What the Mean Measures of Mobility Miss: Learning About Intergenerational Mobility from Conditional Variance

Abstract

A large literature on intergenerational mobility focuses on the conditional mean of children's economic outcomes to understand the role of family background, but ignores the information contained in conditional variance. Using exceptionally rich data free of coresidency bias, we provide evidence on three large developing countries (China, India, and Indonesia) that suggests a strong influence of father's education on conditional variance of children's schooling. We find substantial heterogeneity across countries, gender, and geography (rural/urban). Cohort based estimates suggest that the effects of father's education on the conditional variance has changed qualitatively, in some cases a positive effect in the 1950s cohort turning into a substantial negative effect in the 1980s cohort. We develop a methodology to incorporate the effects of family background on the conditional variance along with the standard conditional mean effects. We derive risk adjusted measures of relative and absolute mobility by accounting for an estimate of the risk premium for the conditional variance faced by a child. The estimates of risk adjusted relative and absolute mobility for China, India and Indonesia suggest that the standard measures substantially underestimate the effects of family background on children's educational opportunities, and may give a false impression of high educational mobility. The downward bias is especially large for the children born into the most disadvantaged households where fathers have no schooling, while the bias is negligible for the children of college educated fathers. Compared to the risk adjusted measures, the standard measures are likely to underestimate gender gap and rural-urban gap in educational opportunities.

Full text

What the Mean Measures of Mobility Miss: Learning About
Intergenerational Mobility from Conditional Variance
1
Md. Nazmul Ahsan, Saint Louis University
M. Shahe Emran, IPD, Columbia University
Hanchen Jiang, University of North Texas
Forhad Shilpi, DECRG, World Bank
First Version: Feb 18, 2022; This Version: Oct 29, 2022
ABSTRACT
A large and growing literature on intergenerational mobility focuses on the conditional
mean of children's economic outcomes given parent's economic status, while ignoring the
information contained in conditional variance. This paper explores the eects of family back-
ground on the conditional variance of children's outcomes in the context of intergenerational
educational mobility in three large developing countries (China, India, and Indonesia). The
empirical analysis uses exceptionally rich data free of sample truncation due to coresidency.
Evidence suggests a strong negative inuence of father's education on the conditional variance
of children's schooling in most of the cases. Children of educated fathers thus enjoy double
advantages: a higher mean and a lower variance. The analysis nds substantial heterogeneity
across countries, gender, and geography (rural/urban). A methodology is developed to incor-
porate the eects of family background on the conditional variance along with the standard
conditional mean eects. We derive risk-adjusted measures of relative and absolute mobility
by accounting for an estimate of the risk premium for the conditional variance faced at birth
by a child. The estimates of risk-adjusted relative and absolute mobility for China, India, and
Indonesia suggest that the existing evidence using the standard measures of mobility substan-
tially underestimates the eects of family background on children's educational opportunities.
The magnitude of underestimation is especially large for the children born into the most dis-
advantaged households where fathers have no schooling, while it is negligible for the children
of college educated fathers.
Key Words:
Conditional Variance, Family Background, Intergenerational Educational
Mobility, Risk Adjusted Mobility Measures, China, India, Indonesia
JEL Codes:
I24, J62, O12
1
Emails for correspondence: nazmul.ahsan@slu.edu (Md. Nazmul Ahsan); shahe.emran.econ@gmail.com
(M. Shahe Emran); Hanchen.Jiang@unt.edu (Hanchen Jiang); fshilpi@worldbank.org (Forhad Shilpi). We
would like to thank James Heckman, Matthew Lindquist, Petra Todd, Charlie Rafkin, Fabian Pfeer, Joni
Hersch, Ira Gang, Tom Vogl, Cheng Chou for valuable comments on an earlier draft. We also benetted from
the comments of and discussions with the participants at the following seminars and conferences: Canadian
Economic Association Annual Conference, May 2022; Asian Meeting of the Econometric Society, June 2022;
Australasia Meeting of the Econometric Society, July 2022; HCEO-IESR Summer School on Socioeconomic
Inequality, July 2022; 100 Years of Economic Development Conference at Cornell University, September 2022;
Deakin University, October 2022. The standard disclaimers apply.
1

(1) Introduction
A large economic and sociological literature provides estimates of intergenerational persis-
tence in economic status.
2
A higher persistence across generations is interpreted as inequality
of economic opportunities for children as their life chances are tied down closely to the so-
cioeconomic status of their parents irrespective of their own choices and eort. The bulk of
the measures used for understanding the transmission of economic status from one generation
to the next are based on a conditional expectation function. The focus is on estimating the
expected value of an indicator of socioeconomic status of children (e.g., permanent income,
education ) conditional on parent's (usually father's) socioeconomic status.
This vast and growing literature largely neglects any information contained in the con-
ditional variance of children's economic outcomes.
3
This is a reasonable approach when (i)
conditional variance of the relevant economic outcome does not vary in a systematic way with
parental economic status, geographic location, gender, race and ethnicity etc.; and/or (ii) par-
ents and children are approximately risk neutral. A large body of evidence accumulated over
many decades rejects risk neutrality, and strongly suggests an important role for risk aversion
in economic choices under uncertainty (see, for example, Eeckhoudt et al. (2005)). There is no
systematic evidence in the literature on the rst condition, but there are a variety of economic
mechanisms that can make the conditional variance a function of parent's economic status and
geographic location. Conditional variance in children's schooling may vary across the house-
holds in a village because of their dierent abilities to cope with adverse weather shocks. With
better access to credit and insurance markets, the highly educated (high income) households
are better able to deal with negative shocks such as ood and drought without any disruption
to children's education. In contrast, such a negative income shock may force the uneducated
2
For excellent surveys of the economic literature, please see Solon (1999), Bjorklund and Salvanes (2011),
Heckman and Mosso (2014), Mogstad and Torsvik (2021) and Cholli and Durlauf (2022). and for the sociology
literature see Hout (2015), Torche (2015). For surveys on developing countries, see Iversen et al. (2019), and
the chapters in the book edited by Iversen et al. (2021).
3
Although largely ignored in the literature on intergenerational mobility, some studies in the related but
distinct literature on inequality of opportunity (IOP) account for the fact that conditional variance is likely
to depend on the circumstances a child is born into (see, for example, Bjorklund et al. (2012)). But their
focus is very dierent. Please see the discussion in section 2 below. There is a small literature that exploits
the information in conditional variance by estimating quantile regression models of intergenerational mobility.
But the focus is still on the conditional mean function at various quantiles. Please see section 2 below for a
detailed discussion.
1

poor parents to take the children out of school and send them for child labor. This adds an
element of uncertainty (on top of ability dierences) for the children born into disadvantaged
households, resulting in a higher conditional variance in completed schooling. The conditional
variance of children's schooling attainment is likely to
decline
with the education of parents
when such economic shocks (income or health shocks) are the primary sources behind the
observed variance in the data.
In this case, children born to higher educated parents not only
have higher expected years of schooling (as found in numerous studies of intergenerational
educational mobility), but also a lower variance in schooling attainment. Under the plausible
assumption of risk aversion, this implies being born to higher educated parents brings double
advantages for children, part of which is ignored by the existing measures of intergenerational
mobility.
We analyze the relationship between family background and conditional variance of chil-
dren's outcome in the context of intergenerational educational mobility. We make two con-
tributions to the literature. First, using data from three large developing countries (China,
India, and Indonesia, with 42 percent of world population in 2000 (2.56 billion)), we provide
the rst empirical evidence that the conditional variance of children's schooling is system-
atically related to his/her family background as captured by father's education.
4
Second,
we develop a methodology that combines the eects of father's education on both the mean
and conditional variance of children's schooling. The accident of birth, in this perspective,
is like a lottery ticket that induces a conditional distribution of schooling outcomes given
parental education. The core insight of our approach is to evaluate this lottery ticket from
an ex ante perspective (i.e., at birth) to understand how the value of the lottery varies with
parental education (more broadly, family background). It is important to recognize that the
risk associated with the conditional variance for a child is largely the outcome of parental
decisions facing credit constraints and various shocks. Parental actions are thus part of the
risk environment inherited by a child by birth. In the terminology of the inequality of op-
portunity approach of Roemer (1998), parental choices constitute "circumstances" children
are born into. Our approach thus builds a bridge between the intergenerational mobility and
4
We are not aware of any studies on intergenerational mobility that estimates the eects of parent's economic
status on the conditional variance of children's economic outcomes.
2

inequality of opportunity perspectives which are often treated as distinct topics.
We propose new (and more complete) measures of relative and absolute mobility that ad-
just the standard mean eects by the risk premium associated with the conditional variance in
educational outcomes faced by children at birth. With risk neutrality, our proposed measures
reduce to the canonical measures of intergenerational educational mobility widely used in the
current literature (see, for example, Hertz et al. (2008), Azam and Bhatt (2015), and Narayan
et al. (2018)). But, under the more plausible assumption of risk aversion, the measures of mo-
bility developed in this paper incorporate the eects of family background operating through
conditional variance.
For our empirical analysis, we use household survey data from China Family Panel Studies
(CFPS) 2010, India Human Development Survey (IHDS) 2012, and Indonesia Family Life
Survey (IFLS) 2014.
5
The estimates from the full sample (1950-1989 birth cohorts) suggest
that the conditional variance in children's schooling
declines
with father's education in all three
countries, thus conrming the conjecture that the children born to more educated fathers enjoy
double advantages in the form of a lower variance in addition to a higher expected (mean)
schooling attainment.
We nd evidence of substantial heterogeneity across countries, geographic location (rural
vs. urban), gender, and birth cohorts. Conditional variance in children's schooling is the
highest in India (18.76) and the lowest in Indonesia (13.58), with China in between (16.83).
The inuence of father's education on conditional variance of children's schooling follows a
reverse cross-country pattern: Indonesia (-0.51), China (-0.48), and India (-0.38). Conditional
variance is higher in the rural areas in a country, but the inuence of father's education on
conditional variance is smaller in magnitude. The rural-urban dierence is specially striking
in India where the estimate is negative and large (-0.77) in the urban sample but small
and statistically not signicant (10 percent level) in the rural sample (-0.022). In contrast,
the rural-urban dierence is small in China: -0.55 (urban) and -0.52 (rural). We also nd
substantial gender dierences with a larger negative eect on conditional variance of sons.
5
These surveys are chosen to ensure that the estimates are not biased because of sample truncation due
to coresidency restrictions. It is well known that truncations biases the estimated variance downward (Cohen
(1991)). Recent evidence suggests that coresidency causes substantial downward bias in the estimate of relative
educational mobility as measured by IGRC; see Emran et al. (2018).
3

The gender dierences in India are the starkest: the estimated eect is negative in the sons
sample, but positive in the daughters sample.
6
The results from cohort-based analysis suggest
that the negative eect of father's education on conditional variance has become stronger over
time in all three countries. In the rural and daughter's samples in India and Indonesia, the
estimate turned from positive in the 1950s cohort to a strong negative eect in the 1980s
cohort.
7
We check some alternative explanations for the observed relations between conditional
variance in children's education and father's education. We provide evidence that functional
form mis-specication is not responsible for the observed relations.
8
Taking advantage of data
on cognitive ability in IFLS 2014 in Indonesia, we explore whether the estimated eect of
father's education on conditional variance is largely due to omitted ability heterogeneity of
children. We nd that the inclusion of quadratic controls for ability reduces the magnitude
of the impact of father's education on conditional variance, but the estimates still remain
substantial and statistically signicant at the 1 percent level.
Perhaps, the most important ndings from our exercise relate to the dierences between
the conclusions about relative and absolute mobility from the risk-adjusted vs. standard
measures of mobility. For relative mobility, the estimates of risk adjusted IGRC (RIGRC)
suggest that the workhorse measure of relative mobility in the literature, IGRC, substantially
underestimates the impact of parental education. The estimates for the full sample (1950-
1989 cohorts) suggest that the extent of underestimation on average is 26 percent in China,
41 percent in India, and 10.4 percent in Indonesia.
9
6
Government policies and social norms can make the relation between father's education and conditional
variance of children's schooling positive. For example. gender based social norms such as son preference and
Purdah may results in low conditional variance in low educated households as parents target a reference level
of schooling for the daughters, and the girls' schooling attainment bunches around that reference point. This
can also give rise to a positive eect in the conditional variance regression. Please see section 2 below.
7
This suggests that the positive eect in the full sample (1950-1989) found earlier for rural India and the
daughters in India is driven by the earlier cohorts.
8
Based on recent theoretical models of intergenerational educational mobility, we allow for a quadratic
mobility CEF in place of a linear functional form (see Becker et al. (2015, 2018), Emran et al. (2021), Ahsan
et al. (2021)). We nd that allowing for a quadratic CEF does not change the relation between the conditional
variance in children's schooling and father's education in any signicant manner.
9
The smaller magnitude of underestimation in Indonesia despite a large inuence of father's education
on the conditional variance noted earlier reects the fact that the ratio of the conditional variance to the
conditional mean is much smaller. This ratio is important in determining the risk premium. Please see section
4

Accounting for the inuence of family background on conditional variance of schooling
makes a dramatic dierence in the estimated relative and absolute mobility for the children
born to the most disadvantaged households (fathers with no schooling).
10
RIGRC estimates
from the full sample (1950-1989 birth cohorts) for this subgroup shows that the standard IGRC
overestimates relative mobility by 37 percent in China, and by 63 percent and 28 percent
in India and Indonesia respectively. In contrast, the gap between the RIGRC and IGRC
estimates for the subgroup with college educated fathers is small. Absolute mobility is also
substantially overestimated for the most disadvantaged subgroup without risk adjustments:
conditional mean of years of schooling is overestimated by 48 percent in China, 127 percent
in India, and 25 percent in Indonesia. Again, for absolute mobility of the children of college
educated father, the risk adjustments does not make any substantial dierence.
The upshot is
that while the standard estimates of relative and absolute mobility seem to capture reasonably
well the educational opportunities of children born to college or more educated fathers, a failure
to account for the eects of family background on conditional variance vastly overstates the
educational opportunities of the most disadvantaged children with father having no schooling.
Ignoring the conditional variance can also lead to wrong conclusions in inter-group com-
parisons. For example, In India, the urban and rural daughters appear to enjoy similar relative
mobility according to the standard IGRC estimates (0.60 (urban) and 0.59 (rural)), but the
RIGRC estimates reveal a substantial disadvantage faced by the rural daughters (0.92 (rural)
and 0.79 (urban)).
The rest of the paper is organized as follows. The next section discusses the relevant
conceptual issues with a focus on the economic mechanisms that can give rise to a negative or
positive eect of father's education on the conditional variance of children's schooling. This
section also lays out the estimating equations for conditional variance and conditional mean.
Section (3) is devoted to a discussion of the surveys and data sets used for our analysis: CFPS
2014 (China), IHDS 2012 (India), and IFLS 2014 for Indonesia. These three surveys are
dierent from many other household surveys available in developing countries as the samples
(5) below.
10
Note that IGRC, the measure of relative mobility in the workhorse linear model, does not vary with father's
education level. But the risk adjusted measure RIGRC varies across low and high educated households because
of dierences in the conditional variance and the conditional mean.
5

do not suer from any signicant truncation. This is important for our analysis as truncation
of a sample is expected to reduce the estimate variance. Section (4) reports the evidence on
the conditional variance. In section (5), we develop a methodology for estimating relative
and absolute mobility that takes into account both the conditional mean and conditional
variance, and provide estimates of the risk adjusted mobility measures. The paper concludes
with summary of the ndings and points out the central contributions of the paper to the
literature.
(2) Conceptual Issues and Estimating Equations
The standard estimating equation for intergenerational educational mobility is:
Sc
i=α+βSp
i+εi;E(εi) = 0
(1)
where
Si
is the years of schooling of child
i
and superscripts
c
and
p
stand for child
and parents respectively. The focus of the analysis is the parameter
β
which is known as
intergenerational regression coecient (IGRC, for short) in the literature.
11
It is implicitly assumed that the variance of the error term
εi
does not depend on father's
education in any systematic way, and thus
β
alone adequately captures the inuence of family
background. This assumption is valid when the error term captures primarily the variations in
children's ability uncorrelated with father's education, and there are no market imperfections.
In a model with perfect credit and insurance markets, the optimal investment in a child's
education depends only on his/her ability, the family background is irrelevant. Under the
plausible assumption that the conditional variance of children's (innate) cognitive ability does
not depend on father's education level, there is no additional information in the conditional
variance of schooling attainment that could be useful for understanding the impact of family
background on educational opportunities of children.
In a more realistic setting where the credit and insurance markets are imperfect (or miss-
ing), we would expect that the conditional variance would reect the interactions of a child's
11
Among many studies relying on this specication, please see Hertz et al. (2008) and Narayan et al. (2018)
for cross country evidence, Azam and Bhatt (2015) on India, Knight et al. (2011), Golley and Kong (2013),
and Emran and Sun (2015) on China. For recent surveys of this literature, see Iversen et al. (2019), Torche
(2019), and Emran and Shilpi (2021).
6

ability with the credit constraint and risk coping strategies of a household. First, consider the
implications of credit market imperfections in the absence of exogeneous shocks. We consider
two types of credit market imperfections. In the rst case, the poor (less educated) households
pay a higher interest rate but can borrow as much as they want for educational investment
(i.e., no quantitative credit rationing).
12
In this case, the poor (less educated) parents in-
vest less, given the ability of a child because of a higher interest rate, but the investment
dierences across children from the same family (or similar family background where fathers
have the same education) are determined solely by the ability dierences among the children.
We thus expect
lower average level
of education for the children of less educated parents,
but the
conditional variance should not depend in any signicant way on father's education
in this case. The second model of credit market imperfections focuses on the quantitative
credit rationing, a special case of which is self nancing by the parents (the case of missing
credit market for investment in education). When the parents have limited investment funds,
they might choose to invest in the most able child to maximize the expected income (Becker
(1991)). Since the probability of success is higher for a child with high cognitive ability, it may
be optimal for the parents to reallocate investment funds from other children, specially when
returns to education are convex.
13
Such investment choices would increase the variance of
children's schooling in the less educated credit constrained families as the less able children's
education level is depressed and the education level of the high ability child is pushed up.
Negative income shocks can amplify the eects of a binding credit constraint, as the family
may need to allocate the funds earmarked for education investment to buy food. It is not
uncommon for one sibling to drop out of school in response to a negative shock to supplement
family income through child labor, while the more promising sibling continues with his/her
study. However, as emphasized by Behrman et al. (1982), equity concerns for a low ability
child may dominate the income maximizing motive, leading to a compensating investment
allocation where the low ability child gets a larger share of the educational investment. If
compensating investment rather than the reinforcing investment is the overriding behaviorial
12
This model of credit market imperfections is adopted by Becker et al. (2015, 2018) in their recent theo-
retical analysis of intergenerational mobility.
13
There is emerging evidence that returns to education function is convex in many developing countries.
See Kingdon (2007) on India, and Fasih et al. (2012) for cross-country evidence.
7

response of parents facing scarcity, then we would expect lower conditional variance for the
children born to low educated fathers.
14
Government policies and social norms can also aect the conditional variance of children's
education. When government policies such as free compulsory primary schooling are well de-
signed and implemented, it ensures that the children from the poor socioeconomic background
attain primary schooling irrespective of a child's ability. This will reduce the conditional vari-
ance in the poor households by eectively eliminating the lower tail of the counterfactual
schooling distribution of children without any government policy interventions. Merit based
scholarships provided by schools or government programs on the other hand usually relax
the credit constraints only for the most able child in a poor family, and thus increase the
conditional variance by expanding the upper tail of educational attainment of poor children.
Social norms can create reference points for the desired level of education of children which
may vary signicantly by gender, specially in the older cohorts. For example, strong son pref-
erence and Purdah may imply that girls in poor households go to school only if schooling is
easily accessible and, more importantly, free. They drop out after primary schooling because
secondary and higher schooling requires substantial private investments by the parents, and
the high school may be far away. We might thus observe low conditional variance in the
households with less educated parents because of bunching around primary schooling or other
thresholds determined by social norms, particularly for daughters. The richer and more edu-
cated households may invest substantially in daughter's education even with son preference,
and their investment would be more closely aligned with the ability of a child irrespective of
gender. The preceding discussion thus suggests that depending on government policy and so-
cial norms, we may in fact observe an increasing conditional variance with father's education,
specially for daughters in rural areas.
To understand the potential inuence of family background as captured by father's edu-
cation, we estimate the following equation for conditional variance:
V(εi) = θ0+θ1Sp
i+υi;E(υi) = 0
(2)
14
There is a large sociological literature on reinforcing vs. compensating parental investments in children's
education. But most of the literature focuses on the developed countries. See, for example, Conley (2004).
8

where
εi
is the error term from the conditional expectation function of children's schooling
given parent's level of schooling (equation 1). We are not aware of any studies on intergener-
ational mobility that provide estimates of equation (2). In the related but distinct literature
on inequality of opportunity that grew out of Roemer's seminal work (Roemer (1998), Roe-
mer and Trannoy (2016)), there are a number of studies that estimate equation (2); see, for
example, Bjorklund et al. (2012) and Hederos et al. (2017) in the context of income mobility
in Sweden. However, their focus is very dierent, they are interested in estimating a clean
measure of eort in order to decompose the observed income of children into two parts: one
due to the circumstances a child is born into, and the other due to a child's own eort and
choices. Similar to this paper, they recognize that the residual from a linear regression of
children's education on a set of variables dening the circumstances is not a clean measure
of eort as it partly reects the eects of family background.
15
As a measure of eort, they
use the sterilized residual from the regression of the residual squared (the residual from the
earlier stage) on circumstances.
There is a small literature on intergenerational mobility that exploits the information
in conditional variance using quantile regressions. See, for example, Grawe (2004) on the
United States and Kishan (2018) on India. The focus in this approach on estimating dierent
conditional mean functions
corresponding to the quantiles of children's education. Grawe
(2004) provides an interesting analysis of the pitfalls in relying on functional form of the CEF
to learn about credit constraints in the context of income mobility, and argues that a quantile
regression approach can be useful in understanding the existence of credit constraints.
(3) Data and Variables
We use the following household surveys for our empirical analysis: China Family Panel
Studies (CFPS) for China 2010, India Human Development Survey (IHDS) for India 2012,
and Indonesia Family Life Survey (IFLS) 2014 for Indonesia. These data sets are suitable
for our analysis because they do not suer from any signicant sample truncation arising
from coresidency restrictions commonly used to dene household membership in a survey. A
15
The circumstances usually include parent's education, occupation, race, ethnicity, geographic location,
and gender.
9

truncated sample is likely to underestimate the conditional variance, for example when the
data miss observations on highly educated children who left the natal house for college.
The data for China come from the China Family Panel Study (CFPS) 2010 wave, which
has a unique T-Table design that presents the complete family network, in which household
members' education information is also available. For a more detailed discussion about the
unique advantage of CFPS in analyzing intergenerational mobility related questions, please
see Fan, Yi and Zhang (2021) and Emran, Jiang, Shilpi (2020). The data for India come
from the India Human Development Survey (IHDS) 2012 wave. We follow Emran, Jiang,
Shilpi (2021) closely, which updates and expands the sample of father-child pairs for years
of schooling in India in two major ways compared to the earlier studies such as in Azam
and Bhatt (2015) and Azam (2016). Our sample includes not only the non-resident fathers
but also other non-resident family members, and non-resident children of household heads in
particular.
The data for Indonesia come from Indonesia Family Life Survey (IFLS) 2014 wave. IFLS's
household roaster, nonresident parents module, and mother's marriage module allow us to
construct father-children pairs whose education information is not subject to truncation bias.
More details about the sample construction procedure, readers are referred to Ahsan, Emran,
Shilpi (2021) and Mazumder et al. (2019).
The summary statistics for our main estimation samples are reported in Table 1. We rst
report the average years of schooling for both father and children in our full sample born
between 1950 and 1989 across three countries respectively. The average years of schooling for
fathers is 4.24 in China, 3.63 in India, and 6.21 in Indonesia. The average years of schooling
for children is 7.52 in China, 6.50 in India, and 9.52 in Indonesia. Therefore, Indonesia has
the best education outcome for both generations while India has the lowest mean education
for both children and parents.
We also report the summary statistics for our four main sub-samples: urban, rural, sons,
and daughters in the following panels of Table 1 respectively. In each country, there is a
consistent rural-urban gap in education for both generations. Children in urban China and
urban India have about 3 more years of schooling than children in rural areas, while the gap
10

is smaller in Indonesia (2 years). These countries exhibit dierent degrees of gender gap in
schooling among children: 1.3 years in China, 2.3 years in India, and 0.6 years in Indonesia.
Gender gap in Indonesia is much smaller, consistent with a large literature showing that girls
in Indonesia do not face any signicant disadvantages compared to the boys.
(4) Evidence on Conditional Variance
Estimates of equations (1) (conditional mean function) and (2) (conditional variance func-
tion) for our full estimation samples (1950-1989 birth cohorts) are reported in Table 2. The
estimates for the mobility equation (1) are in odd columns and those for the conditional
variance equation (2) are in even columns.
The evidence is consistent across the three countries:
conditional variance of children's
schooling is a negative function of father's education.
Estimates from the mobility equation
show that father's education has a substantial positive inuence on the expected schooling
of children, consistent with a large literature that focuses solely on the mean eects. When
considered together, the evidence on the mobility and conditional variance equations suggests
that
being born to a higher educated father is equivalent to winning an education lottery ticket
with higher mean (expected years of schooling) and a lower variance.
There are some impor-
tant cross-country heterogeneity: while father's impact on the expected education of children
(IGRC) is the highest in India (0.62), the eect on conditional variance is the smallest (-0.38).
The inuence of father's education on conditional variance is of comparable magnitude in
China (-0.48) and Indonesia (-0.51), but the estimate for the mean schooling is much smaller
in China (0.38) compared to that in Indonesia (0.48).
(4.1) Heterogeneity: Rural vs. Urban, and Sons vs. Daughters
The top panel of Table 3 reports the estimates of equations (1) and (2) separately for rural
and urban samples. The evidence suggests striking rural/urban dierences which vary across
countries. Conditional variance on average is higher in rural areas, although the rural-urban
gap is small in China.
16
In India, the eects of father's education on conditional variance is
large in urban sample (
−0.77
), but we cannot reject the null hypothesis of no inuence in the
16
The higher conditional variance in rural areas is consistent with the observation that the rural economy
is more exposed to weather shocks and the credit and insurance markets are less developed.
11

rural sample (
−0.02
). As we discuss below this null eect hides important gender dierences
in the rural areas. The estimates are similar in magnitude across rural and urban areas in
the case of China (
−0.55
(urban) and
−0.52
(rural)). In contrast, in Indonesia, the urban
estimate is much larger (
−0.71
(urban) and
−0.29
(rural)).
The lower panel of Table 3 contains the estimates for the son's and daughter's samples.
In India, the estimate for sons is negative, and large in magnitude (-0.93), but the estimate
in the daughter's sample is positive and numerically much smaller (0.33) (both estimates are
signicant at the 1 percent level). The evidence in Table 3 thus suggests that the idea that
being born into a highly educated household confers on you double dividends is valid only
for the sons in India. However, the evidence below on the evolution of educational mobility
across cohorts shows that conclusions change across cohorts (see below). In China, higher
education of a father lowers the conditional variance of schooling for both sons and daughters,
but the magnitude of the impact is substantially larger for sons (-0.48 for sons, and -0.36 for
daughters). The evidence is dierent in Indonesia: there is no signicant dierence across
gender.
17
In the online appendix, we discuss the estimates for four subsamples dened by gender
and rural/urban location of a child (see Table A.1 in the online appendix section OA.1). The
evidence on India suggests that the rural daughters face very dierent educational prospects:
the impact of father's education is positive and numerically large for this subgroup, while
the eect is negative in the other three subgroups. The nding that the rural daughters are
qualitatively dierent from the other three groups also holds in China: there is no signicant
impact on conditional variance of rural daughter's schooling, while the eect is negative and
signicant in the other three subgroups.
(4.2) The Evolution of Conditional Variance: Evidence from Decade-wise Birth
Cohorts
Table 4 reports the estimates for equations (1) and (2) for decade-wise birth cohorts:
17
The standard mean eects (see the IGRC estimates in the odd numbered columns of Table 3) show that
the inuence of father's education is much higher for daughters in terms of the rst moment (expected years
of schooling) in China. The gender advantages thus are opposite in terms of the mean vs. conditional variance
eects. We propose and estimate summary measure of relative mobility that combines these two aspects in
section 5 below.
12

1950-1959, 1960-1969, 1970-1979, 1980-1989. The evidence shows interesting pattern in the
evolution of the inuence of family background on conditional variance of children's schooling.
If we focus only on the mean eect as is done in the existing literature, the evidence
suggests that relative mobility has improved in India and Indonesia over time, while it has
worsened in China. However, the impacts on the conditional variance show a much stronger
role of the family background in the recent decades which counteracts the improvements in
the mean eects. In all three countries, the inuence of father's education on the conditional
variance is negative and substantial in magnitude in the 1980s, suggesting that the children
born to educated parents gain in terms of a much lower conditional variance, in additional to a
higher conditional mean. There are dramatic dierences in the earlier cohorts across countries:
the estimate is negative in China, positive in Indonesia, and a zero eect in India for the 1950s
cohort. The estimate turns negative and signicant in Indonesia in the 1960s, and in India
a decade later in the 1970s. The inuence of family background on conditional variance has
increased dramatically, and relative mobility is substantially overestimated in both countries
in the recent decades if we ignore the impact of father's education on conditional variance.
In section (5) below, we combine the mean and conditional variance eects to provide risk
adjusted relative and absolute mobility measures.
The estimates disaggregated across gender and geography for dierent cohorts are reported
in the online appendix Tables A.2, and A.3 (please see online appendix section OA.1). Again,
the evidence suggests important heterogeneity across gender and rural-urban locations. The
inuence of family background on conditional variance in early cohorts is negative in the
urban and son's samples for India and China, but there is no signicant eect in Indonesia.
It is positive and numerically substantial in the rural and daughters samples for India and
Indonesia, but no signicant eect in China. The estimates turned negative in the 1980s even
in the rural and daughters samples in all three countries.
(4.3) Robustness Checks
We rst check whether the observed patterns in conditional variance of children's schooling
are primarily driven by functional form misspecication. As noted briey earlier, there is a
growing theoretical and empirical literature that suggests that the intergenerational educa-
13

tional mobility equation is quadratic (Becker et al. (2018) , Emran et al. (2020) ):
18
Sc
i=α+βSp
i+δ(Sp
i)2+ζi
(3)
If the true conditional expectation function is given by equation (3), but we estimate
the linear equation (1), the error term is
εi=δ(Sp
i)2+ζi
, and the conditional variance of
εi
is a function of father's education simply because of a misspecied functional form. To
check this, we estimate the mobility equation (3) and the impact of father's education on the
conditional variance dened in terms of
ζi
. The estimates for various samples are reported
in Tables A.4-A.8 in the online appendix section OA.2. The evidence suggests strongly that
the relationship between family background and conditional variance of children's schooling
uncovered in Tables 2-4 are not driven by functional form misspecication of the mobility
CEF.
The next question we address is whether the estimated impact of father's education on
conditional variance largely reects the omitted cognitive ability heterogeneity of children. For
this analysis, we take advantage of the IFLS-2014 survey in Indonesia which collected data on
multiple indicators of cognitive ability of a child (measurement taken in 2014 when the children
are adult): raven test scores and two memory tests. We construct an index of cognitive ability
in two steps. First, we construct the rst principal component of the dierent measures of
cognitive ability. In the second step, we regress the rst principal component on age and age
squared of a child to take out the Flynn eect. The residual from this regression is our index
of cognitive ability of a child. We control for the ability index and its squared in the regression
for conditional variance in equation (2) above. The estimates for the full sample are reported in
online appendix Table A.4 (see online appendix section OA.3). The main message that comes
out is that the estimated eects of father's education on conditional variance of schooling
of children are not driven by omitted ability heterogeneity. Even though ability controls
18
Most of the studies on intergenerational income mobility use a specication linear in logs. Bratsberg et al.
(2007) nd that it is convex in Norway, Denmark, and Finland, but closer to linear in the United States and
the United Kingdom. However, Chetty et al. (2014) report evidence of a concave relation (see their Figure 1)
in the United States, and a recent analysis by Mitnik et al. (2018) provides evidence that the income mobility
equation is convex in the United States.
14

reduce the estimated coecient, the inuence of father's education still remains substantial
and statistically signicant at the 1 percent level. The estimates for other subsamples are
available from the authors.
(5) Combining the Mean and Conditional Variance Eects: New (and More
Complete) Measures of Relative and Absolute Mobility
The evidence presented above suggests strongly that it is important to understand the
inuence of family background on the conditional variance in addition to the standard mean
eects. In this section, we develop an approach that combines the mean and variance eects
using standard results from the theory of decisions under uncertainty.
Assume a concave payo function (utility function) dened over the possible schooling
outcomes of a child
i
,
W(Sc
i)
. Denote the expected schooling conditional on parental education
as
E(Sc
i|Sp
i)
, and
i=Sc
i−E(Sc
i|Sp
i)
. So we can rewrite
W(Sc
i) = W(E(Sc
i|Sp
i) + i)
.
Using the intergenerational mobility equation (1) above,
E(Sc
i|Sp
i) = α+βSp
i
, which implies
W(Sc
i) = W(α+βSp
i+i)
.
We have the following:
EW (Sc
i) = W(α+βSp
i−Πi)
(4)
where
Πi
is the risk premium which depends on the variance of
εi
.
Assuming a CRRA form of the W(.) function and using second order Taylor series expan-
sions around the conditional mean, the risk premium can be written as:
Πi=1
2
σ2
i
(α+βSp
i)R
(5)
where
V ar(εi) = σ2
i
, and
R
is the parameter of relative risk aversion in the CRRA util-
ity/payo function (see, for example, Eeckhoudt et al. (2005)). Using equation (2) and denot-
ing an estimated parameter by a hat, we can have an estimate of the risk premium conditional
on parent's education as below:
ˆ
Πi|Sp
i=1
2
nˆ
θ0+ˆ
θ1Sp
io
ˆα+ˆ
βSp
iR
(6)
15

Combining (4) and (6), we have:
EW (Sc
i|Sp
i) = W
ˆα+ˆ
βSp
i−1
2
nˆ
θ0+ˆ
θ1Sp
io
ˆα+ˆ
βSp
iR

(7)
Since
W(.)
is a monotonically increasing function, the rankings remain the same if we use
ˆα+ˆ
βSp
i−1
2
nˆ
θ0+ˆ
θ1Sp
io
ˆα+ˆ
βSp
iR
instead of the RHS of equation (7).
We propose measures of absolute and relative mobility based on
ˆα+ˆ
βSp
i−1
2
nˆ
θ0+ˆ
θ1Sp
io
ˆα+ˆ
βSp
iR
.
This has some important advantages compared to the measures of mobility based on equation
(7) above, as we will see below. Let
Ψi(Sp
i) = ˆα+ˆ
βSp
i−1
2
nˆ
θ0+ˆ
θ1Sp
io
ˆα+ˆ
βSp
iR
(8)
Ψi(Sp
i)
is our measure of absolute mobility for child
i
which shows the risk adjusted ex-
pected years of schooling of children conditional on father's schooling (called
RESi
for short).
This measure is similar to the other measures of absolute mobility based on the conditional
mean function; see, for example, Chetty et al. (2014) in the context of intergenerational income
mobility.
The measure of relative mobility is:
RIGRCi=∂Ψ
∂Sp
i
=ˆ
β−R
2ˆα+ˆ
βSp
i

ˆ
θ1−
ˆ
βnˆ
θ0+ˆ
θ1Sp
io
ˆα+ˆ
βSp
i


(9)
The measures of mobility in equations (8) and (9) are based on a linear conditional variance
function as in equation (2). Our empirical analysis is based on the measures in equations
(8) and (9). In the appendix, we derive the risk adjusted measures for the case of a semilog
formulation of the conditional variance function as is done in some models of heteroskedasticty.
An important advantage of the measures of relative and absolute mobility in equations
16

(8) and (9) is that they are readily comparable to the standard estimates of mobility (they
are measured in the same units: years of schooling). A second perhaps more important
feature of the proposed measures is that they yield the standard measures of relative and
absolute mobility currently used in the literature under risk neutrality. For example, consider
the workhorse measure of relative educational mobility in the current literature called IGRC,
estimated as the parameter
β
in equation (1). For the risk neutral case, we have
R= 0,
and
relative mobility from equation (9) is equal to
β
(IGRC). Under risk aversion, the extent of
underestimation when we omit the eects of family background on the conditional variance is
given by the second term in equation (9).
It is also important to appreciate some of the dierences between the standard measures
and the risk-adjusted measures proposed here. Even though all the estimates of
β
as a
measure of relative mobility we are aware of fall in the open interval
(0,1)
, the risk adjusted
measures may not be contained in this interval. For example, when the ratio of conditional
variance to conditional mean is large, the risk premium in equation (9) can be large enough
to make RIGRC estimate greater than 1.
19
This implies that the conventional argument that
1−β
can be interpreted as a measure of mobility (while
β
is a measure of intergenerational
persistence) may not be useful in this context. We propose the inverse of RIGRC for such an
interpretation.
20
To operationalize equations (8) and (9), we need an estimate of the CRRA coecient
R
.
A substantial literature suggests that a CRRA utility function with risk aversion parameter
of 1 is consistent with a variety of evidence (see, for example, Chetty (2006) on the United
States, and Gendelman and Hernández-Murillo (2014) for cross country evidence including
many developing countries). We will thus set
R= 1
for our estimation below.
21
19
This, however, does not mean an explosive process, as the magnitude of RIGRC declines with father's
education.
20
Note that we use the linear mobility CEF as the default specication for the mobility equation because it
is almost universally used in the existing studies on intergenerational educational mobility with a few recent
exceptions. As noted earlier, recent evidence suggests that the mobility CEF is likely to be concave or convex
in many cases. In such cases, relative mobility varies across the distribution without any risk adjustments, and
one can nd that the marginal eect of father's education on children's schooling is larger than 1, especially
in the lower tail (for concave CEF) or the upper tail (for convex CEF). Thus, in a nonlinear model, using the
inverse of the marginal eect of father's schooling as a measure of mobility seems more appropriate.
21
While a CRRA coecient of 1 across countries helps understand the role played by the inuence of family
background on conditional variance, one might prefer to use country-specic estimates of the CRRA coecient
17

Observe that when the inuence of father's education on the conditional variance is nega-
tive (i.e.,
θ1<0)
, the second term in equation (9) is unambiguously positive, and the estimate
of risk adjusted relative immobility is necessarily larger than the standard estimate. However,
the term in brackets can be negative even when
θ1>0
, for example, when the conditional
variance term
nˆ
θ0+ˆ
θ1Sp
io
is large (more likely in rural areas subject to weather shocks to
agriculture). When comparing dierent groups, the risk adjusted estimates may be very dif-
ferent from the canonical IGRC estimates even if the impact of father's education on the
conditional variance (i.e.,
ˆ
θ1
) is similar across groups, because of dierences in the magnitudes
of
ˆ
θ0
across groups.
(5.1) Estimates of Risk Adjusted Measures: Mobility across the Distribution
of Father's Education
The standard measure of relative mobility in the workhorse linear model given by the slope
of the mobility equation, IGRC, does not vary across the distribution of father's schooling.
In contrast, the RIGRC estimates from a linear mobility model vary with father's education
level because the risk premium is dierent across dierent levels of parental education. As
noted earlier, the risk premium depends on the ratio of conditional variance to conditional
mean. Figures 1A (China), 1B (India), and 1C (Indonesia) present the graphs of the estimated
conditional mean and conditional variance functions using the full sample (1950-1989). The
graphs show that the ratio of conditional variance to conditional mean is large in the low
educated households, and the ratio declines with father's education. This suggests that the
risk premium at the lower end of the distribution is substantially higher, and we expect risk
adjustments to substantially reduce the estimates of both relative mobility (RIGRC larger than
the IGRC) and absolute mobility (RES lower than ES) of the most disadvantaged children.
The estimates of the risk adjusted relative and absolute mobility for the full sample are
reported in Table 5 along with the standard estimates for ease of comparison. Figures 2A
(China), 2B (India), and 2C (Indonesia) present the graphs of RIGRC and IGRC estimates,
and the corresponding estimates of absolute mobility (RES and ES) are in Figures 3A (China),
3B (India) and 3C (Indonesia). Consistent with the discussion above, the evidence conrms
when the focus is on interregional and intergroup dierences within the same country.
18

that accounting for risk reveals much worse educational opportunities for the children born
to fathers with low or no education. The gap between the RIGRC and IGRC estimates
is the largest for the children of fathers with no schooling, and the same is true for the
gap between
ES
(expected years of schooling) and
RES
(risk adjusted expected years of
schooling). For relative mobility, the canonical IGRC estimate underestimates the inuence
of family background for this most disadvantaged subgroup of children by 41 percent in China,
63 percent in India, and 28 percent in Indonesia.
For absolute mobility, a comparison of the
RES
estimates with the
ES
estimates (see Table
4) show that a failure to take into account the eects on conditional variance overestimates
the expected years of schooling for this subgroup of children by 48 percent in China, and by
about 26 percent in India and Indonesia.
A second important conclusion that comes out of the evidence is that, for the children
of college educated fathers, the standard estimates are reasonably close to the risk adjusted
estimates. For example, the standard IGRC overestimates relative mobility of the children
of college educated fathers by 6.2 percent and absolute mobility by 4.1 percent in India, and
the corresponding numbers for Indonesia are 5.6 percent and 2.1 percent. The biases in the
corresponding estimates for China are larger, but even then, the biases are about half of that
found for the subgroup where fathers have no schooling. The evidence thus suggests that the
failure to consider the implications of family background for the second moment of data may
not be as consequential for the children born into highly educated households.
The estimates of the risk adjusted and standard measures of relative and absolute mobility
across the distribution for rural vs. urban areas are reported in Table 6A for all three countries.
The estimates of gender dierences are reported in Table 6B. The evidence suggests that the
standard measures of mobility consistently overestimate the educational opportunities for
the disadvantaged children (father with low education). The risk adjustments make a big
dierence specially for the rural areas and the daughters.
(5.2) Estimates of Risk Adjusted Measures: Relative Mobility across Countries,
Regions, and Gender
Since the risk adjusted relative mobility varies across the distribution, it does not provide
19

us with a summary statistic such as IGRC which can be easily compared across countries,
regions, and dierent social groups. For such comparisons, we calculate a weighted RIGRC
using the proportion of children as weights. As a summary measure of relative mobility,
weighted RIGRC may be specially useful for policymakers.
The weighted RIGRC for various sub-samples dened by gender and geography (ru-
ral/urban) are reported in the odd numbered columns in Table 7 for our main estimation
sample of 1950-1989 birth cohorts. For ease of comparison, the corresponding standard IGRC
estimates are in the even numbered columns. The estimates show that the RIGRC estimates
are uniformly larger than the corresponding IGRC estimates, and the dierence is substantial
in magnitude. For example, the estimates for the aggregate sample in row 1 of Table 7 suggest
that the magnitude of underestimation in the standard IGRC estimate is 26 percent in China,
41 percent in India and 10.4 in Indonesia. The cross-country rankings do not change when we
use RIGRC instead of IGRC estimates.
However, when comparing dierent subgroups (based on gender and geography), the rank-
ings based on the weighted RIGRC may be dierent (compared to the rankings based on
standard IGRC). For example, in India, the rural-urban gap in educational mobility seems
negligible according to the standard IGRC estimates (a 4.6 percent higher estimate in rural
areas), but the gap is much larger according to the weighted RIGRC estimates (20 percent
larger estimate in rural). Similarly, the standard IGRC estimates suggest no signicant gender
gap in India, while the RIGRC estimates reveal a substantially lower relative mobility for the
daughters. In India, the urban and rural daughters enjoy similar educational mobility accord-
ing to the standard IGRC estimates with a slight advantage in favor of the rural daughters (a
2.9 percent higher IGRC estimate for urban daughters). But the weighted RIGRC estimates
reveal a substantial disadvantage faced by the rural daughters (a 16.5 percent higher estimate
for rural daughters).
The estimates for decade wise birth cohorts show that the evolution of intergenerational
educational mobility has been very dierent in China compared to India and Indonesia (see
Table 8). China has become less mobile from the 1960s to the 1980s after experiencing a slight
improvement from 1950s to 1960s. In contrast, the estimates of both weighted RIGRC and
20

IGRC suggest that mobility has improved from the 1950s to the 1980s in India and Indonesia.
While both measures pick the time trend correctly, the standard IGRC underestimates the
improvements substantially, especially in India.
(6) Conclusions
A large literature on intergenerational mobility focuses on the eects of family background
on the conditional mean of children's economic outcomes and ignores any information con-
tained in the conditional variance. We provide evidence on three large developing countries
(China, India, and Indonesia) that suggests a strong inuence of father's education on the
conditional variance of children's schooling. We nd substantial heterogeneity across coun-
tries, gender, and geography (rural/urban). Cohort based estimates suggest that the eect
of father's education on the conditional variance has changed qualitatively, in some cases a
positive eect in the 1950s cohort turning into a substantial negative eect in the 1980s cohort.
The evidence on the eects of family background on the mean and conditional variance
suggests that being born into a more educated father brings in double advantages for children
in the form of a lower expected variance in schooling in addition to the standard higher ex-
pected years of schooling. We develop a methodology to incorporate the inuence of family
background on the conditional variance along with the standard conditional mean estimates.
Based on the standard results from the theory of decisions under uncertainty, we adjust the
canonical measure of intergenerational relative and absolute mobility by an estimate of the
risk premium associated with the conditional variance in schooling attainment faced by chil-
dren. The risk premium is determined by the ratio of conditional variance to conditional
mean along with the coecient of relative risk aversion. The estimates of the risk adjusted
relative and absolute mobility for China, India and Indonesia suggest that the current prac-
tice of ignoring the conditional variance results in substantial underestimation of the eects
of family background on children's educational opportunities. More important, the magni-
tude of underestimation in the standard measures is the largest for the most disadvantaged
children born into households where fathers have no schooling. The existing literature on
intergenerational educational mobility thus substantially overestimates the intergenerational
educational mobility of disadvantaged children. The standard (but partial) measure may lead
21

to incorrect ranking of countries in terms of relative mobility and underestimate the gender
gap and rural-urban gap in educational opportunities.
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Library of Munich, Germany.
Azam, M. and Bhatt, V. (2015). Like Father, Like Son? Intergenerational Educational
Mobility in India.
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Becker, G. (1991).
A Treatise on the Family
. Harvard University Press.
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