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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 eects 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 inuence 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 eects of family background on the conditional variance along with the standard

conditional mean eects. 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 eects 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 Pfeer, Joni

Hersch, Ira Gang, Tom Vogl, Cheng Chou for valuable comments on an earlier draft. We also benetted 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 eort. 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 dierent 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 dierent. 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 dierences) 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 eects 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 eects 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 eects 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 eects 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 conrming 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 inuence 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 inuence of father's education on

conditional variance is smaller in magnitude. The rural-urban dierence is specially striking

in India where the estimate is negative and large (-0.77) in the urban sample but small

and statistically not signicant (10 percent level) in the rural sample (-0.022). In contrast,

the rural-urban dierence is small in China: -0.55 (urban) and -0.52 (rural). We also nd

substantial gender dierences with a larger negative eect 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 dierences in India are the starkest: the estimated eect is negative in the sons

sample, but positive in the daughters sample.

6

The results from cohort-based analysis suggest

that the negative eect 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 eect 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-specication 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 eect 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 signicant at the 1 percent level.

Perhaps, the most important ndings from our exercise relate to the dierences 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 eect in the conditional variance regression. Please see section 2 below.

7

This suggests that the positive eect 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 signicant manner.

9

The smaller magnitude of underestimation in Indonesia despite a large inuence of father's education

on the conditional variance noted earlier reects 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 inuence of family background on conditional variance of schooling

makes a dramatic dierence 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 dierence.

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 eects 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 eect 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

dierent 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 dierences in the conditional variance and the conditional mean.

5

do not suer from any signicant 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 coecient (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 inuence 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 reect the interactions of a child's

11

Among many studies relying on this specication, 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

dierences across children from the same family (or similar family background where fathers

have the same education) are determined solely by the ability dierences 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 signicant 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 eects 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 aect 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 eectively 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 signicantly 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 inuence 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 dierent, they are interested in estimating a clean

measure of eort 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 eort and

choices. Similar to this paper, they recognize that the residual from a linear regression of

children's education on a set of variables dening the circumstances is not a clean measure

of eort as it partly reects the eects of family background.

15

As a measure of eort, 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 dierent

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 suer from any signicant sample truncation arising

from coresidency restrictions commonly used to dene 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 dierent 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 signicant 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 inuence on the expected schooling

of children, consistent with a large literature that focuses solely on the mean eects. 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 eect on conditional variance is the smallest (-0.38).

The inuence 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 dierences 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 eects of father's education on conditional variance is

large in urban sample (

−0.77

), but we cannot reject the null hypothesis of no inuence 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 eect hides important gender dierences

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

signicant 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 dierent in Indonesia: there is no signicant dierence across

gender.

17

In the online appendix, we discuss the estimates for four subsamples dened 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 dierent educational prospects:

the impact of father's education is positive and numerically large for this subgroup, while

the eect is negative in the other three subgroups. The nding that the rural daughters are

qualitatively dierent from the other three groups also holds in China: there is no signicant

impact on conditional variance of rural daughter's schooling, while the eect is negative and

signicant 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 eects (see the IGRC estimates in the odd numbered columns of Table 3) show that

the inuence 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

eects. 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 inuence of family background on conditional variance of children's schooling.

If we focus only on the mean eect 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 eects. In all three countries, the inuence 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 dierences in the earlier cohorts across countries:

the estimate is negative in China, positive in Indonesia, and a zero eect in India for the 1950s

cohort. The estimate turns negative and signicant in Indonesia in the 1960s, and in India

a decade later in the 1970s. The inuence 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 eects to provide risk

adjusted relative and absolute mobility measures.

The estimates disaggregated across gender and geography for dierent 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

inuence 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 signicant eect in Indonesia.

It is positive and numerically substantial in the rural and daughters samples for India and

Indonesia, but no signicant eect 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 misspecication. As noted briey 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 misspecied functional form. To

check this, we estimate the mobility equation (3) and the impact of father's education on the

conditional variance dened 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 misspecication of the mobility

CEF.

The next question we address is whether the estimated impact of father's education on

conditional variance largely reects 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 dierent 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 eect. 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 eects 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 specication 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 coecient, the inuence of father's education still remains substantial

and statistically signicant at the 1 percent level. The estimates for other subsamples are

available from the authors.

(5) Combining the Mean and Conditional Variance Eects: New (and More

Complete) Measures of Relative and Absolute Mobility

The evidence presented above suggests strongly that it is important to understand the

inuence of family background on the conditional variance in addition to the standard mean

eects. In this section, we develop an approach that combines the mean and variance eects

using standard results from the theory of decisions under uncertainty.

Assume a concave payo function (utility function) dened 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

iR

(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

iR

(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

iR

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

iR

.

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

iR

(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

2ˆα+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 eects 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 dierences 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 coecient

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 specication 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 eect 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 eect of father's schooling as a measure of mobility seems more appropriate.

21

While a CRRA coecient of 1 across countries helps understand the role played by the inuence of family

background on conditional variance, one might prefer to use country-specic estimates of the CRRA coecient

17

Observe that when the inuence 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 dierent 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 dierences 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 dierent across dierent 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 conrms

when the focus is on interregional and intergroup dierences 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 inuence

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 eects 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 dierences 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

dierence 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 dierent 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 dened 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 dierence 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 dierent subgroups (based on gender and geography), the rank-

ings based on the weighted RIGRC may be dierent (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 signicant 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 dierent 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 eects 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 inuence 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 eect

of father's education on the conditional variance has changed qualitatively, in some cases a

positive eect in the 1950s cohort turning into a substantial negative eect in the 1980s cohort.

The evidence on the eects 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 inuence 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 coecient 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 eects

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.

References

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ucational Mobility: Theory and Evidence from Indonesia. MPRA Paper 111125, University

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.

Becker, G., Kominers, S. D., Murphy, K., and Spenkuch,<