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Occupational Dualism and Intergenerational Educational Mobility in the
Rural Economy: Evidence from China and India
M. Shahe Emran1
IPD, Columbia University
Francisco Ferreira
World Bank
Yajing Jiang
Charles River Associates
Yan Sun
World Bank
ABSTRACT
This paper extends the Becker-Tomes model of intergenerational educational mobility
to a rural economy characterized by farm-nonfarm occupational dualism and provide a com-
parative analysis of rural China and rural India. The model provides a micro-foundation
for the widely used linear-in-levels estimating equation. Returns to education for parents
and productivity of financial investment in children’s education determine relative mobility,
as measured by the slope, while the intercept depends, among other factors, on the degree
of persistence in nonfarm occupations. Unlike many existing studies based on coresident
samples, the estimates do not suffer from truncation bias. The sons in rural India faced
lower educational mobility compared with the sons in rural China in the 1970s to 1990s.
To understand the role of genetic inheritance, Altonji et al. (2005) sensitivity analysis
is combined with the evidence on intergenerational correlation in cognitive ability in eco-
nomics and behavioral genetics literature. The observed persistence can be due solely to
genetic correlations in China, but not in India. Fathers’ nonfarm occupation and educa-
tion were complementary in determining a sons’ schooling in India, but separable in China.
There is evidence of emerging complementarity for the younger cohorts in rural China.
Structural change in favor of the nonfarm sector contributed to educational inequality in
rural India. Evidence from supplementary data on economic mechanisms suggests that the
model provides plausible explanations for the contrasting roles of occupational dualism in
intergenerational educational mobility in rural India and rural China.
Key Words: Educational Mobility, Rural Economy, Occupational Dualism, Farm-Nonfarm,
Complementarity, Coresidency Bias, China, India
JEL Codes: O12, J62
1We are grateful to Forhad Shilpi for help with REDS data and insightful comments throughout this
project, and to Yang Huang for help with the CFPS data. We would like to thank the participants in Equal
Chances conference 2018, and LACEA conference 2019, and Matthew Lindquist, Guido Neidhofer, Reshad
Ahsan, and Hanchen Jiang for helpful comments on an earlier draft and Rakesh Gupta Nichanametla
Ramasubbaiah for excellent research assistance. An earlier version of the paper was titled “Intergen-
erational Educational Mobility in the Rural Economy: Evidence from China and India”. This project
was partially funded by World Bank RSB. The standard disclaimers apply. Email for correspondence:
shahe.emran@gmail.com.
(1) Introduction
Intergenerational persistence in economic status in developing countries has attracted
the attention of policymakers and researchers in recent years, partly in response to growing
evidence that economic liberalization increased income inequality in many countries, despite
a significant reduction in poverty.2In the absence of reliable income data over the life-cycle
of parents and children, the focus of the recent literature on developing countries has been
on intergenerational educational mobility.3However, most of the recent studies are devoted
to urban households, and intergenerational mobility in rural areas remains particularly
under-researched, even though the bulk of the poor live in villages in developing countries.
This paper provides a comparative analysis of intergenerational educational mobility in the
rural areas of the two most populous countries in the world: China and India, with more
than 1.5 billion people living in villages in 2000/2001.4
While understanding the role of family background in the educational opportunities of
1.5 billion people is an important research agenda in itself, the policy differences between
China and India make such a comparative study especially interesting.5Perhaps, the most
important difference in the 1970s to 1990s, the period during which the children in our
empirical analysis went to school, was the restrictions on rural-urban migration in China
because of the Hukou registration system. In contrast, there were no policy restrictions
on rural-urban migration in India. Returns to education in farm vs. nonfarm occupations
are also likely to be different in rural China because of policies such as the household
responsibility system, rural industrialization (TVEs), and a lack of a well-functioning labor
market in the 1970s to 1990s. Another important aspect in which rural India and rural
China differed in this period is their schooling systems, with private schools playing a
2For recent contributions on China, see, among others, Fan et al. (2020), Park and Zou (2019), Sato
and Li (2007), Emran and Sun (2015a)), on India see, among others, Azam and Bhatt (2015), Emran and
Shilpi (2015), Asher et al. (2018), Ahsan et al. (2019), Emran et al. (2020). For cross-country analysis,
see Behrman (2000), Hertz et al. (2007), and Neidhofer et al. (2018), among others. Among the few
contributions on intergenerational persistence in health, see Bhalotra and Rawlings (2013).
3Educational mobility in this paper relates to schooling attainment. For a discussion on the broader
concept of education in and outside the classroom as input to human capital production, see, for example,
Behrman (2019).
4The rural population in India was 742.62 million in 2001 (72.16 percent of the total), according to the
census of India 2001. In China, the rural population in 2000 was 807.39 million (64 percent of the total),
according to the China Statistical Yearbook, 2011.
5China opened up its economy gradually from 1978, and the rural economy went through substantial
policy changes starting with the household responsibility system that introduced market incentives at the
margin. India liberalized its economy with a big bang in 1991, but the rural economy was relatively
less affected as the initial trade protections were focused on the industrial sector as part of a planned
industrialization strategy.
1
much more prominent role in rural India. In our analysis, we pay close attention to the
implications of these cross-country differences.
The standard model of intergenerational educational mobility where parent’s education
is the sole indicator of family background is not suitable for our analysis because it ignores
occupational dualism in the rural economy.6Children born into a nonfarm household
may face different educational opportunities compared to the children born into a farming
household even when the parents have similar educational background. At a given level of
education, the parent’s nonfarm occupation may affect investment in children’s education
through two major channels. First, higher income from nonfarm occupations may relax
binding credit constraints on investment in schooling.7Second, the probability of a child
getting a nonfarm job may be higher when the parents themselves are employed in nonfarm
occupations because of network, referral, and role model effects (Emran and Shilpi (2011)),
and this would increase the optimal investment when returns to education are higher in
nonfarm occupations.
There is substantial evidence that structural change in favor of non-farm occupations is
an important source of increasing income inequality in villages of many developing coun-
tries.8According to the estimates of Lanjouw et al. (2013) based on the data from Palanpur
in the Indian state of Uttar Pradesh, the contribution of non-farm income to income in-
equality was only 4 percent in 1974/75, which increased to 67 percent in 2008/09.9The
evidence on China also suggests that nonfarm income contributes to income inequality in
rural areas (Rozelle ( 1994), Yang and An (2002)). Such a rise in inequality associated with
the expansion of the nonfarm sector is of special concern when it reflects lower intergener-
ational mobility.
We develop a theoretical model in the tradition of Becker and Tomes (1986) that in-
corporates the role played by parental farm and nonfarm occupations in shaping children’s
educational opportunities, and yields the almost universally used linear-in-levels estimat-
ing equation.10 As emphasized by Mogstad (2017), in the absence of an explicit theoretical
6Although there is a long tradition in development economics following Lewis (1954) that emphasizes
dualism as a central feature of underdevelopment, to the best of our knowledge, ours is the first paper to
incorporate occupational dualism in an analysis of intergenerational educational mobility.
7However, in some countries, low-skilled nonfarm activities might be occupations of last resort, with
low income, lower than the income of the farming households (Lanjouw and Lanjouw (2001)).
8For an excellent survey of the literature on rural nonfarm economy in developing countries, see Lanjouw
and Lanjouw (2001). On rural China see Rozelle (1994), Yang and An (2002), and on rural India see Lnjouw
et al. (2013).
9The Gini coefficient of income in Palanpur was 0.253 in 1974/75 and 0.427 in 2008/09.
10The estimating equation used in the literature on intergenerational income mobility is log linear. In
2
model, it is difficult to understand and interpret the economic content of the estimated
intergenerational persistence. The theoretical analysis identifies a set of economic mech-
anisms determining the intercept and the slope of the intergenerational educational per-
sistence equation. In particular, the household-level returns to education in the parental
generation determine relative mobility as measured by the slope of the regression function
(called intergenerational regression coefficient ( IGRC, for short) in the literature). The
intercept which shows the expected schooling attainment of the children from the most
disadvantaged family background (fathers with no schooling) is determined by intergenera-
tional persistence in occupation, among other factors.11 A substantial literature shows that
Hukou restrictions affected intergenerational persistence in nonfarm occupations in rural
China (Wu and Treiman (2007)).
A credible empirical analysis of the role of occupational dualism in intergenerational
educational persistence needs to address two major challenges highlighted in the recent
literature: (i) truncation bias due to coresidency restrictions in surveys, and (ii) the role
of genetic correlations in the observed intergenerational persistence. Most of the available
household surveys, especially in developing countries, suffer from serious sample truncation
as household membership is defined in terms of coresidency.12 Recent evidence indicates
that the standard measures of relative mobility, such as IGRC, suffer from substantial
downward bias in coresident samples (Emran, Greene, and Shilpi (2018)). Our empirical
analysis focuses on the father-son linkage in education, and takes advantage of two excep-
tionally rich data sets: the rural sample from the China Family Panel Studies (2010) for
China and the Rural Economic and Demographic Survey (1999) for India. Both of these
surveys are unique in that they include all the children of the household head irrespective of
their residency status at the time of the survey.13 This is especially important in a compar-
ative study such as ours, because cross-country comparisons based on coresident samples
can lead to wrong conclusions (see Emran, Greene, and Shilpi (2018) on Bangladesh and
contrast, all of the papers on intergenerational educational mobility we are aware of use a linear-in-levels
estimating equation. This is partly motivated by the fact that, in many developing countries, 20-40 percent
of fathers have zero schooling. However, we are not aware of any published work on developing countries
that derives the estimating equation from a theoretical model.
11This deserves especial attention because the focus in much of the existing literature has been on the
slope-based measures of mobility such as the intergenerational regression coefficient (IGRC) and intergen-
erational correlation (IGC).
12For example, widely used surveys such as LSMS and DHS collect information only on the coresident
children.
13Although some surveys collect limited information on the non-resident parents of the household head
and spouse, we are aware of only a few surveys that include all children of the household head.
3
India).
A longstanding concern in the literature has been whether the observed correlations
are primarily mechanical, driven largely by genetic transmissions from parents to children
(see, for example, the discussion by Black and Devereux (2011)). We address this issue
in two ways. First, we develop a simple but plausible approach to check whether the
estimated intergenerational persistence could be due solely to genetic correlations. The
approach combines the recent evidence on intergenerational correlation in cognitive ability
from the behavioral genetics and economics literature with the Altonji, Elder, and Taber
(2005) biprobit sensitivity analysis (henceforth called augmented AET (AAET) analysis).
Second, the theoretical foundation for the empirical specification allows us to use economic
mechanisms as a test for the importance of parental economic choices.
The substantive conclusions of this paper can be summarized as follows. Intergenera-
tional educational mobility was substantially lower for sons in rural India compared to sons
in rural China for the cohorts that went to school in the 1970s-1990s. The point estimates
of intergenerational persistence are larger in nonfarm households in both countries. The
difference between farm and nonfarm households is statistically significant in rural India,
but not in rural China, and this conclusion applies to both the slope and the intercept of
the intergenerational educational persistence regression. The evidence suggests that while
parent’s education and nonfarm occupation were complementary in determining a son’s
education in rural India, they were separable in rural China.14 The long-term variance in
schooling was significantly higher for the sons born into nonfarm households in rural India,
and structural change from agriculture to the nonfarm sector contributed to educational
inequality. The evidence from the augmented AET sensitivity analysis shows that the
observed persistence in rural India cannot be accounted for by genetic correlation alone,
while the persistence in China can be explained away by an ability correlation of plausible
magnitude.15 An important advantage of this approach is that the conclusions refer to the
whole population of interest, rather than a subset as usually is the case with other standard
approaches such as instrumental variables strategies.
14It is important to recognize that separability in rural China does not imply that nonfarm income did
not play any role in rural income inequality; in fact, we cite a substantial literature to the contrary. The
evidence in this paper suggests that intergenerational educational linkage is unlikely to be an important
mechanism through which the nonfarm sector influenced the observed inequality in rural China in the
1980s and 1990s.
15This evidence on rural China is similar to the recent analysis on urban China based on a sample of
monozygotic twins by Behrman et al. (2020). They find that the estimated impact of father’s education
can be explained fully by genetic correlations and unobserved family endowments.
4
Under the null hypothesis that the observed persistence is due solely to genetics, the
economic mechanisms identified in the theory are unlikely to provide a coherent explanation
of the pattern of mobility across countries. We use household income data from Chinese
Household Income Project (CHIP 2002, CHIP 1995) and National Sample Survey (NSS
1993) of India to explore the mechanisms behind the pattern of relative mobility (the
IGRCs) across farm and nonfarm households. The evidence suggests an important role
for the economic forces (returns to education and occupational persistence) in explaining
the pattern of educational persistence across farm and nonfarm households, both in rural
India and rural China. The theory also suggests that we should observe changes in the
intergenerational educational persistence in rural China for the younger generation because
of the effects of reform on the relevant mechanisms such as higher returns to education in
nonfarm occupations. In contrast to the separability observed for the older cohorts, we
indeed find evidence of emerging complementarity between father’s education and nonfarm
occupation in rural China for the educational attainment of the younger generation (18-28
years old in 2010).
The rest of the paper is organized as follows. Section 2 develops a model of intergen-
erational persistence with credit constraint that incorporates the salient features of farm
vs. nonfarm households relevant for educational attainment. The next section describes
the estimating equations derived from the theory and the empirical issues in understanding
potential complementarity between parent’s education and nonfarm occupation in deter-
mining children’s schooling. Section 4 discusses the data and section 5 reports the main
empirical estimates. The following section explores the evidence on the mechanisms identi-
fied by the theory underlying the observed pattern of slope (IGRC) and intercept estimates
for the cohorts who went to school in the 1990s or earlier. Section 7 provides evidence
on possible changes in the pattern of educational mobility in rural China for the younger
generation (18-28 years old in 2010). The paper concludes with a summary of the main
results from the theoretical and empirical analysis.
(2) A theory of Intergenerational Educational Persistence in a Dualistic Ru-
ral Economy
We develop an extension of the Becker-Tomes model with credit constraint (Becker
and Tomes (1986)) to understand the role played by nonfarm occupations of parents in
intergenerational educational mobility of children in a rural economy. The differences in
expected returns to education in farm vs. nonfarm households are expected to play an
5
important role. Expected returns to education in our context depends on two factors:
the probability of getting a non-farm employment, and the difference between returns to
education in farm vs. nonfarm occupations. The goal in this section is to derive an
estimating equation that incorporates these differences in farm and nonfarm households.
The Basic Set-up
The economy consists of households with a father and a son. We couch the discussion in
terms of father and son given that our empirical analysis focuses on the father-son linkages
in schooling attainment. The father of child iis described by a pair SP
i, Op
iwhere Sp
i
is the education (years of schooling) and Op
i∈ {f, n}with fdenoting farming occupation
and ndenoting nonfarm occupation of the father. Given his education and occupation, the
father’s income is determined as follows:16
Yp
i=Ypj
0+Rpj Sp
i;j=f, n (1)
The income determination equation assumes that the fathers with zero years of schooling
working in occupation jearns Ypj
0>0, and the returns to education in occupation jis Rpj
for the parental generation. The assumption that Ypj
0>0 is motivated by our empirical
context where a substantial proportion fathers has zero years of schooling, but positive
household income. It is important to underscore that the focus is on how a household’s
ability to invest in education changes with the education of the father. The “returns to
education” relevant here thus relate to permanent household income, not an individual’s
labor market earnings in a given year which has been the focus of much of the literature on
the Mincerian returns to education.17 In general, the intercepts are likely to be different,
but whether Ypn
0is larger or smaller than Ypf
0will depend on the quality of the nonfarm
activities at low education level (Sp
i= 0) which is likely to vary across countries. If low-end
nonfarm activities have low-productivity, then it is possible that Ypn
0< Y pf
0.
The father allocates Yp
ito own consumption Cp
iand investment in child’s education Ii;
thus the budget constraint is
Yp
i=Cp
i+Ii(2)
The educational investment is made from a father’s own income, as there is little or no
16This specification is similar to that in Solon (2004) and Becker et al. (2015).
17This point may be especially important in rural China during 1980s and early 1990s when the labor
market was still not functioning very well, and the labor market earnings would be a poor measure of a
household’s economic status.
6
financing available from the credit market for such investments in developing countries.
The education production function for the child is as follows:
Sc
i=F(Ii) = θ0+θ1ϕi+θ2Ii(3)
The a priori sign restrictions are: θ0≥0, θ1, θ2>0. We would expect θ0to be higher
when government policies such as free primary schooling (including free books and midday
meals etc) are in place so that a child can get a certain level of education, for example,
primary schooling without any significant investment by the parents. ϕiis the ability of
child iand a higher ability produces more schooling, ceteris paribus. We normalize the
ability measure such that E(ϕi) = 0.
The productivity of parental financial investment is represented by the parameter θ2
which captures, among other things, the quality of schools available (and affordable) to a
family. For example, there is evidence that children have better learning outcomes in rural
India when they attend private schools (Kingdon (2017)). The parents need to pay fees for
private school while the public schools do not charge any fees, but the quality of schooling
is, in general, low in the public schools. The productivity of financial investment is likely
to be higher when the private education market is well-developed and parents can buy
better quality by paying higher tuition and/or donations for admission. In contrast, when
schooling is primarily provided by the government free of charge (including free books and
midday meals) and the private market is thin or nonexistent, the role played by parent’s
investment in children’s education is expected to be rather limited, making θ2small.18 Note
that the access to better quality schools does not depend on a parent’s occupation in the
formulation in equation (3) (i.e., θis not indexed by j).
Parent’s Optimization
The consumption sub-utility function of the parent is given by:
U(Cp) = α1Cp−α2(Cp)2(4)
Denote the expected income of a child iwith education Sc
iat the time of the parental
investment choice by E(Yc
i|Sc
i). The parent’s optimization problem is (denoting the
18However, the “free schooling” offered by the governments may not be free, especially for the poor
households, because of corruption when the enforcement system is not unbiased and impersonal. Emran,
Islam, and Shilpi (forthcoming) show that, in Bangladesh, the poor parents are more likely to pay bribes
for admission into “free” public schools.
7
Lagrange multiplier on the budget constraint by λ):
MaxCp,I Vp=U(Cp) + σE (Yc
i|Sc
i) + λ[Yp
i−Cp
i−Ii] (5)
subject to (1) and (3). In this formulation, the parameter σis the degree of parental
altruism. The expected income of the child E(Yc
i|Sc
i) depends on the probability of
getting a nonfarm job, and is given as follows:
E(Yc
i|Sc
i) = πnj
iRcn +1−πnj
iRcf Sc
i(6)
where πnj
i≥0 is the probability that child igets a nonfarm job when the father is employed
in occupation j=n, f . To simplify notation, we write πn
i(Op
i=j)≡πnj
i;j=n, f. If there
is intergenerational persistence in non-farm occupations then the probability that a child
gets a nonfarm job is higher when the parent is also in the nonfarm occupations, i.e.
πnn
i> πnf
i. This may reflect learning by doing at parent’s workplace through informal
apprenticeship, referral and network effects in the labor market, and role model effects (for
a discussion, see Emran and Shilpi (2011)). Government policies also affect the strength
of occupational persistence. As noted earlier, a major policy difference between rural
India and rural China during our study period is the restrictions on rural-urban migration
in China. These restrictions implied that many more children had to stay back in the
rural areas in China compared to the counterfactual of no such restrictions (the India
case). A substantial literature on occupational mobility in rural China shows that the
Hukou restrictions reduced the persistence in non-farm occupations, as many children of
the nonfarm parents had to take up farming activities because they could not migrate to
the urban labor market. This implies that we should expect πnn
i(India)> πnn
i(China).
The first order conditions for parent’s optimization are:
α1−2α2Cp−λ= 0
σθ2πnj
iRcn +1−πnj
iRcf −λ= 0 (7)
The first order conditions and the budget constraint together yield the following solution
for the optimal investment in a son’s education:
I∗
i=χj
0+Rpj Sp
i(8)
8
where
χj
0=Ypj
0+1
2α2σθ2πnj
iRcn +1−πnj
iRcf −α1(9)
Intergenerational Persistence Equation
Combining equations (3) and (8) above, we get the following relationship between the
education of the father and that of a son, determined by the optimal investment decision:
Scj∗
i=ψj
0+ψj
1Sp
i+ ˜εi(10)
where
ψj
0i=θ0+θ2χj
0
ψj
1=θ2Rpj ; ˜εi=θ1ϕi
(11)
Equation (10) is consistent with the almost universally used specification for inter-
generational schooling persistence in the literature, but it allows for possible differences
in educational opportunities across the farm and nonfarm households. Some examples of
studies that use this linear-in-levels specification are: Neidhofer et al. (2018), Narayan et
al. (2018) and Hertz et al. (2007) on cross-country analysis, Azam and Bhatt (2015) and
Emran and Shilpi (2015) on India, and Emran and Sun (2015a) on China. However, we are
not aware of any studies on intergenerational educational mobility in developing countries
that derive the estimating equation from a theoretical model.
It is standard to assume homothetic functional forms in the analysis of intergenera-
tional income mobility, as the estimating equation is log-linear (see, for example, Solon
(1999, 2004)). The reliance on the linear in levels (years of schooling) specification in the
literature on intergenerational educational persistence partly reflects the fact that a sub-
stantial proportion of fathers have no schooling. This is especially relevant in the rural areas
of developing countries such as India where about 40 percent of fathers have no schooling
(estimate based on REDS 1999 data). The estimating equation (10) is also consistent with
the common assumption in the literature that the omitted ability is captured in the error
term of the intergenerational persistence regression, and can lead to ability bias in the OLS
estimates of the parameters.19
An important implication of equation (10) is that both the slope and the intercept of
19Although most of the existing studies on intergenerational mobility adopt this additively separable
specification for the impact of ability, there is little evidence on the validity of this assumption. In a recent
paper, Ahsan et al. (2020) use measures of ability based on Raven’s test and two memory tests in Indonesia
and find evidence in favor of this assumption.
9
the persistence equation capture the differences in educational opportunities faced by the
children in farm vs. nonfarm households, although the existing literature focuses largely on
the slope (IGRC).20 An interpretation of the intercept term in our context is that it provides
an estimate of the expected education of the children from the subset of households where
the fathers have zero schooling. Thus, the intercept estimate may be especially important in
developing countries where a significant proportion of the households have parents with zero
schooling in the data. In the empirical analysis, we thus pay close attention to the estimated
intercepts across farm and nonfarm households in addition to the standard relative mobility
measures based on slopes.
Equally important, equations (10) and (11) help improve our understanding of the eco-
nomic mechanisms behind the observed pattern of mobility. For example, consider the
factors that determine the intercepts across farm and nonfarm households. The intercept
is, ceteris paribus, higher (lower) for the nonfarm children when the income of the parents
with zero schooling is higher (lower) in the nonfarm occupations. These nonfarm occupa-
tions are, however, likely to be unskilled as they do not require any schooling. In some
countries, the low-skilled nonfarm occupations may yield very low income, lower than the
income of the farmers (Lanjouw and Lanjouw (2001), World Bank (2011)), making the in-
tercept for the nonfarm households smaller. Another important implication, noted before,
is that intergenerational persistence in occupational choices is likely to affect the relative
magnitudes of the intercept terms. When ˆπnn
i>ˆπnf
i, it is more likely to have ˆ
ψn
0>ˆ
ψf
0,
ceteris paribus, assuming that Rcn > Rcf . Conversely, if ˆπnn
i>ˆπnf
ibut Rcn < Rcf , then
it is more likely to have ˆ
ψn
0<ˆ
ψf
0,ceteris paribus. This implies that the evidence on in-
tergenerational occupational persistence (farm vs. nonfarm) accumulated independently in
a sub-strand of the literature is necessary to understand the pattern of intergenerational
educational mobility in a rural economy. As emphasized by Emran and Shilpi (2019), the
interactions between occupational and educational mobility are not considered in the ex-
isting literature on developing countries; there are two sub-strands of the literature that
grew independently: one focusing solely on education and the other focusing solely on
occupation.
The relative magnitudes of the slope parameters (IGRC) across farm and nonfarm
20For example, none of the 13 studies on educational mobility in developing countries summarized in
Emran, Greene, and Shilpi (2018) report estimates of intercepts. Some of the more recent works report
measures of absolute mobility that combines both the slope and the intercept effects (following Chetty et
al. (2014)), but do not report the intercept estimates separately.
10
households depend on the household returns to education in the parental generation (Rpj )
according to equation (11). Thus, Rpn > Rpf generates complementarity between parent’s
education and occupation in determining children’s schooling.21 This provides testable
implications to check the importance of economic forces in the observed differences in
relative mobility across farm and nonfarm households in China vs. India.22
(3) Empirical Approach
Equation (10) above suggests the following estimating equation for the combined farm
and nonfarm sample which we take as a benchmark:
Sc
i=ψ0+ψ1Sp
i+εi(12)
where εi= ˜ϵi+ηi=θ1ϕi+ηi, and ηicaptures exogenous idiosyncratic shocks to chil-
dren’s schooling. We normalize so that E(ηi) = 0.The corresponding estimating equation
allowing for different intercepts and slopes for the farm and nonfarm households is:
Sc
i=ψf
0+ψf
1Sp
i+λ0Dnp
i+λ1(Sp
i∗Dnp
i) + ΦXi+εi(13)
where Dnp
iis a dummy variable that takes on the value of 1 when the father of child i
is employed in nonfarm occupations, and zero otherwise. In this formulation, the measure
of relative mobility is IGRC: ψf
1for the farm households and ψf
1+λ1for the nonfarm
households; we denote ψf
1+λ1≡ψn
1. Similarly, the intercepts are given by ψf
0(farm) and
ψn
0≡ψf
0+λ0(nonfarm). Xiis a set of controls used in the regressions. Following the seminal
contribution of Solon (1992), it is standard in the literature on intergenerational income
mobility to include quadratic age controls for both the parents and the children. This helps
reduce the biases that arise from life-cycle effects in estimating permanent income.23 The
life-cycle bias is not likely to be a concern in our application, as we chose the age cut-off
to ensure that most of the children completed schooling by the time the survey was done.
21The analysis shows that different roles are played by the parental returns to education and the expected
returns to education in children’s generation, a point not adequately recognized in the current literature. It
is important to appreciate that the children’s expected returns to education at the time of the investment
decision do not affect the slope (IGRC), their effects are mediated only through the intercept of the
persistence regression.
22Returns to education are identified as a major factor in changes in intergenerational income persistence
(see Becker and Tomes (1979, 1986), Solon (1999, 2004)).
23When data on many years spanning the appropriate phases of life-cycle are available, the age controls
are not necessary. Some recent contributions do not include any age controls, as it may wipe out the
inter-cohort differences in income mobility.
11
Our main estimates thus do not include any age controls; but, as a robustness check, we
report estimates including age controls.
It is important to appreciate that a comparison of farming and nonfarming households
based solely on the most widely used measure of mobility, i.e., IGRC (ψf
1and ψn
1), may be
misleading. The caveat that IGRC or other measures of relative mobility such as intergener-
ational correlation (IGC) may be misleading in comparing mobility across groups has been
emphasized by Hertz (2005), Mazumder (2014) and Bhattacharya and Majumder (2011)
in their analysis of racial (black-white) differences in intergenerational income mobility in
United States of America. But it has not been adequately appreciated in the literature on
intergenerational educational mobility, both in economics and sociology.24 This is especially
so in developing countries, as is evident from the fact that most of the available studies on
China and India we are aware of focus exclusively on relative mobility measures such as
IGRC, IGC (intergenerational correlation) and IRC (intergenerational rank correlation).
To see the pitfalls in relying on IGRC alone in our context, it is instructive to con-
sider the case where ψn
1> ψf
1so that intergenerational persistence is higher in nonfarm
households. However, whether this higher persistence leads to convergence or divergence
in schooling attainment of children born into farm and nonfarm households depends on
the relative magnitudes of the intercepts. When the intercepts are ψn
0> ψf
0, the expected
schooling is higher for children born into nonfarm households across the distribution of
parental schooling, and the gap between the two groups widens as parental education in-
creases (please see figure 1). On the other hand, we can have two sub-cases when the
intercepts are: ψn
0< ψf
0(please see figure 2). If the IGRC for the nonfarm group is high
enough, the children born to lower educated nonfarm households are disadvantaged com-
pared to the children of low-educated farmer parents, but at the higher end of parental
education distribution they are relatively advantaged (see nonfarm(a) line in figure 2).
When the difference between IGRC estimates is small enough, the farmer’s children are
better off in educational attainment over the entire distribution, and only in this special
case, the conclusion based on IGRC that nonfarm children face lower relative mobility is
consistent with the idea that they are at a disadvantage in educational attainment (please
see the nonfarm(b) line in figure 2).
Rank-Based Measures of Intergenerational Mobility
While most of the existing studies on intergenerational educational mobility in de-
24See the discussion on this point by Torche (2015) in the context of Sociological literature on mobility.
12
veloping countries rely on years of schooling as the indicator of educational attainment,
following the influential contribution of Chetty et al. (2014), the recent literature is in-
creasingly adopting the rank-based measures where the indicator of educational status is
the percentile rank in the relevant distribution. A growing literature suggests that the rank-
based measures of mobility are significantly more robust to data limitations compared to
the measures based on years of schooling.25
Denote rc
ias the percentile rank of child iin the over-all (including both farm and
nonfarm) schooling distribution of children, and rp
ithe percentile rank of the father of iin
the over-all schooling distribution in fathers generation. For the rank-based estimates, the
estimating equations are as follows:
rc
i=δ0+δ1rp
i+ξi∀i(14)
rc
i=δf
0+δf
1rp
i+λ2Dnp
i+λ3(rp
i∗Dnp
i) + ξi(15)
The slope parameters of regression equations (14)- (15) represent intergenerational rank
correlation (IRC, for short) which is a measure of relative mobility similar to IGRC. The
IRCs are given by δf
1(farm) and δn
1≡δf
1+λ3(nonfarm). Similar relations hold for the
intercepts. However, there are important differences between IGRC and IRC as measures
of mobility. While the IGRC estimates reflect the effects of changing marginal distributions
across generations, the IRC provides a measure of fundamental dependence between the
schooling of father and son largely unaffected by the changes in the marginal distributions.
However, the interpretation of rank correlation (IRC) in education (a discrete variable) is
somewhat different than that of income (a continuous random variable). With continuous
variables, Spearman rank correlation is a copula, completely unaffected by the changes
in the marginal distributions. In contrast, rank correlation in discrete variables such as
education is not completely immune to changes in the marginal distributions (see the
discussion in Neslehova (2007)).
25Nybom and Stuhler (2017) find that rank-based measures are much less affected by attenuation bias
due to measurement error in income, and Emran and Shilpi (2018) show that the truncation bias due
to coresidency restrictions in surveys is significantly lower in rank-based measures compared to the most
widely used measure IGRC in the context of educational persistence. For a more in-depth discussion on
these issues, see Emran and Shilpi (2019).
13
Interaction between Parent’s Education and Occupation: Complementary,
Substitutes or Separable?
An important advantage of the empirical models discussed above is that they provide
a straight-forward way to test the nature of interaction between parent’s occupation and
education in determining intergenerational persistence in schooling. Consider, for example,
the estimating equation (13) above; from the theoretical analysis in section (2), it is easy to
derive the conditions under which parental education and non-farm occupation can be com-
plementary, i.e., λ1>0 implyingψn
1> ψf
1, substitutes, i.e., λ1<0 implying ψn
1< ψf
1,
or separable, i.e., λ1= 0 implying ψn
1=ψf
1. The prevailing view among many observers
is that nonfarm occupation and education are likely to be complementary in determining
children’s education, leading to cumulative forces of inequality in educational attainment
and income in villages in developing countries (see, for example, Rama et al. (2015)). Yet,
to the best of our knowledge, there is no evidence in the literature on the existence and the
nature of the interaction between parent’s education and occupation in determining chil-
dren’s educational attainment. Also, without a formal model, the economic mechanisms
behind the hypothesized complementarity cannot be assessed. According to the theoreti-
cal model above, such complementarity requires that returns to education for the parents
is higher in non-farm occupations, i.e., Rpn > Rpf .26 This is one of the predictions that
we take to the data as a test of the importance of economic mechanisms underlying the
observed pattern of intergenerational educational persistence.
(4) Data
For our main empirical analysis, we use two exceptionally rich surveys that collected
data on children irrespective of their residency status at the time of the survey. The data
for rural India come from the Rural Economic and Demographic Survey (REDS) carried
out by the National Council for Applied Economic Research, and the source of the data
for rural China is the China Family Panel Studies (CFPS) implemented by the Institute of
Social Science Survey unit of Peking University.27
26If private school locations are motivated by higher income associated with nonfarm activities, then
school quality may also play a role in generating complementarity. In this case, the productivity of parental
investment θ2will be correlated with occupation, i.e., θn
2> θf
2.
27One might wonder why we chose not to use the IHDS 2012 round survey for India which would provide
a survey year close to the survey year of CFPS in China. The CFPS and REDS are the most comparable
in that they provide a random sample of parents with information on all their children irrespective of the
residency status of a child at the time of the survey. The IHDS, in contrast, contains a random sample of
children with information on their parents irrespective of their residency status at the time of the survey.
14
This is an important advantage for the empirical analysis, as most of the evidence on
intergenerational educational mobility in India and China currently available are based on
data that suffer from truncation due to coresidency restrictions used to define household
membership. Emran, Greene, and Shilpi (2018) summarize 13 studies on intergenerational
educational mobility in developing countries, only two of which use data not affected by
coresidency bias.28 While Emran, Greene and Shilpi (2018) provide evidence of substantial
downward bias (average 18 percent) in the IGRC estimate from the coresident sample in
rural India, we are not aware of any similar estimate for rural China. In online appendix
A, we provide evidence on the extent of coresidency bias in rural China in a widely used
household survey: the Chinese Household Income Project (CHIP). In particular, we com-
pare the estimates from the CFPS (without any sample truncation) with those from the
CHIP 2002 for the overlapping age cohorts. The evidence shows that the IGRC estimate
from the CHIP 2002 is 25 percent smaller because of truncation of the sample arising from
coresidency restrictions (see Table A.2 in the online appendix). A comparison of CHIP
2002 with the CFPS is also of independent interest, because CHIP 1995 and 2002 have
been used by many researchers to study intergenerational mobility in China.29 For a more
complete discussion, please see online appendix A.
We use the 1999 round of the REDS and the first round of the CFPS in 2010. From
the REDS data, we obtain the relevant information for our analysis on all father-son pairs
irrespective of residency status at the time of the survey. For the CFPS data, we restrict to
rural communities subsample, given our focus on intergenerational mobility in rural areas,
and use the family roster to obtain a complete list of father-son pairs that includes all sons
of the household head irrespective of their residency status at the time of the survey.
The main samples for our analysis consist of children aged 18 - 54 in the 1999 REDS
survey, and 29 - 65 in the 2010 CFPS survey. This ensures that we focus on the same age
cohorts of children who went to school mostly during the 1980s and 1990s. It is important to
recognize that such an analysis for the overlapping age cohorts is meaningful for education,
as most of the children under focus (29-65 years old in 2010) in China have completed
their schooling by 1999, even though the information was gathered later in 2010. The
28The exceptions are Fan et al. (2019) and Azam and Bhatt (2015).
29Two of the authors of this paper, M. Shahe Emran and Yan Sun, used CHIP 2002 data to analyze
the effects of farm and nonfarm occupations on intergenerational educational mobility in rural China (see
Emran and Sun (2015b)). We decided not to publish that paper because of the worry about the biases
due to sample truncation arising from coresidency. This paper replaces Emran and Sun (2015b) and the
conclusions on rural China here supersede those in Emran and Sun (2015b).
15
observations with fathers aged over 100 years or missing, or sons aged over 65 years are
excluded from the samples used in the empirical analysis.
In each data set, we observe the education level and an indicator of whether the main
occupation is agriculture or nonfarm activity for both the father and the son. Our main
analysis of educational mobility is based on years of schooling as the measure of educational
attainment. Father’s schooling is used as the indicator of parental education to avoid
complications from many missing observations on mother’s schooling. In our data sets,
the maximum of parental education coincides with the education level of the father in
most of the cases. We define the parental occupation dummy Dnp
i= 0 when the father
of child ireports agriculture as the main occupation (corresponding to Op
i=fin the
theoretical model), Dnp
i= 1 otherwise. This means that the households who are primarily
engaged in farming with some nonagricultural sources of income are classified as agricultural
occupation.
Online appendix Table A.1 shows the descriptive statistics of our main data samples
from the REDS and the CFPS. In the REDS sample, we have 6887 observations, and the
children’s age is 29 years on average in the survey year 1999. Fathers are 60 on average.
About half of the children’s main occupation is agriculture, while 60% of the fathers also
reported agriculture as their main occupation. The children attain significantly higher
levels of education than the fathers, when comparing their average years of schooling (6.26
vs. 4.13.)
In CFPS sample, a similar pattern is observed. We have 3,305 father-son pairs, and
children’s age is about 40 years in the survey year, 2010 (29 years in 1999, same as that
for India in 1999 REDS data). Fathers are aged 68 years on average in 2010. About half
of the fathers work in the agricultural sector. Children receive 6.31 years of schooling on
average, significantly higher than their fathers (less than 3.81 years).
While our main empirical analysis is based on the CFPS 2010 and REDS 1999, we
take advantage of a number of additional data sets for exploring the economic mechanisms
identified by the theoretical analysis. To understand how the relation between father’s
education and household income varies by farm and nonfarm occupation in rural China we
utilize the data from the Chinese Household Income Project (CHIP) 1995 and 2002. To
estimate the relation between father’s education and household income in rural India, we
use the data on household total expenditure from the National Sample Survey 1993.
16
(5) Empirical Results
(5.1) Evidence on Relative Mobility and Test of Complementarity
Table 1 reports the estimates of relative mobility using two measures: intergenerational
regression coefficient (IGRC) and intergenerational rank correlation (IRC). In addition to
the separate estimates for the farm and nonfarm households, we report the estimates from
the combined farm and nonfarm sample as a benchmark.
The point estimates of IGRC show that, both in rural India and rural China, intergen-
erational persistence in schooling is higher for the sons born into nonfarm households, but
the estimates for farm and nonfarm households are similar in magnitude in China. A son
of a father with 1 year more schooling in India is expected to gain 0.49 year of schooling if
the father is a farmer, while the expected gain increases to 0.56 year of schooling when the
father is employed in nonfarm occupation (column 2 of Table 1). The corresponding esti-
mates for rural China are 0.31 year (farm) and 0.32 year (nonfarm) of additional schooling
for the sons born to a father with 1 year of more schooling (column 1 of Table 1). Another
important conclusion from the evidence in Table 1 is that all of the IGRC estimates in rural
China are smaller compared to the corresponding estimates in rural India, providing strong
evidence that the sons in rural China who went to school in the 1980s and 1990s enjoyed
substantially more relative mobility in schooling. The conclusions above remain valid when
we include age controls in the specifications (see Table A.3 in the online appendix ).30
The estimates of intergenerational rank correlation (IRC) reported in columns 3 and 4
of Table 1 also tell a similar story: the point estimates of the effect of father’s schooling
rank on the son’s schooling rank are higher for the nonfarm households, both in China and
India. Again, the effect of parental education does not vary substantially between farm
and nonfarm household in rural China, but there is substantial difference in rural India.
The magnitudes of the IRCs are consistently smaller in rural China compared to those in
India, reinforcing the conclusion from the IGRC estimates that the sons in rural India faced
lower educational mobility. These conclusions from the IRC estimates remain intact when
we include age controls in the specification (see Table A.4 in the online appendix).
The contrasting evidence in China vs. India suggests that father’s education and non-
farm occupation are likely to be complementary in India, but separable in China. We
formally test the null hypothesis of separability H0:ψf
1=ψn
1. The results are reported
30Since life-cycle bias is not likely to be a major issue in our context, our preferred estimates are from
the specification without age controls.
17
in the lower panel of Table 1, with standard errors clustered at the primary sampling unit
(village in REDS data, and county in CFPS data). The evidence from both IGRC and
IRC estimates shows that, in rural China, the null hypothesis of separability cannot be
rejected at the 10 percent significance level; the F statistic for IGRC estimates is 0.014
with a P-value of 0.90, and the corresponding numbers for IRC are 0.13 (F statistic) and
0.72 (P-value). In contrast, in rural India, the null hypothesis of separability is rejected
at the 10 percent level for IGRC (F=3.80, P-value=0.052), and at the 5 percent level for
IRC (F=6.42, P-value=0.012). Since the estimated effect of parental schooling is larger
in the nonfarm households in rural India, the evidence suggests complementarity between
nonfarm occupation and father’s education in determining a son’s schooling.
Relative Mobility and Long-Term Variance in Schooling
When interpreted as a dynastic model of the evolution of schooling across generations,
a higher IGRC implies a higher long-term variance in schooling.31 To see this, note that
for the IGRC equation (12), we can write the long-term variance of education as:
σ2
s=1
(1 −ψ2
1)σ2
ε(16)
where σ2
sis the long-term variance of education and σ2
εis the long-term variance of
the error term capturing all other factors unrelated to father’s schooling such as market
luck, and macro and trade shocks. 1
(1 −ψ2
1)is called the ‘family background multiplier’
by Emran and Shilpi (2019), which amplifies the impact of the shocks to education. Using
equation (16) and the estimates of ψf
1and ψn
1reported in Table 1, we have the following
estimates for sons in farm and nonfarm households in rural India:
σ2
s,If = 1.31σ2
ε(farm)
σ2
s,In = 1.45σ2
ε(nonfarm)
The subscripts Iand sdenote India and schooling, respectively, and as before, n=nonfarm
and f=farm. The long-term variance of education of sons in the farming sample is 31 per-
cent higher than the variance due to idiosyncratic factors alone (i.e., σ2
ε), and is 45 percent
higher in the nonfarm sample. Thus the contribution of family factors to the long-term
variance is 14 percentage points higher in the nonfarm households.
31For a discussion on the dynastic interpretation of the model and the implications for long-term variance,
see Acemoglu and Autor (undated).
18
The long-term variances in schooling for the farm and nonfarm households in China
are:
σ2
s,cf = 1.107σ2
ε(farm)
σ2
s,cn = 1.111σ2
ε(nonfarm)
The multiplier effect of family background is much smaller in the case of China; the long-
term variance in schooling is only about 10 percent higher than the variance of idiosyncratic
shocks, and the estimates are virtually identical across the farm and nonfarm samples.
(5.2) Intercepts and Steady States
As noted earlier, measures of relative mobility give us an incomplete, and sometimes
misleading, picture of intergenerational mobility across groups such as farm and nonfarm
households. A simple but important reason is that different groups may be converging
to different steady states due to different intercepts in the intergenerational persistence
equations. Perhaps more importantly, the theory in section (2) suggests that factors such
as persistence in occupation choices, and expected returns to investment in schooling for
children work through the intercept, leaving relative mobility as measured by IGRC and
IRC largely unaffected.
The estimated intercepts of equations (12)-(13) and (14)-(15) above are reported in
Table 2. The point estimates show that the intercept of the IGRC equation in India is
significantly higher for the farm households (p-value 0.013). The evidence for the intercept
of the IRC equation is similar (p-value 0.006). When considered along with the evidence
that the slope estimates (IGRC and IRC) are smaller for the farm households in India,
the evidence implies a set of interesting conclusions. First, whether the sons born to
fathers in farm or nonfarm occupation enjoy educational advantage depends on the level
of their fathers’ education with a switching threshold of 9-10 years of schooling. Please
see figure 3. An interpretation of the evidence is that the national public examination
administered at 10th grade (known as Matriculation examination, or all India Secondary
School Examination (SSC)) represents a bifurcation point. The children of non-farm fathers
with Matriculation or more schooling are expected to achieve better schooling attainment
when compared to the children of farmer fathers with similar educational credential, but the
children of nonfarm fathers with lower education (and probably unskilled nonfarm jobs) are
likely to be worse-off when compared to the children of low educated farmer fathers (who
likely own land). Second, the steady state level of education is not substantially different
across farm and nonfarm households: 10.81 years of schooling (farm) and 11.20 years of
19
schooling (nonfarm). This reflects the fact that the sons born into nonfarm households gain
more from the higher schooling of a father, although they start from a lower intercept.
The picture for rural China is different (please see figure 4). The evidence in Table
2 shows that there is no statistically significant difference across the farm and nonfarm
households in the intercepts of the intergenerational persistence regressions (p-values are
0.279 (IGRC intercept) and 0.43 (IRC intercept)). When combined with the evidence on
IGRC and IRC in Table 1, this implies that the schooling attainment of the sons in rural
China converges to virtually the same steady state (8.53 years of schooling) irrespective of
whether the father is a farmer or is engaged in a nonfarm occupation.32
(5.3) Structural Change and Cross-Sectional Schooling Inequality
To understand the implications of the higher variance in the nonfarm households in
India for the cross-sectional variance in rural schooling, it is important to consider the
structure of the rural economy (i.e., proportion of fathers employed in the nonfarm sector)
and both the within group and between groups variances. Denote the proportion of nonfarm
households by ω, then we can write the long-term variance as:
V ar (S) = ωσ2
s,n + (1 −ω)σ2
s,f +ω(1 −ω) (µf−µn)2(17)
where µnand µfare the long-term means (the steady state) of father’s education in farm
and nonfarm households, respectively. The effects of a marginal increase in the proportion
of nonfarm sector is given by:
dV ar(S)
dω =σ2
s,n −σ2
s,f + (1 −2ω) (µf−µn)2(18)
As discussed in sections (5.1) and (5.2) above, there are no significant differences in the
long-term means or long-term variances across the farm and nonfarm households in rural
China. This implies that both terms in equation (18) are zero, indicating that structural
change in favor of the non-farm sector during the decades of 1970s-1990s is unlikely to
contribute to the cross-sectional variance of schooling. As noted earlier, this, however, does
not imply that the nonfarm sector did not play any role in the increasing income inequality
in rural China during this period, only that the nonfarm sector’s effect is not mediated
through intergenerational educational persistence.
32The estimate of the steady state is based on the combined farm and nonfarm sample. Although they
are not statistically different, the point estimates differ numerically across farm and nonfarm subsamples.
20
In India, the evidence in section (5.1) shows that the long-term variance is substantially
higher in the nonfarm households because of a large family background multiplier. The
estimates of the long-term (steady state) means also show a higher mean for the nonfarm
households. When we plug in the estimates from sections (5.1) and (5.2) for rural India in
equation (18) above, we get (using ω= 0.40 from the summary statistics table in online
appendix):
dV ar(S)
dω |India = 0.078 + 0.13σ2
ε>0
Thus, the evidence suggests that structural change in favor of the nonfarm sector con-
tributed to higher cross-sectional variance in rural India during our study period.
(6) Economic Mechanisms: Towards an Explanation of the Differences be-
tween Rural China and Rural India
A major concern in the literature has been whether the observed pattern of intergen-
erational linkages is primarily driven by omitted variables bias due to unobserved genetic
correlations between parents and children. An obvious approach to this question is to try
to correct the estimates for possible positive bias due to genetic correlations in cognitive
ability. We develop a simple but plausible approach by taking advantage of the recent
evidence on intergenerational correlation in cognitive ability from economics and behav-
ioral genetics. There is substantial evidence that intergenerational correlation in cognitive
ability (denoted as ρ) falls in a narrow interval, ρ∈[0.20,0.40]; see, for example, Black
et al. (2009), Bjorklund et al. (2010) on economic literature, and Plomin and Spinath
(2004) on behavioral genetics literature. We use this information in a biprobit sensitivity
analysis as developed by Altonji et al. (2005) to check if the estimates of intergenerational
persistence in schooling remain positive and statistically significant for plausible values of
intergenerational correlation in ability. We call this approach augmented AET (AAET)
sensitivity analysis, and it requires binary indicators of educational attainment instead of
years of schooling. We use a dummy for higher than primary schooling for fathers. For
sons in rural China a dummy for higher than 9 years of schooling (higher middle school),
and for sons in rural India, a dummy for more than 10 years of schooling (called SSC or
matriculation) are used. The details of this approach are provided in online appendix B,
and the estimates are reported in Table 3.
The evidence from the AAET sensitivity analysis suggests that, the estimated intergen-
erational schooling persistence in India is very strong, and the estimates remain statistically
21
significant and numerically substantial even when we impose ρ= 0.40 in the biprobit model.
In contrast, the estimates turn negative in the case of rural China when ρ= 0.30, suggesting
that the observed positive effect of father’s education could be explained away by ability
correlation between parents and children.33 This evidence strengthens substantially the
conclusions that educational mobility was much lower in India in the 1970s-1990s, and that
economic forces are likely to be important in explaining the differences between India and
China. The advantage of this approach is that it is easily implementable, and thus could
be used fruitfully by other researchers. However, it is also important to appreciate the lim-
itations of such an a-theoretical approach. For example, the evidence that the persistence
in rural China could be explained by genetic correlations alone does not necessarily imply
that economic forces were not at play. The theoretical analysis in section (2) provides us a
way to explore the question by focusing on the economic mechanisms behind the pattern
of the slope and intercept estimates across farm and nonfarm households. We turn to this
exercise next.
Under the null hypothesis that genetic transmission is the main force at work, we should
not expect the economic mechanisms identified in the model to offer a consistent explanation
of the observed pattern of intergenerational persistence across India and China. If economic
forces are important, the theory provides us with testable implications even in the case of
rural China; the equality of the slopes (IGRCs) across the farm and nonfarm households
in this case implies equality of the returns to education for the farm and nonfarm parents.
(6.1) Differences in the IGRCs
The estimates of IGRC in Table 1 imply the following (denoting an estimate by a hat):
(China)ˆ
ψf
1=ˆ
ψn
1⇒θ2ˆ
Rpf =θ2ˆ
Rpn
(India)ˆ
ψf
1<ˆ
ψn
1⇒θ2ˆ
Rpf < θ2ˆ
Rpn
The theoretical analysis thus highlights the importance of household-level returns to school-
ing in the father’s generation (Rpj ) across occupations for understanding the pattern of
relative mobility. We have ˆ
ψf
1−ˆ
ψn
1=θ2ˆ
Rpf −ˆ
Rpn,and the effects of a widening gap
in returns to education for household income between farm and nonfarm households would
be low if θ2, the productivity of financial investment in children’s education, is low. We
would expect θ2to be low when the private market for education is not well-developed in a
33These conclusions remain robust when we define the schooling cut-off to be the same in the two
countries, and also when age controls are included in the specification. The details are available from the
authors.
22
country.34 Since the expansion of private schooling has been much larger in India compared
to that in China during the study period, the value of θ2is likely to be higher in India.
It is important to recognize that the “returns to education” for the parents (i.e., Rpj )
differ from most of the available estimates of returns to education for three reasons. First,
we are interested in the total income of all household members rather than the individual
income (i.e., not only father’s income). Second, the focus of the existing literature has been
on labor market returns, while our analysis requires both labor and non-labor income.
Third, father’s education in our analysis is not only a measure of human capital, but a
summary statistic for a family’s socio-economic status and captures the effects of other
correlated factors, for example, mother’s education due to assortative matching in the
marriage market.35 Thus, we need a measure of permanent household income.
The Chinese Household Income Project (CHIP) provides us with high quality household
income data for rural households for multiple years (5 years in CHIP 2002, and 3 years in
CHIP 1995).36 Unlike China, the data on household income in rural India are, however,
more limited; we are not aware of any household survey data set that has good quality
income information for consecutive multiple years, similar to the CHIP data on China. We
thus take household expenditure reported in the National Sample Survey as our measure
of household permanent income.
Table 4 (panel A) provides estimates of household-level returns to education, Rpn and
Rpf , in rural China and tests the null hypothesis that Rpn =Rpf using data from two
rounds (1995 and 2002) of the Chinese Household Income Project (CHIP) survey. The
standard errors are clustered at the primary sampling unit (county). The estimates based
on the 5-year average income of a household in CHIP 2002 data in the last two columns
of Table 4 show that the null hypothesis cannot be rejected with a P-value equal to 0.58.37
The evidence from the 1995 data (three year average income) also delivers a similar conclu-
sion: the null hypothesis cannot be rejected with a P-value of 0.33.38 The conclusion that
34To see this clearly, consider the polar case where schooling is provided only by the government free of
charge and there is no private schools (or private tutoring). In this case, the scope for parental financial
investment to improve a child’s educational attainment is effectively nonexistent, making θ2≈0.
35The available estimates on Mincerian labor market returns to education at the individual level in China
show low returns in the early years after the reform, but there is evidence of increasing returns in the later
years, as one would expect with the deepening of the labor market. The evidence also suggests higher labor
market returns in nonfarm occupations (DeBrauw and Rozelle (2008)).
36Note that the estimates of the effects of father’s education on household permanent income using CHIP
data do not suffer from truncation bias, unlike the estimates of intergenerational persistence; whether some
of the children were nonresident at the time of the survey is not relevant for this analysis.
37The 5 year income data cover from 1998 to 2002 in the CHIP 2002.
38The 3 years income data in CHIP 1995 cover 1991, 1993, and 1995.
23
returns to education measured in permanent household income do not differ significantly
across farm and nonfarm households in rural China during the study period is robust to
inclusion of number of children in the household as a control (see online appendix Table
A.5). The evidence on returns to education when put together with the evidence on comple-
mentarity discussed earlier in Table 1 provide a theoretically consistent explanation: a lack
of difference in returns to education across farm and non-farm occupations leads to sepa-
rability between father’s education and nonfarm occupation in determining son’s schooling
in rural China.
Also, the magnitude of θ2is likely to be low in rural China during the relevant period
(the children who went to school during 1970s-1990s) which would reduce the impact of
any emerging advantage in favor of nonfarm households in returns to education. Recall
that θ2is the efficiency of parental investment, determined primarily by the supply side
of the education market such as availability of high-quality private schools. In China, the
availability of private schools was limited; in 1996, only 4 percent of the schools in China
were private (Kwong (1996)). Most of the private schools in rural areas in the 1990s were
primary schools with limited facilities and equipment, and they catered to children from
the low-income households. At the secondary level, the private schools primarily met the
demand by the students who were unsuccessful in the admission test given after grade
9 to screen for the senior secondary public schools (Lin (1999)). This implies that, in
contrast to many other countries, any quality advantage in education in rural China is
associated with better quality public schools. While local financing and various types of
fees increasingly played a role in public schools after the fiscal decentralization, it is unlikely
to create a significant impact on the magnitude of θ2for the following reason: the share of
private expenditure remained small compared to the public expenditure during the 1980s
and 1990s; for example, tuition and other fees paid by the parents amount to only 4.42
percent of total educational expenditure in 1991 and 10.72 percent in 1995 (see Table 7.2
in Hannum et al. (2008)).
Rural India
For the estimates of IGRCs across farm and nonfarm households in India to be consistent
with the extended Becker-Tomes model of section (2), the returns to schooling in nonfarm
households need to be higher than that in the farming households in the parental generation.
Table 4 (panel B) reports the estimates of household-level returns to education in rural
India using household expenditure data from the NSS 1993 survey (the employment and
24
unemployment round). The returns to education are, in fact, higher in nonfarm occupations
and the difference is significant at the 5 percent level (P-value= 0.02). The conclusion that
returns to education at the household level are higher for the nonfarm activities is robust;
for example, the null hypothesis of equality is rejected with a P-value=0.002 when we
control for number of children in the household (see the online appendix Table A.5).
The available evidence also suggests that the magnitude of θ2is likely to be much higher
in rural India when compared to that in rural China. A higher value of θ2would act as a
multiplier for higher returns to schooling in nonfarm activities for the parents, and amplify
the difference between farm and nonfarm slopes (IGRCs). This can lead to the complemen-
tarity we found earlier in Table 1 above. In India, private schools have historically been
more important than in rural China, and they have become more important over time,
especially after the liberalization in 1991. Muralidharan and Kremer (2008) report that,
in 2003, 28 percent of rural households had access to fee-charging private schools. They
also provide evidence that private schools are more likely to be established in places where
public school quality is low, and the students in private schools perform better academi-
cally.39 Thus, the relative quality of private and public schools in rural India is opposite
to that in rural China. This suggests that the higher income (and better educated) house-
holds can take advantage of the high-quality private schools making θ2higher. Since the
private schools are more likely to locate in villages where the public school quality is low,
the differential effects of school quality are likely to be strong in rural India, as the better
educated nonfarm parents with high income send children to private schools, and the other
children (including the children of low-educated and low-skilled nonfarm parents) go to low
quality public schools.
(6.2) Differences in the Intercepts
According to the theory, the estimated intercepts in Table 2 discussed above imply the
following relations (using a hat to denote an estimate):
(China)ˆ
ψf
0≈ˆ
ψn
0=⇒Ypf
0+1
2α2σθ2ERI cf −α1≈Ypn
0+1
2α2
[σθ2E(RI cn )−α1]
(India)ˆ
ψf
0>ˆ
ψn
0=⇒Ypf
0+1
2α2σθ2ERI cf −α1> Y pn
0+1
2α2
[σθ2E(RI cn )−α1]
(19)
39Private schools have more teachers with college degree and teacher absenteeism is less of a problem
compared to the public schools. Azam et al. (2016) find that the students in private secondary schools
in rural Rajasthan scored about 1.3 standard deviation (SD) higher than their counterparts in the public
schools in a comprehensive standardized math test.
25
where E(RIcj ) = πnj
iRcn +1−πnj
iRcf is the expected return to financial investment
in son’s education when the father is employed in occupation j=n, f.
Rural China
The following observations are important for understanding the role played by occupa-
tional persistence in educational mobility in rural China. First, when πnn
i≃πnf
i, we have
E(RIcn)≃ERI cf , irrespective of whether Rcn > Rcf or Rcn ≤Rcf . Since expected
returns to education for the children do not vary significantly across farm and nonfarm
households in this case, we would expect parental investment in education and thus edu-
cational mobility to be similar also. The second observation is that when there is low or
no intergenerational persistence in nonfarm (or farm) occupations, we have πnn
i≃πnf
i.
A substantial body of independent evidence, in fact, suggests that, for the relevant
cohorts, there was no significant intergenerational persistence in nonfarm occupation choices
(πnn
i≃πnf
i) in rural China. Wu and Treiman (2007) use the 1996 national probability
sample of Chinese men and show that there is high degree of mobility into agriculture;
the sons of nonfarm parents also face a substantial probability of becoming a farmer.
They identify the geographic restrictions on mobility of rural people because of the Hukou
registration system as the primary factor behind this weak intergenerational persistence in
nonfarm occupations.40 Using CHIP 2002 data, Emran and Sun (2015) report evidence
supporting Wu and Treiman (2007) finding.
The evidence that E(RIcn) = ERI cf , along with equation (19), above implies that
a sufficient condition for the equality of the intercepts of the intergenerational persistence
equations is that Ypn
0=Ypf
0, i.e., the intercepts of the returns to education function in
parent’s generation are the same across farm and nonfarm households. We would expect
Ypn
0=Ypf
0when the fathers with zero schooling have similar income (permanent income)
and face similar credit constraint, irrespective of their occupation.
The estimates in panel A of Table 4 show that the null hypothesis Ypn
0=Ypf
0cannot be
rejected at the 10 percent level with a p-value of 0.78 for the CHIP 2002 data on five-year
average income. The evidence from 1995 data is also similar (p-value is 0.81). Again, these
conclusions from CHIP 2002 and CHIP 1995 remain intact when we include number of
40The link between restrictions on geographic mobility of rural people and a lack of intergenerational
occupational persistence (farm/nonfarm) is, however, not unique to China, similar evidence is available on
Vietnam where the Ho Khau registration system has been in place since 1964; see the evidence and the
analysis in Emran and Shilpi (2011). This enhances the credibility of Wu and Treiman (2007) analysis that
the Hukou restrictions played an important role in the low occupational persistence in rural China.
26
children in the household as a control (please see online appendix Table A.5).
The evidence above is also consistent with other available studies on the nonfarm sector
and rural industries (TVEs) in rural China. The income gap between the farm and non-
farm households was mitigated in the early years of reform by two factors: the household
responsibility reform increased farmer’s income, and, in many cases, people employed on
the farm were paid wages similar to the wages paid to workers in the township village
enterprises (TVEs), the growing TVE sector in effect subsidizing the agricultural employ-
ment (Peng, 1998). This also reflects in part the lingering effects of policies during the
cultural revolution that were successful in eliminating any significant differences between
the peasants and non-peasants in rural China (Hannum et al. (2008)).
Rural India
In contrast to China, there were no restrictions on rural-urban migration in India dur-
ing the study period. A substantial body of independent evidence on occupational mobil-
ity in rural India suggests strong intergenerational persistence in farm/nonfarm occupa-
tions (Reddy (2015), Motiram and Singh (2012), Azam (2015), Hnatvoska et al. (2013)).
Hnatvoska et al. (2013) show that there is strong persistence in rural occupations both
in 1983 and 2004-2005; the son of a farmer is highly likely to be a farmer himself. Using
the IHDS (2005) survey, Motiram and Singh (2012) also provide similar evidence. The
fact that there was significant persistence in farm/nonfarm occupations implies that the
expected returns to investing in children’s education are likely to differ across farm and
nonfarm households. But whether the intercept in the nonfarm households would be higher
or lower depends partly on the expected relative returns to education in the children’s gen-
eration, i.e., whether Rcn > Rcf or Rcn < Rcf . It is, however, much more difficult to
estimate expected returns to education for children. One can argue that parent’s expecta-
tion would depend on their information set, a salient element in which is his own returns
to education. In other words, the evidence of higher returns to education in nonfarm in
the parental generation suggests that the parents would expect similarly higher returns for
children in nonfarm occupations. Note that even when Rcn > Rcf , the intercept for the
nonfarm households can be smaller as we find in the empirical analysis above (Table 2), if
the households with zero (or very low) parental schooling have sufficiently lower income in
nonfarm occupations, i.e., Ypn
0< Y pf
0.
The estimates of Ypn
0and Ypf
0, i.e., the intercepts of the income equation for parents,
using data from NSS 1993 round (employment and unemployment round), are reported
27
in panel B of Table 4. The estimated intercept is larger for the farm households and the
difference is statistically significant at the 10 percent level (standard errors clustered at the
PSU level). The evidence in favor of a larger intercept in the farm households is stronger
when we add controls to the regression; for example, the difference is significant at the 1
percent level when number of children is added to the specification (see online appendix
Table A.5). This conclusion is also supported by other available evidence on India; for
example, the All India Debt and Investment Survey 1991 (NSS 48th round) shows that
the assets of farming households (“cultivators”) are higher than those of the nonfarming
households (see P. ii, NSSO report No. 491, 1998).
The evidence in panel B of Table 4 also accords well with a substantial body of re-
lated evidence available on the nonfarm activities in India. Note that it is likely to have
Ypn
0< Y pf
0if the low-end nonfarm occupations are primarily low productivity residual ac-
tivities and provide the last resort for the poorest households. Lanjouw and Murgai (2011)
use three rounds of NSS data (1983, 1993/94, and 2004/2005) and show that nonfarm
employment is positively associated with rural poverty in India, consistent with the obser-
vation that nonfarm employment involves primarily low productivity economic activities
(see also World Bank (2011)).
This evidence on the intercepts of the income equation provides an explanation for the
higher intercept for farm households in the intergenerational mobility equation as discussed
earlier.
(7) Evolution of Mobility: Evidence on the Younger Generation in Rural
China
The rural economy and educational policies in China went through significant changes
in recent decades. The changes include gradual relaxation of Hukou restrictions, increasing
returns to education as the labor market matured, accelerated structural change in favor
of the nonfarm sector, and a more prominent role for private educational expenditure after
the fiscal decentralization (for an excellent discussion, see Fan et al. (2020)).41 There
is credible evidence that the economic changes have adversely affected intergenerational
mobility of the younger generation in China. Fan et al. (2020) find that intergenerational
income persistence has increased over time; they report an IGE estimate of 0.390 for the
41The share of tuition and miscellaneous fees in educational expenditure rose from 4.42 percent in 1991
to 18.59 percent in 2004 (Hannum et al. (2008). The spread of better quality public schools to the rural
areas has accelerated. All these changes would increase the magnitude of θ2in the extended Becker-Tomes
model for the younger generation.
28
1970-1980 birth cohorts, which increased to 0.442 for the 1981-1988 birth cohorts. The
extended Becker-Tomes model suggests that the pattern of educational persistence across
farm and nonfarm households should also change for the younger generation because of the
changes in the economic mechanisms.
To check if the pattern of educational mobility across farm and nonfarm households has
changed in the younger generation, we estimate the intergenerational educational mobility
equation for 18-28 years age cohorts who were excluded from our main estimation sample.42
The estimates are reported in Table 5, with the upper panel containing the results for years
of schooling, and the lower for rank-based estimates. There is, in fact, evidence of emerging
divergence between farm and nonfarm households in relative mobility as measured by IGRC
and IRC. For example, the IGRC estimate for the farm households has declined a bit from
0.31 (main sample) to 0.27 (younger sample), while the IGRC estimate has increased for the
nonfarm households from 0.316 (older) to 0.34 (younger). Similarly, the IRC estimate for
farm households declined from 0.331 (main sample) to 0.304 (younger sample), and it has
increased from 0.337 (main sample) to 0.373 (younger sample) for the nonfarm households.
The difference between farm and nonfarm households is significant at the 10 percent level
in the case of IRC estimates (P-value=0.097). While the difference in IGRC estimates is
not significant at the 10 percent level, the p-value in the younger sample is much smaller:
0.107 (younger sample) vs. 0.90 (main sample), providing evidence in favor of emerging
complementarity between father’s education and nonfarm occupation.
(8) Conclusions
This paper develops a model of intergenerational educational persistence in a rural
economy taking into account the role of parental farm vs. nonfarm occupations, and derives
a theoretically-grounded estimating equation which we take to the data from rural India
and rural China. We use two unique data sets that include the required information for all
the children of the household head irrespective of their residency status at the time of the
survey; thus eliminating the truncation bias common in the existing studies based on the
standard surveys that use coresidency criteria to define household membership.
The empirical analysis delivers the following conclusions for the sons who went to school
in the 1990s or earlier: (i) the intergenerational educational mobility in rural China was
significantly higher compared to that in rural India, (ii) the farm/nonfarm occupations
42Our main estimation sample consists of 29-65 age cohorts in 2010 to ensure that the sample of children
in China refers to the same age groups as in the data for India.
29
did not play any significant role in the intergenerational schooling linkage in rural China,
and this is true for both the intercept and the slope of the intergenerational persistence
regressions, (iii) both the slopes and intercepts were significantly different across farm and
nonfarm households in rural India. The estimates suggest that father’s education and non-
farm occupation were complementary in determining son’s schooling in rural India, but
separable in rural China. Structural change in favor of the nonfarm sector contributed
to higher educational inequality in rural India during the study period, in part due to
the complementarity. In contrast, such structural change was not an important factor in
schooling inequality in rural China. Evidence from an approach that combines the bipro-
bit sensitivity analysis of Altonji et al. (2005) with recent evidence on intergenerational
correlation in cognitive ability suggests that the observed educational persistence in rural
India is unlikely to be due solely to mechanical transmission of ability across generations,
while the persistence in rural China could be explained by genetic correlations alone.
We analyze whether the economic forces identified in the extended Becker-Tomes model
provide a coherent explanation of the observed pattern of educational mobility across coun-
tries (rural China vs. rural India) and over time (older vs. younger cohorts in rural China).
A lack of intergenerational persistence in nonfarm occupations in rural China because of
the Hukou restrictions seems to have played an important role in making the intercepts
similar in rural China, but strong intergenerational occupational persistence in rural India
resulted in significant differences between farm and nonfarm households. In rural India,
the observed complementarity can be explained by higher returns to education in nonfarm
occupations in the parental generation. The separability between father’s education and
occupation in rural China was driven by the absence of any significant differences in the
household-level returns to education across farm and nonfarm occupations. However, be-
cause of economic forces unleashed by the policy reform in China, the returns to education
in nonfarm occupations for parents have increased and Hukou restrictions have been re-
laxed progressively. According to the theory, this should tighten the link between father’s
education and son’s schooling in the nonfarm sector. Indeed, we find evidence that the
separability between father’s education and occupation broke down for the 18-28 years
old sons, implying that structural change in favor of the nonfarm sector is increasingly
contributing to educational inequality in rural China.
30
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Figure 1
Son’s
Schooling
g
Nonfarm
Farm
Father’s Schooling
𝜓0
𝑛
𝜓0
𝑓
𝜓1
𝑛
𝜓1
𝑓
Figure 2
Son’s
Schooling
g
Nonfarm (a)
Farm
Father’s Schooling
𝜓0
𝑓
𝜓0
𝑛
𝜓1
𝑛(𝑎)
𝜓1
𝑓
𝜓1
𝑛(𝑏)
Nonfarm (b)
Table 1: Relative Mobility and Test of Complementarity:
Rural China and Rural India
IGRC (𝝍𝟏
𝒋)
IRC (𝜹𝟏
𝒋)
CHINA
INDIA
CHINA
INDIA
Combined Sample
0.313
0.518
0.337
0.456
(0.025)
(0.020)
(0.017)
(0.014)
Farm
0.311
0.488
0.331
0.422
(0.033)
(0.027)
(0.032)
(0.024)
Nonfarm
0.316
0.555
0.344
0.500
(0.029)
(0.027)
(0.031)
(0.024)
Test of Complementarity (Farm/Nonfarm)
H0: Farm and Nonfarm Coefficients are Equal
IGRC(𝝍𝟏
𝒏= 𝝍𝟏
𝒇)
IRC (𝜹𝟏
𝒏= 𝜹𝟏
𝒇)
CHINA
INDIA
CHINA
INDIA
F Statistic
0.014
3.803
0.134
6.421
P-Value
0.906
0.052
0.715
0.012
Notes: (1) IGRC stands for Intergenerational Regression Coefficient, and IRC stands for
Intergenerational Rank Correlation. (2) The numbers in parenthesis are robust standard errors
clustered at the Primary Sampling Unit level. (3) The number of observations for China:
Combined (3305), Farm (1662), Nonfarm (1643), and for India: Combined (6952), Farm (4035),
Nonfarm (2917).
Table 2: Estimates of Intercepts and Test of Equality
IGRC Intercept (𝝍𝟎
𝒋)
IRC Intercept (𝜹𝟎
𝒋)
CHINA
INDIA
CHINA
INDIA
Combined Sample
5.862
5.339
0.381
0.340
(0.221)
(0.165)
(0.010)
(0.009)
Farm
5.713
5.612
0.371
0.364
(0.282)
(0.219)
(0.025)
(0.017)
Nonfarm
6.012
4.980
0.391
0.307
(0.237)
(0.193)
(0.022)
(0.015)
Test of Equality (Farm/Nonfarm)
H0: Farm and Nonfarm Intercepts are Equal
IGRC Intercepts
(𝝍𝟎
𝒏= 𝝍𝟎
𝒇)
IRC Intercepts
(𝜹𝟎
𝒏= 𝜹𝟎
𝒇)
CHINA
INDIA
CHINA
INDIA
F Statistic
1.181
6.233
0.626
7.784
P-Value
0.279
0.013
0.430
0.006
Notes: (1) The numbers in bold in the upper panel are estimates of the intercepts from
intergenerational persistence regression using years of schooling (Called IGRC intercepts),
and from rank-rank regressions (called IRC intercepts). (2) the numbers in parenthesis are
robust standard errors clustered at the Primary Sampling Unit level.
Table 3: AET (2005) Sensitivity Analysis for Ability Bias
The Effects of Father's Higher Education on the
Probability of Higher Education of Sons.
CHINA
INDIA
Farm
Nonfarm
Farm
Nonfarm
ρ=0
1.72
2.83
8.68
9.99
(0.38)
(0.46)
(0.44)
(0.45)
ρ=0.10
1.17
2.14
7.64
9.46
(0.44)
(0.51)
(0.47)
(0.48)
ρ=0.20
0.38
1.2
6.27
8.65
(0.50)
(0.57)
(0.51)
(0.53)
ρ=0.30
-0.66
-0.02
4.53
7.48
(0.57)
(0.63)
(0.55)
(0.58)
ρ=0.40
-1.99
-1.52
2.39
5.88
(0.64)
(0.68)
(0.58)
(0.63)
Notes: (1) AET (2005) stands for Altonji, Elder and Taber (2005, Journal of Political Economy)
Biprobit sensitivity analysis. (2) ρ stands for correlation in cognitive ability of father and son.
Estimates in the first row are the univariate Probit estimates. The upper bound ρ=0.40 is based on
economics and behavioral genetics literature. (3) The numbers in bold are percentage points
increase in the probability of higher education of sons when the father has higher education. (3)
Higher education for parents implies more than primary, and for sons in India more than 10 years
of schooling, for sons in China more than 9 years of schooling. (4) The numbers in parenthesis are
standard errors clustered at the PSU level.
Table 4: Father's Education and Household Income
Panel A: Estimates for Rural China
Intercept
Slope (Returns to Education)
Farm
Nonfarm
Farm
Nonfarm
CHIP 2002
8344.64
8582.80
275.32
335.42
(670.34)
(832.97)
(91.38)
(108.72)
CHIP 1995
4608.86
4457.28
34.21
107.45
(666.28)
(383.14)
(71.14)
(43.19)
Test of Equality Between Farm and Nonfarm
H0: Intercepts are Equal
H0: Slopes are Equal
CHIP 2002
F Statistic
0.08
0.30
P-value
0.78
0.58
CHIP 1995
F Statistic
0.06
0.96
P-value
0.81
0.33
Panel B: Estimates for Rural India
Intercept
Slope (Returns to Education)
Farm
Nonfarm
Farm
Nonfarm
NSS 1993
1199.27
1172.17
68.17
77.92
(9.67)
(13.57)
(2.52)
(3.28)
Test of Equality Between Farm and Nonfarm
H0: Intercepts are Equal
H0: Slopes are Equal
F Statistic
2.99
5.71
P-value
0.08
0.02
Notes: (1) The dependent variable for Rural China is the average household income (total). CHIP 2002 is
the average of the last 5 years of total household income, and CHIP 1995 is the average of the last 3 years
of household income. The dependent variable for India is total household expenditure. (2) The numbers in
parenthesis are standard errors. (3) H0 stands for Null Hypothesis. (4) The number of observations for CHIP
1995: Farm (1709), Nonfarm (3893), and for CHIP 2002: Farm (4457), Nonfarm (4087). For NSS (1993),
the number of observations are Nonfarm (20535), and Farm (48196).
Table 5: Intergenerational Persistence in Education (18-28 Age Cohort, CFPS)
Panel A: Estimates Based on Years of Schooling
Intercept (𝝍𝟎
𝒋)
IGRC (𝝍𝟏
𝒋)
Farm
Nonfarm
Farm
Nonfarm
6.997
7.173
0.274
0.337
(0.341)
(0.308)
(0.035)
(0.032)
Test of Equality Between Farm and Nonfarm
H0: Intercepts are Equal
(𝝍𝟎
𝒏= 𝝍𝟎
𝒇)
H0: IGRCs are Equal
(𝝍𝟏
𝒏= 𝝍𝟏
𝒇)
F Statistic
0.244
2.632
P-Value
0.622
0.107
Panel B: Estimates Based on Schooling Ranks
Intercept (𝜹𝟎
𝒋)
IRC (𝜹𝟏
𝒋)
Farm
Nonfarm
Farm
Nonfarm
0.399
0.404
0.304
0.373
(0.027)
(0.027)
(0.034)
(0.035)
Test of Equality Between Farm and Nonfarm
H0: Intercepts are Equal
(𝜹𝟎
𝒏= 𝜹𝟎
𝒇)
H0: Slopes are Equal
(𝜹𝟏
𝒏= 𝜹𝟏
𝒇)
F Statistic
0.028
2.792
P-Value
0.868
0.097
0
2
4
6
8
10
12
14
16
18
012345678910 11 12 13 14 15 16 17 18 19 20
Sons' Years of Schooling
Fathers' Years of Schooling
Figure 3: Regression of Fathers' Years of Schooling against Sons'
Years of Schooling in Rural India
Farm
Non-Farm
0
2
4
6
8
10
12
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
Sons' Years of Schooling
Fathers' Years of Schooling
Figure 4: Regression of Fathers' Years of Schooling against Sons' Years
of Schooling in Rural China
Farm Non-Farm
Online Appendix A: Coresidency and Truncation Bias in Rural China: CFPS
2010 vs. CHIP 2002
An important advantage of the data used in this study is that the estimates are free
of truncation bias that arises from using coresidency to define household membership in a
survey. Emran, Greene, and Shilpi (2018) provide an in-depth discussion on the magnitude
of truncation bias in the context of rural India. To the best of our knowledge, there are
no studies on the effects of sample truncation due to coresidency in the context of rural
China in the existing literature. To understand the extent of truncation bias in the context
of rural China, we compare the estimates free of truncation in Tables 1 and 2 with the
corresponding estimates using data from the Chinese Household Income Project (CHIP
2002). This may be of independent interest to many researchers as CHIP data sets have
been widely used to study intergenerational mobility in China including by some of the
authors of the current paper.
Using CHIP 2002 data, appendix Table A.2 reports estimates for two age ranges: (i)
the same age cohorts as in Tables 1 and 2 in the main text of the paper (21-57 years old
in 2002),43 and (ii) the full sample with 18-65 years old children in 2002. The estimates of
IGRC from CHIP 2002 are about 25 percent lower on average compared to the CFPS 2010
estimates (taking the CHIP 2002 estimate as the base). The estimates of the intercepts
are, in contrast, biased upward in CHIP 2002, about 15-18 percent higher than the corre-
sponding estimate from the CFPS data. The evidence that the coresident sample causes
substantial downward bias in the slope estimates, but upward bias in the intercept esti-
mates from the CHIP 2002 data is consistent with the evidence from India and Bangladesh
provided by Emran, Greene and Shilpi (2018), and Emran and Shilpi (2018). The sub-
stantive conclusions are also less robust; the test of separability shows different results for
IGRC and IRC for the age cohorts overlapping with the main estimation samples from
the CFPS used in Tables 1 and 2. While the null hypothesis of separability cannot be
rejected for IGRC estimates at the 10 percent level, the IRC estimates reject separability
at the 5 percent level. An analysis based on the coresident sample thus can lead to wrong
conclusions about the interaction between parent’s education and occupation.44
43This ensures that the age cohorts in CHIP 2002 overlap with the 29-65 age cohorts used for CFPS
2010 data.
44A full analysis of CHIP 2002 data is presented in an unpublished work by Emran and Sun (2015b).
As noted in the main text, the evidence and conclusions in this paper supersede those in Emran and Sun
(2015b).
36
Online Appendix B: An Approach to Nature vs. Nurture
The approach developed here exploits the restrictions implied by the recent estimates
of intergenerational correlation in cognitive ability in economics in a triangular biprobit
model a′la Altonji et al. (2005), and performs sensitivity analysis over a narrow interval
of the correlation parameter. This approach requires binary classification of educational
attainment. We define a dummy Dp
ithat takes on the value 1 when the father of a child has
more than primary schooling and zero otherwise. Analogously we define a binary variable
for children’s education Dc
iwhich takes on the value of 1 when a child’s schooling years
is higher than a threshold (junior high schooling for China and secondary schooling for
India). This means that we have a [2 ×2] occupation and education set-up. Consider the
following triangular model of children’s and parent’s education:
P r (Dc
i= 1) = Φ (λj
0+λj
1Dp
i+X′
iΠj+ςi)
P r (Dp
i= 1) = Φ (γj
0+X′
iΓj+ϵi)
where Φ is the normal CDF and superscript jrefers to parental occupation, i.e., j∈ {f, n}.
The error terms capture the unobserved factors including ability, part of which is genetically
transmitted from father to son in our application.
The choice of the educational cut-offs described above is based on the following con-
siderations. For parental generation, the cut-off is primary schooling, which equals 5 years
of schooling in India and 6 years in China. For children in India, the cut-off we chose
is 10 years of schooling that correspond to the completion of secondary schooling. The
10th year is a natural focal point for India as the students take one of the most important
public examinations at the end of 10th grade. For China the cut-off used is junior high
schooling which corresponds to 9 years of schooling. The 9th year cut-off is a focal point
in China because of the 9-year compulsory schooling policy adopted by the government in
1986. While a lump in the distribution of children’s schooling attainment at the 9th year
of schooling may be driven by government policy, whether a child goes beyond 9 years of
schooling would reflect more faithfully the effects of family background. Thus we define
all the dummies as strict inequalities; for example, for rural China, we set Dc= 1 when
a child attains higher than 9 years of schooling and zero otherwise. The conclusions be-
low, however, do not depend on the precise cut-off chosen for the educational attainment
dummies.45
45As part of robustness checks, we estimated biprobit models for China using 5 years cut-off for father
37
It is useful to decompose the error terms in the triangular model into two parts, one
genetically transmitted (denoted as ϕi) and the other orthogonal to the genetic component:
ςi=ϕc
i+ ˜ςi
ϵi=ϕp
i+ ˜ϵi
So Cov (ςi, ϵi) = Cov (ϕc
i, ϕp
i)+Cov (˜ςi,˜ϵi). The focus is on the role played by the genetic
component represented by Cov (ϕc
i, ϕp
i).
We take advantage of a substantial literature in economics and behavioral genetics
that provides estimates of correlation between parents and children in cognitive ability.
According to the estimates reported by Black et al. (2009) and Bj¨orklund et al. (2010),
Cov (ϕc
i, ϕp
i)∈[0.35,0.38]. A meta-analysis of behavioral genetic studies by Plomin and
Spinath (2004) reports a correlation of 0.40.
Let ρ=Corr (ςi, ϵi).We estimate the bivariate probit model above by imposing ρ=
0.10,0.20,0.30,0.40.46 Thus we allow for different degrees of correlation in the error terms of
the triangular model driven by genetic transmissions across generations. It is important to
appreciate that the estimates of intergenerational schooling persistence from the sensitivity
analysis with ρ= 0.40 can be interpreted as the lower bounds on the true intergenerational
effects due to economic and social factors. The estimates of ability correlations in the
literature discussed above are likely to be biased upward as measures of genetic correlations
at birth because they partly capture the dynamic interactions between family environment
and genetics up to the age when the ability measurements are taken.47 For example, the
careful recent analysis by Gronqvist et al. (2017) uses measures of cognitive ability taken
at age 13.
The results from the biprobit sensitivity analysis are reported in Table 3 of the main
text and discussed at the beginning of section (6). We report the marginal effects of
and 10 years cut-off for children, so that the educational attainment dummies in China match exactly those
in India in terms of years of schooling. The estimates are very close to those reported in Table 3 of the
main text. The details are available from the authors.
46In an interesting recent paper, Gronqvist et al. (2017) show that the estimates of ability correlation
may be biased downward because of measurement error, and they report estimates in the range of 0.42-0.48.
However, note that the educational attainment as measured by years of schooling is also usually measured
with error. It thus seems reasonable to use 0.40 as the upper bound for our analysis, assuming that the
measurement errors in schooling and cognitive ability largely offset each other.
47This includes the in-utero effects on a child’s health which is found to be of substantial magnitude
according to a large literature. Please see the survey by Almond and Currie (2011). Recent evidence shows
that socioeconomic status a child born into affects the development of brain in a significant way (Noble et
al. (2015)).
38
switching the parental educational dummy from zero (primary or below) to one (more than
primary) which implies that the estimates of intergenerational persistence depend on all of
the probit coefficients in the model, including the intercept term.48 The main text of the
paper provides a concise discussion of the main results from this analysis. Here we provide
a more detailed discussion.
Effects of Positive Ability Correlations in Rural India
The estimates from the univariate probit model for India reported in row 1 of Table 3
of the main text shows that the pattern of the effects is broadly similar to that found in the
estimates based on years of schooling in Table 1 and Table 2 in the main text. The sons
born to fathers with more than primary schooling enjoy a higher probability of attaining
more than secondary schooling, and this effect is larger for the children with fathers in
nonfarm occupation.
More important and interesting for our purpose is how the estimates are affected when
we relax the assumption of ρ= 0 imposed in the univariate probit estimates. Consistent
with a priori expectation, the magnitude of the estimated effects declines monotonically
with higher values of intergenerational ability correlation ρ. However, the estimated effect
of having a better educated father remains positive and statistically significant at the 1
percent level across the board even when we set the value of ρat its upper bound of 0.40.
This can be interpreted as strong evidence that the estimated effects in India are not likely
to be driven exclusively by mechanical effects of genetic transmission of ability.
Effects of Positive Ability Correlations in Rural China
The estimates of father’s effect in rural China for alternative values of genetic correlation
in ability are reported in the first two columns of Table 3 in the main text. The estimates
from the univariate probit model under the assumption that ρ= 0 show that the effects for
both farm and nonfarm households in China are much smaller in magnitude when compared
to the corresponding estimates for India. This confirms the conclusion based on years of
schooling as a measure of educational attainment that the sons in rural China enjoy much
higher educational mobility compared to the sons in rural India. More important is the
evidence that the estimated effects become very small in China when we set ρ= 0.20.
The advantage due to the higher educated father declines effectively to zero when we set
ρ= 0.30,as the estimated effects turn negative for both the farm and nonfarm households.
48The AET sensitivity analysis including the quadratic age controls yield similar conclusions to those
based on Table 3 in the main text. The results are available from the authors upon request.
39
The evidence thus suggests that the estimates of intergenerational persistence in China
reported in Table 1 and Table 2 in the main text could be entirely driven by genetic
correlations in ability. This suggests high intergenerational educational mobility during
the decades of 1980s and 1990s in rural China, for the sons of both the farmer and non-
farmer fathers. However, as discussed in details in the main text (see sections (6.1) and
(6.2)), the evidence that the observed persistence in rural China could be explained away
by genetic correlation in cognitive ability does not necessarily imply that economic forces
did not play a role in determining the pattern across farm and nonfarm households.
40
APPENDIX TABLES
Table A.1: Summary Statistics
(Main Overlapping Samples)
Mean
SD
Min
Max
CFPS 2010
Son's Schooling (years)
6.31
4.14
0
19
Father's Schooling (years)
3.81
4.14
0
16
Father in Agriculture (dummy)
0.48
0.50
0
1
Son's Age (years)
39.78
7.69
29
65
Father's Age (years)
67.92
8.83
45
96
REDS 1999
Son's Schooling (years)
6.26
5.14
0
21
Father's Schooling (years)
4.13
4.41
0
20
Father in Agriculture (dummy)
0.59
0.49
0
1
Son's Age (years)
28.65
7.88
18
54
Father's Age (years)
59.67
9.86
34
98
NOTES: (1) CFPS stands for China Family Panel Studies and REDS stand for Rural Economic and Demographic
Survey. (2) SD stands for standard deviation. (3) No. of observations for CFPS is 3305, and for REDS 6887.
Table A.2: Estimates of Intergenerational Educational Persistence in Rural China
from CHIP 2002
Panel A: Children
18-65 Years
SLOPE
INTERCEPT
IGRC (𝝍𝟏
𝒋)
IRC (𝜹𝟏
𝒋)
(𝝍𝟎
𝒋)
(𝜹𝟎
𝒋)
Combined
0.265
0.295
7.105
0.357
(0.018)
(0.019)
(0.163)
(0.016)
Farm
0.245
0.263
7.075
0.353
(0.025)
(0.026)
(0.202)
(0.019)
Non-farm
0.266
0.305
7.29
0.376
(0.024)
(0.027)
(0.219)
(0.022)
Test of Separability
Test of Equality
(𝝍𝟏
𝒏= 𝝍𝟏
𝒇)
(𝜹𝟏
𝒏= 𝜹𝟏
𝒇)
(𝝍𝟎
𝒏= 𝝍𝟎
𝒇)
(𝜹𝟎
𝒏= 𝜹𝟎
𝒇)
F-statistics
0.410
1.375
0.700
0.917
P-value
0.521
0.243
0.403
0.340
Panel B: Children of 21-57 years age in 2002
SLOPE
INTERCEPT
IGRC (𝝍𝟏
𝒋)
IRC (𝜹𝟏
𝒋)
(𝝍𝟎
𝒋)
(𝜹𝟎
𝒋)
Combined
0.262
0.283
7.074
0.360
(0.019)
(0.021)
(0.174)
(0.017)
Farm
0.226
0.237
7.127
0.361
(0.027)
(0.027)
(0.216)
(0.021)
Non-farm
0.277
0.310
7.180
0.372
(0.026)
(0.028)
(0.234)
(0.023)
Test of Separability
Test of Equality
(𝝍𝟏
𝒏= 𝝍𝟏
𝒇)
(𝝍𝟎
𝒏= 𝝍𝟎
𝒇)
F-statistics
2.216
4.205
0.039
0.189
P-value
0.139
0.043
0.844
0.664
Table A.3: Evidence on Complementarity and Intercept Differences
with Quadratic Age Controls (Years of Schooling)
Estimates with Son's Age and Age Squared as Controls
China
India
Farm
Nonfarm
Farm
Nonfarm
IGRC (𝝍𝟏
𝒋)
0.306
0.308
0.489
0.556
H0 : Farm = Nonfarm
(𝝍𝟏
𝒏= 𝝍𝟏
𝒇)
F Statistic
0.004
3.785
P-value
0.950
0.053
Intercept (𝝍𝟎
𝒋)
7.502
7.885
5.146
4.515
H0 : Farm = Nonfarm
(𝝍𝟎
𝒏= 𝝍𝟎
𝒇)
F Statistic
1.790
6.053
P-value
0.183
0.015
Estimates with Both Son's and Father's Age and Age Squared
China
India
Farm
Nonfarm
Farm
Nonfarm
IGRC (𝝍𝟏
𝒋)
0.301
0.314
0.497
0.569
H0 : Farm = Nonfarm
(𝝍𝟏
𝒏= 𝝍𝟏
𝒇)
F Statistic
0.141
4.330
P-value
0.708
0.039
Intercept (𝝍𝟎
𝒋)
14.43
14.80
4.329
3.536
H0 : Farm = Nonfarm
(𝝍𝟎
𝒏= 𝝍𝟎
𝒇)
F Statistic
1.677
9.308
P-value
0.198
0.025
Table A.4: Evidence on Complementarity and Intercept Differences
with Quadratic Age Controls (Schooling Rank)
Estimates with Son's Age and Age Squared as Controls
China
India
Farm
Nonfarm
Farm
Nonfarm
IRC (𝜹𝟏
𝒋)
0.328
0.341
0.421
0.499
H0 : Farm = Nonfarm
(𝜹𝟏
𝒏= 𝜹𝟏
𝒇)
F Statistic
0.119
6.377
P-value
0.731
0.012
Intercept (𝜹𝟎
𝒋)
0.456
0.479
0.370
0.314
H0 : Farm = Nonfarm
(𝜹𝟎
𝒏= 𝜹𝟎
𝒇)
F Statistic
0.761
7.433
P-value
0.385
0.007
Estimates with Both Son's and Father's Age and Age Squared
China
India
Farm
Nonfarm
Farm
Nonfarm
IRC (𝜹𝟏
𝒋)
0.322
0.350
0.428
0.511
H0 : Farm=Nonfarm
(𝜹𝟏
𝒏= 𝜹𝟏
𝒇)
F Statistic
0.578
7.199
P-value
0.449
0.008
Intercept (𝜹𝟎
𝒋)
0.928
0.946
0.303
0.237
H0 : Farm=Nonfarm
(𝜹𝟎
𝒏= 𝜹𝟎
𝒇)
F Statistic
0.456
10.27
P-value
0.501
0.002
Table A.5: Father's Education and Household Income
(Control for Number of Children)
Panel A: Estimates for Rural China
Intercept
Slope
Farm
Nonfarm
Farm
Nonfarm
CHIP 2002
5654.30
8311.39
294.37
339.45
(747.55)
(1418.46)
(89.78)
(114.91)
CHIP 1995
3434.95
3242.18
43.66
114.72
(523.84)
(617.94)
(68.88)
(44.65)
Test of Equality Between Farm and Nonfarm
H0: Intercepts are Equal
H0: Slopes are Equal
CHIP 2002
F Statistic
0.16
0.03
P-value
0.69
0.87
CHIP 1995
F Statistic
0.06
0.94
P-value
0.81
0.34
Panel B: Estimates for Rural India
Intercept
Slope
Farm
Nonfarm
Farm
Nonfarm
NSS 1993
823.87
770.09
63.46
75.60
(11.49)
(16.16)
(2.48)
(3.10)
Test of Equality Between Farm and Nonfarm
H0: Intercepts are Equal
H0: Slopes are Equal
F Statistic
591.19
9.98
P-value
0.000
0.002
Notes: (1) The dependent variable for Rural China is the average household income (total). CHIP 2002 is
the average of the last 5 years of total household income, and CHIP 1995 is the average of the last 3 years
of household income. The dependent variable for India is total household expenditure. (2) The numbers in
parenthesis are standard errors. (3) H0 stands for Null Hypothesis. (4) The number of observations for CHIP
1995: Farm (1709), Nonfarm (3893), and for CHIP 2002: Farm (4457), Nonfarm (4087). For NSS (1993),
the number of observations is Nonfarm (20535), and Farm (48196).
