Player 2 is then informed about Player
1’s decision and gets to decide whether to accept or reject the offer. If Player 2 accepts the offer,
Player 2 gets whatever Player 1 allocates to him, and Player 1 takes home whatever he does not
allocate to Player 2. If Player 2 rejects Player 1’s offer, then both players get $0.
Let’s go through an example:
Imagine that Player 1 chooses to allocate 50 yuan to Player 2. If Player 2 accepts the
offer, then, Player 2 will get 50 yuan. Player 1 will get 50 yuan (100 yuan minus 50
yuan equals 50 yuan). If, however, Player 2 rejects the offer, both Player 2 and Player
1 will get 0 yuan.
Note that this is an example only. The actual decision is up to you.
Each of you will play as both Player 1 and Player 2 in this task. Each of you will be paired with two
different people. In one pair you will be Player 1 and in the other pair you will be Player 2. So you
will play this task once as Player 1 and once as Player 2. The important thing to remember is that
you will NOT be paired with the same person twice and you will always remain anonymous to
each other. No-one will be told who they are paired with. We will hand out all forms that you
will record your decisions on throughout this experiment in envelopes to ensure this.
If this task is chosen for payment, I will then toss a coin to determine which pairing you will
be paid for. So for any given toss of the coin, half of you will go home with what you kept
as Player 1, half of you will go home with what the Player 1s have given you.
Are there any questions? If you are ready, we will proceed. You will write your decision on the
form provided. Please turn over the page and look at the form that you will record your decision
on. There is an example question and a table for you to record your decision. Please complete the
example question first and then fill in Boxes A and B of the table. Once done, please place your
form back into the envelope, raise your hand and we will collect the form from you.

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For experimenter use only
Player ID #: ____________________

Paired Player ID #: _______________

Form for Recording Decisions for Task #1

Before you fill out this form, please complete the example below:

1. Say you are Player 1 and you have 100 yuan. You choose to give 60
yuan to Player 2. If Player 2 accepts the offer how much will you have and
how much will Player 2 have?
Player 1(yourself):_______________

Player 2:________________

If Player 2 rejects the offer how much will you have and how much will
Player 2 have?

Player 1(yourself):_______________

Player 2:________________

2. When you have completed the example above, please enter the amount,
in dollars, that you wish to keep and the amount that you wish to give to
Player 2 in the table below.

Total amount
A

Amount I wish to keep

B

Amount I wish to send to anonymous Player 2

100 yuan

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TASK #2 Instructions
We are about to begin the 3rd task. How much you will be paid in this task depends on your own
decision and your luck. No money will be given at this point. All actual payments will be decided
at the end of the experiment as to whether this task will be chosen as the one that you will be
paid for. Please listen carefully to the instructions.
In this task, you need to answer 11 questions. For each question, you are given two choices,
Choice A and Choice B. You can choose one of them. Let’s have a look at these questions.
Choice A
1

45 Yuan for sure

Choice B
60 if you roll 1,2,3
0 if you roll 4,5,6

I
2

45 Yuan for sure

75 if you roll 1,2,3
0 if you roll 4,5,6

3

45 Yuan for sure

90 if you roll 1,2,3
0 if you roll 4,5,6

4

45 Yuan for sure

105 if you roll 1,2,3
0 if you roll 4,5,6

5

45 Yuan for sure

120 if you roll 1,2,3
0 if you roll 4,5,6

6

45 Yuan for sure

135 if you roll 1,2,3
0 if you roll 4,5,6

7

45 Yuan for sure

150 if you roll 1,2,3
0 if you roll 4,5,6

8

45 Yuan for sure

165 if you roll 1,2,3
0 if you roll 4,5,6

9

45 Yuan for sure

180 if you roll 1,2,3
0 if you roll 4,5,6

10

45 Yuan for sure

195 if you roll 1,2,3
0 if you roll 4,5,6

11

45 Yuan for sure

210 if you roll 1,2,3
0 if you roll 4,5,6

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There are two important rules in your choice you need to take notice of:
First, you cannot choose Choice B first and then switch in subsequent questions to choice A.
Second, you cannot switch twice from Choice A to Choice B and then back to Choice A.
You can choose all A, or all B, or switching from A to B once.
When you finish answering all 11 questions, we will choose one person from the group to come
up and pick one ball from this bag, which has 11 balls, all the same size but each has a different
number on it. The number on the ball which is picked by that person will be the question for
which we will pay you according to the answer you are given to that question.
For example, if number 10 were chosen, we will ask another person from the group to roll a dice
to see if the choice is 1, 2, or 3; or 4, 5, or 6. Once we made these decisions, we can decide how
much you will get paid for this task if this task is chosen at the end of the games. For example, if
your answer to question number 10 was A, you will be paid 45 yuan. Otherwise, if your answer
was B, then we will pay you 195 yuan if the number on the dice was 1, 2, or 3 and 0 yuan if the
number on the dice was 4, 5, or 6.

Do you have any questions? If you are ready, we will proceed. Please answer the 11 questions
on the form in front of you. I will then collect the forms. Then, we will choose somebody to select
the question number and another person to roll the dice.

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Player ID #: __________________________

Task 2

Answer Sheet

Choice A
1

45 Yuan for sure

Choice B
60 if you roll 1,2,3
0 if you roll 4,5,6

I
2

45 Yuan for sure

75 if you roll 1,2,3
0 if you roll 4,5,6

3

45 Yuan for sure

90 if you roll 1,2,3
0 if you roll 4,5,6

4

45 Yuan for sure

105 if you roll 1,2,3
0 if you roll 4,5,6

5

45 Yuan for sure

120 if you roll 1,2,3
0 if you roll 4,5,6

6

45 Yuan for sure

135 if you roll 1,2,3
0 if you roll 4,5,6

7

45 Yuan for sure

150 if you roll 1,2,3
0 if you roll 4,5,6

8

45 Yuan for sure

165 if you roll 1,2,3
0 if you roll 4,5,6

9

45 Yuan for sure

180 if you roll 1,2,3
0 if you roll 4,5,6

10

45 Yuan for sure

195 if you roll 1,2,3
0 if you roll 4,5,6

11

45 Yuan for sure

210 if you roll 1,2,3
0 if you roll 4,5,6

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TASK #3 Instructions
We are about to begin the 2nd task. Please listen carefully to the instructions.
This task is performed by pairs of individuals. Each pair is made up of a Player A and a Player B.
Each Player A has 50 yuan. No money will be given at this point. All actual payments will be
decided at the end of the experiment if this task is chosen as the one that you will be paid for.
Each Player A will have the opportunity to keep all of 50 yuan to himself or allocate some or all of
it to a Player B. However, each yuan that Player A sends to Player B will be tripled by the
experimenter and given to player B.
Player B will then have an opportunity to keep all of the money sent to him from Player A or to
send some or all of it back to Player A. This time the money will not be tripled again. The
experiment ends at this point.
Player B takes home whatever money that he/she does not give back to Player A. Player A takes
home whatever he/she did not give to Player B and whatever money Player B gave back to him.
Here are 2 examples of what could happen:
1) Say Player A gives Player B 25 yuan. This will be tripled and it will be 75 yuan when it reaches
Player B. Then Player B sends back to Player A, say, 35 yuan. Then Player A will have 60 yuan
(50 yuan minus the 25 yuan sent to Player B plus the 35 yuan sent back by Player B). Player
B will have 40 yuan (75 yuan minus the 35 yuan sent back to Player A).
2) Say Player A gives Player B 40 yuan. This will be tripled and it will be 120 yuan when it reaches
Player B. Then Player B sends back to Player A 60 yuan. Then Player A will have 70 yuan (50
yuan minus the 40 yuan sent to Player B plus the 60 yuan sent back by Player B). Player B will
have 60 yuan (120 yuan minus the 60 yuan sent back to Player A).
Note that these are only examples. The actual decisions are up to you.
Each of you will play as both Player A and Player B in this task. Each of you will be paired with
two different people in the other prison cell. (Note that the pairings in Task 2 are different from the
pairings in Task 1.) In one pair you will be Player A and in the other pair you will be Player B. So
you will play this task once as Player A and once as Player B. The important thing to remember is
that you will NOT be paired with the same person twice and you will always remain anonymous to
each other. No-one will be told who they are paired with. If this task is chosen for payment, I will
then toss a coin to determine which pairing you will be paid for. So for any given toss of the coin,
half of you will go home with what you kept as Player A, half of you will go home with what the
Player As have given you.
Are there any questions? If you are ready, we will proceed. You will convey your decisions using
the form provided. Please turn over the page and look at the form that you will record your decision
on.
I will read through the form first. Please do not write anything until instructed to.

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For experimenter use only
Player ID #: ____________________

Paired Player ID #:

Form for Recording Decisions for Task #3
Part A
Before you fill out this form, please complete the example below:
1. You are Player A and you have 50 yuan. You choose to give 40 yuan
to Player B. How much will Player B have?
$_______ x_______ =____________
Player B decides to send 20 yuan back. How much will you have in
total and how much will Player B have in total?
Player A:$_____ - $_____+$_____= _____
Player B:$_____-$_____ = _____
When you have completed the example above, please fill out Boxes A, B
and C of the table below. When you have made your decision as Player A,
your task as Player A is done at this point. Once you have completed Boxes
A, B and C, raise your hand and I will collect the form from you. You will be
informed of how much the Player B gave back to you at the end of the
experiment when you collect your payment.
2.
Your decision as Player A
Starting amount
A

Amount I wish to keep as Player A

B

Amount I wish to send to anonymous Player B

C

Amount that Player B will receive (Box B x 3)

50 yuan

When you have completed Part A, please read the instructions for Part B over
page.

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Form for Recording Decisions for Task #3

Part B
Recall that you will also be a Player B in another pairing. I will record how much
Player A in this pairing has sent to you in Box D when I collect your forms after you
fill in Boxes A, B and C. The amount in Box D will already be tripled. I will then return
the form to you and you will then decide how much money to keep and how much to
send back to Player A. You will need to fill in Boxes E and F.
When you have read the above paragraph, place your form for Task #2 into the
envelope, raise your hand and I will collect your form from you.

3.
Your decision as Player B
D

Amount received from Player A (already tripled)

E

Amount I wish to keep

F

Amount I wish to send back to Player A

Once you have completed boxes E and F, your task is done. Please place this form
into your envelope, raise your hand, and I will collect the form from you.

Two additional tasks (which are not used in this paper and which we do not explain here) were
then conducted for use in another paper. The experimental session was then concluded,
payments were determined and participants paid.

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A.3

Time Preference Choices

G. Time preferences

Suppose that you can get some money in two ways. Choice A gets you 1000 Yuan after
one month, and Choice B gets you more money but after seven months. Mark your choice
for the 11 situations listed below.
1

A
To get 1000 Yuan after one month

B
To get 1025 Yuan after seven months

2

To get 1000 Yuan after one month

To get 1075 Yuan after seven months

3

To get 1000 Yuan after one month

To get 1125 Yuan after seven months

4

To get 1000 Yuan after one month

To get 1175 Yuan after seven months

5

To get 1000 Yuan after one month

To get 1225 Yuan after seven months

6

To get 1000 Yuan after one month

To get 1275 Yuan after seven months

7

To get 1000 Yuan after one month

To get 1325 Yuan after seven months

8

To get 1000 Yuan after one month

To get 1375 Yuan after seven months

9

To get 1000 Yuan after one month

To get 1425 Yuan after seven months

10

To get 1000 Yuan after one month

To get 1475 Yuan after seven months

11

To get 1000 Yuan after one month

To get 1525 Yuan after seven months

45

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B

Appendix: Weight Generation

In 2012 there were 767,130,000 migrant residents of Shenzhen (with non-local hukou),
Social and Economic Development Statistical Report. Assuming that about 90% of these
are rural-urban migrants and about half are male, we estimate there are 3.45 million
rural-urban male migrants in Shenzhen.
The same data source tells us that there were 50,315 arrests made in Shenzhen in
2012/2013. Using the prison administration data we calculate a prison inflow ratio (equal
to the inflow in 2012/2013 divided by the total number of prisoners in this period) of
0.55. Dividing the total number of arrests in Shenzhen in 2012/2013 by this inflow
rate we obtain an estimate of the rural-urban migrant prison population in the city of
50,315/0.55=91,481. In 2012 94.17% of prisoners were male, China Statistical Yearbook
(2004-2013). So our estimate of the male prison population is 86,148.
These numbers are used to calculate the poulation weights used in this study.

46

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C

Appendix: Tables

Table C1: Marginal Effects from Weighted Logit and Unweighted (Corrected) Logit

Dependent Variable: Prisoner
Left-behind
Parent(s) migrated
Age
Married
Cognitive ability score
Siblings
Only child
Paternal education
Maternal education
Han ethnicity
Parent had been in jail

Weighted Logit
Results
(1)
(2)
0.026∗∗∗ 0.025∗∗∗
(0.007)
(0.008)
-0.007∗
0.004
(0.004)
(0.005)
0.001
(0.000)
-0.020∗∗∗
(0.006)
-0.005∗∗∗
(0.001)
-0.000
(0.002)
-0.000
(0.008)
-0.001
(0.001)
-0.003∗∗∗
(0.001)
-0.025**
(0.012)
0.017
(0.017)

Regional Variables:
ln(GDP capita)

0.017∗∗∗
(0.006)
0.118∗∗
(0.058)
0.079∗∗∗
(0.021)
0.167∗∗∗
(0.046)
-1.503∗∗∗
(0.358)
968

Gini coefficient
Ethnic minority share
Sex ratio
Teacher/student ratio
N

968

Unweighted (Corrected)
Logit Results
(3)
(4)
0.004∗∗∗
0.007∗∗∗
(0.001)
(0.002)
-0.001∗
0.000
(0.001)
(0.001)
0.000
(0.000)
-0.005∗∗∗
(0.001)
-0.001∗∗∗
(0.000)
0.000
(0.001)
-0.001
(0.002)
-0.000
(0.000)
-0.001∗∗∗
(0.000)
-0.005*
(0.003)
0.005
(0.007)

968

0.002
(0.001)
0.017
(0.013)
0.017∗∗∗
(0.005)
0.042∗∗∗
(0.013)
-0.205∗∗
(0.083)
968

Note: Columns 1 and 2 present marginal effects from weighted probit estimation where we weight by the ratio of the
population size (of migrants/inmates) to the sample size (of migrants/inmates). Columns 3 and 4 present marginal effects
from logistic regressions where we correct for choice-based sampling following King and Zeng (2001). All specifications
include province fixed effects. Standard errors are shown in parentheses.

47

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48

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968
0.004

968

0.001

(2)
Length of
absence
20.182∗∗
(10.253)
44.511∗∗
(21.505)

0.181

968

(3)
Parent(s)
migrated
-0.197
(0.552)
2.603∗
(1.409)

0.004

968

(4)
Leftbehind
1.841∗∗
(0.839)
3.337∗
(1.756)
-0.070∗∗∗
(0.026)

0.181

968

(5)
Parent(s)
migrated
-0.197
(0.552)
2.603∗
(1.409)

For specifications also
including education

0.012

968

(6)
Leftbehind
1.760∗∗
(0.849)
2.885
(1.835)
-0.069∗∗∗
(0.026)
-0.112∗
(0.063)
0.008
(0.005)
-0.009
(0.013)

0.275

968

(7)
Parent(s)
migrated
-0.208
(0.553)
2.299
(1.432)
-0.016
(0.018)
-0.031
(0.049)
0.001
(0.004)
-0.001
(0.010)

For specifications also
including education and
behavioral preferences

0.010

(8)
Leftbehind
1.838∗∗
(0.838)
2.797
(1.852)
-0.065∗∗
(0.026)
-0.114∗
(0.063)
0.008∗
(0.005)
-0.009
(0.013)
0.088
(0.151)
-0.015
(0.177)
0.006
(0.182)
-0.101
(0.183)
-0.022
(0.177)
968

0.228

(9)
Parent(s)
migrated
-0.260
(0.563)
2.489∗
(1.450)
-0.020
(0.018)
-0.034
(0.050)
0.002
(0.004)
-0.001
(0.011)
-0.035
(0.110)
-0.029
(0.136)
0.165
(0.126)
0.163
(0.130)
-0.118
(0.127)
968

For specifications also including
education, behavioral preferences
and personality traits

Note: All columns except for Column 2 report coefficients and standard errors from probit estimation. Column 2 reports coefficients and standard errors from interval
regression. The county left-behind rate and county out-migration rate are the instrumental variables. All standard errors are clustered by county of birth. All specifications
also included all of the control variables used in Table 3 and province fixed effects. Standard errors are shown in parentheses.

Observations
Test of joint significance
of instruments (p-value):

Conscientious

Extroverted

Agreeable

Openness

Neurotic

Patience

Risk aversion squared

Risk aversion

Years of education

County out-migration rate

County left-behind rate

(1)
Leftbehind
1.733∗∗
(0.830)
4.102∗∗
(1.738)

For the base specification

Table C2: First Stage Regressions for Control Function Estimation

Table C3: Selected Marginal Effects for the Sample of Individuals whose Parents Ever
Migrated
Dependent Variable: Prisoner (0/1)
(1)
A. Not allowing for Endogeneity
Left-behind

(2)

0.025∗∗∗
(0.008)
0.003∗∗∗
(0.001)

Length of Parental Absence
B. Control Function Results
Left-behind

0.128∗
(0.070)

Length of Parental Absence
Test of jt sig. of generalized residuals (p-value)
F-Test of weak IVs:
Observations

0.035
12.75
412

0.004
(0.004)
0.50
11.41
412

Note:
1. The results presented here are from the estimation of Equation 1 for a sample of individuals whose
parents ever migrated. The full results are available upon request from the authors.
2. We present marginal effects from weighted probits where we weight by the ratio of the population
size (of migrants/inmates) to the sample size (of migrants/inmates). All specifications also include the
control variables and province fixed effects.
3. Robust standard errors are shown in parentheses. Panel B reports jackknifed standard errors.
4. The results used to calculate generalized residuals for Panel B are available upon request from the
authors.

49

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Table C4: Effect of Being Left-Behind on Additional Behavioral Preferences
(1)

Dependent variables:
Estimation type:
Left-behind
Parent(s) migrated
Age
Married
Cognitive ability score
Siblings
Only child
Paternal education
Maternal education
Han ethnicity
Parent had been in jail
Regional Variables:
Ln(GDP/capita)
Gini coefficient
Ethnic minority share
Sex ratio
Teacher-Student Ratio
Test of α1 + α2 = 0 (p-value):
Observations

(2)
Trust Game
Trust
Trust-worthiness
(% sent)
( % returned)

(3)
(4)
Ultimatum Game
Altruism Punishment
(% sent)
(0/1)

tobit
0.006
(0.005)
0.000
(0.003)
0.000
(0.000)
-0.006∗
(0.003)
0.001∗∗
(0.001)
0.000
(0.001)
0.004
(0.006)
-0.000
(0.000)
-0.000
(0.000)
-0.005
(0.005)
0.005
(0.009)

tobit
0.010∗
(0.006)
-0.005
(0.003)
0.001∗∗∗
(0.000)
-0.005∗
(0.003)
-0.001∗∗∗
(0.001)
0.002
(0.001)
0.005
(0.006)
0.000
(0.000)
-0.000
(0.000)
-0.014∗
(0.007)
-0.005
(0.006)

tobit
0.001
(0.000)
0.000
(0.000)
0.000
(0.000)
-0.000
(0.000)
-0.000
(0.000)
0.000
(0.000)
-0.000
(0.000)
-0.000
(0.000)
-0.000
(0.000)
-0.000
(0.001)
-0.000
(0.001)

probit
0.008
(0.039)
0.023
(0.025)
-0.006∗∗∗
(0.002)
0.076∗∗∗
(0.027)
0.011∗∗∗
(0.004)
0.002
(0.009)
-0.003
(0.046)
0.001
(0.003)
0.002
(0.003)
-0.065
(0.050)
0.096
(0.088)

-0.000
(0.003)
-0.046
(0.031)
-0.001
(0.008)
0.011
(0.022)
-0.208
(0.173)
0.218
964

-0.002
(0.003)
-0.002
(0.033)
-0.005
(0.011)
0.049∗
(0.028)
-0.312
(0.193)
0.293
951

0.000
(0.000)
-0.001
(0.003)
0.001
(0.001)
0.002
(0.002)
-0.009
(0.014)
0.108
968

-0.002
(0.026)
-0.132
(0.275)
-0.088
(0.080)
0.024
(0.205)
0.567
(1.543)
0.423
968

Note:
1. We present marginal effects from probits and tobit estimation.
2. Robust standard errors are shown in parentheses.
3. All specifications also include province fixed effects.

50

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D

Appendix: Mediation Analysis

The median analysis closely follows that of Heckman et al. (2013) and Heckman and
Pinto (2015). Details of the model underlying the mediation analysis can be found in
these references. Here we explain the steps underlying the analysis. In the notation below
for simplicity we suppress the individual index, i, and ignore the existence of control
variables in the regressions.
Our analysis uses estimates from the model estimated in Column 3 of Table 8 where
P risoneri is regressed on the treatment variables (LB and M ig P ) and the mediating
variables (education, riskiest and patience); the regressions of each of the mediating
variables on the treatment variables reported in Column 3 of Table 5 for education,
Column 4 of Table 6 for riskiest and Column 6 of Table 6 for patience. If we notate these
models as follows:
P risoner = τ0 + τ1 LB + τ2 M ig P + αE Education + αR Riskiest + αP P atience + , (8)
E
E
P
E
Education = µE
0 + µ1 LB + µ2 M ig +  ,

(9)

R
R
P
R
Riskiest = µR
0 + µ1 LB + µ2 M ig +  ,

(10)

P atience = µP0 + µP1 LB + µP2 M ig P + P ,

(11)

then, as demonstrated in the above references, and assuming an underlying linear model
between the estimated marginal effects, the total effect of being left-behind (and parental
migration) can be expressed as:
E[P risoner1 − P risoner0 ] =

X

X

τk +

X

k∈{1,2}

j∈{E,R,P } m∈{1,2}

| {z }

|

direct effect

µjm αj ,

{z

indirect effect

(12)

}

where P risoner1 is the probability of being incarcerated if left-behind and P risoner0 is
the probability of being incarcerated if not left-behind; τk capture the direct effects of
the treatment variables (left-behind and parental migration) on the probability of being
incarcerated; µjm are the effect of the treatment variables on the mediating variables; and
αj are the effects of the mediating variables on the probability of being incarcerated.
The first element in equation 12 thus is the total direct effect of being left-behind (and
parental migration) and the second expression is the sum of the indirect effects of being
left-behind which operate through the mediating variables.

51

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