Estimating Intergenerational Mobility in Developing...

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Estimating Intergenerational Mobility inDeveloping Countries:

New Methods and Evidence from India

Sam Asher, World BankPaul Novosad, Dartmouth College

Charlie Rafkin, MIT

DEC Policy Research Talk

June 13, 2019

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Outline

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Motivation and Context

Estimating IGM in Developing Countries

Data

Results: Intergenerational Mobility in India

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Understanding local growth and development

I Broader agenda examines determinants of growth andstructural transformation in developing countries

I Explore within-country distribution of economic activity

I Assemble high spatial resolution administrative datasetscovering every business and individual in India

I Different papers testing the role of:I Natural resourcesI Local politicsI Infrastructure (roads, canals)I Urban-rural spillovers

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Motivation

I WDR 2006: Equity and Development starts with a comparisonof expected life outcomes for two children in South Africa

I Nthabiseng is black, poor parents, ruralI Pieter is white, rich parents, urban

I Then only three pages dedicated to intergenerational mobility,due to constraints on data and methods

I Since then: much progress in rich countries, much less indeveloping countries

I Today’s talk:I Methods to generate estimates of mobility that are valid for

comparisons across groups, time, geographyI Application to India: Ram vs Rahim

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Preview of PresentationOriginal Goal: Estimate intergenerational mobility in India, acrosssubgroups and across time (fathers and sons mostly, some newresults from women’s data)

Challenge: Changing education distribution, coarse measurementof education

Solution: Partial Identification of expected child rank given parentrank

Some Results:I No change in mobility from pre-liberalization to presentI Scheduled Castes and Tribes doing better, Muslims doing

worseI Substantial geographic variation

Other Applications of These Methods:I Rising Mortality in the U.S.I Fertility, Marriage, Bond Ratings, etc..

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Outline

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Data


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Motivation

The last three decades have been an economic miracle in India

1983

2012

0

.0002

.0004

.0006

.0008

.001

2000 4000 6000 8000 10000Real Household Per Capita Monthly Consumption (INR 2012)

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Motivation

The last three decades have been an economic miracle in India

0

2

4

6

Den

sity

0.00 2.00 4.00 6.00 8.00Education Level

1983 2012

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Two stories about modern India:

1. Markets overturn old hierarchies

I Caste identities less important in cities

I Political mobilization of marginalized groups

I Growing equality of opportunity?

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Two stories about modern India:

2. Persistence of Traditional Social Structure

I Punishment of norm violators, even in cities

I Identity-based politics

I Persistent inequality

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Research Agenda

Intergenerational Mobility: the dependence of children’s socialstatus on their parents’ social status

I A measure of equality of opportunity

I Implications for income inequality, but can moveindependently

I A central political issue in many countries, including U.S., andesp. subgroup mobility

I Affirmative action, tolerance of inequality and POUM (Benabou

and Ok 2001), criminal politics in India (Vaishnav 2017)

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Outline

Preview



Data


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Standing on the Shoulders of Giants

2006world development report

Equity and Development

32204

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Measurement of Mobility (Chetty et al. 2014)

I Common measures:I Absolute Upward

Mobility (p25)I Absolute Downward

Mobility (p75)I Rank-Rank Gradient (β)

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Estimating IM in Developing Countries: Challenges

I Matched parent-child income data is rarely availableI And almost never at same age → life cycle bias

I Matched parent-child income data is unreliableI Key issue: measurement error → higher measured mobilityI Measuring rural income is hardI How to attribute household income to coresident

parents/children?

I Most studies in developing countries use education as YI Arguably the best available proxy for lifetime income

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Limitations of Conventional Method for IM Estimation

Standard approach:

I Linear estimation of child education (rank) on fathereducation (rank)

I High coefficient → Low mobility

Some weaknesses of this measure:

1. Pools information from top and bottom of rank distribution

2. Not useful for subgroup analysis

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Gradient Not Useful for Subgroup Analysis

0

20

40

60

80

100C

hild

Ran

k

0 20 40 60 80 100

Parent Rank

Group 1

Group 2

Group 2 has a lower rank-rank gradient → more mobile?

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Limitations of Conventional Method for IM Estimation

Standard approach:

I Linear estimation of child education (rank) on fathereducation (rank)

I High coefficient → Low mobility

Some weaknesses of this measure:

1. Pools information from top and bottom of rank distribution

2. Not useful for subgroup analysis

3. Education is observed coarselyI 57% of fathers of 1960s birth cohort in India have < 2 years

educationI Internationally comparable datasets (e.g. IPUMS) use ≤5 ed

bins

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Parent-Child Education Rank Distribution, India

Mean Son Rank by Father Rank (1960s birth cohorts, India)

0

20

40

60

80

100

Son

Ran

k

0 20 40 60 80 100

Father Rank

1960s Bin Means

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Comparing CEFs across time: India 1960s vs. 1980s

0

20

40

60

80

100S

on R

ank

0 20 40 60 80 100

Father Rank

1960s Bin Means1980s Bin Means

How should we compare the 1980 and 1960 birth cohorts?

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Other Approaches in the Recent Literature

I Card et al. (2018) on educational mobility (IEM) in the 1920sI Definition: the 9th grade completion rate of children whose

parents have 5–8 years of schoolI This is approximately E(y > 50|x = 50)

I Compare this in 1980s with Chetty measure E (y |x = 25)

I Alesina et al. (2019) on IEM in Sub-Saharan AfricaI Definition: Probability that a child completes primary school

conditional on a parent who didn’tI This is E(y > 52|x ∈ [0, 76]) in Mozambique...I ... and E(y > 18|x ∈ [0, 42]) in South Africa

I Our goal: calculate E (y |x ∈ [a, b]) for any a and b

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conditional on a parent who didn’tI This is E(y > 52|x ∈ [0, 76]) in Mozambique...

I ... and E(y > 18|x ∈ [0, 42]) in South Africa


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conditional on a parent who didn’tI This is E(y > 52|x ∈ [0, 76]) in Mozambique...I ... and E(y > 18|x ∈ [0, 42]) in South Africa


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Our Strategy: A Partial Identification Approach

I Key Idea: Under minimal assumptions, we can bound the setof feasible mobility functions

I Goal: Conditional expectation function of child rank givenparent education percentile rank

I Call this E (y |x = i)I From this function, we can calculate p25, p75, β, and other

measures of mobility

I Problem: Education rank X is interval censored — onlyobserved in coarse bins

I Solution: Use techniques from partial identification to boundchild rank (Manski and Tamer 2002; Asher, Novosad, andRafkin 2018)

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Two Candidate Father-Son CEFs: India (1960s birthcohort)

Key question: What can we say about the latent conditionalexpectation function?

I Both of these CEFs Y (i) fit the data with zero MSE

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Overview of Methods

I Assumption 1: There exists a latent education rank, observedin coarse intervals

I Arises out of the most standard human capital investmentmodel (e.g. Card 1999, Card et al. 2018)

I Schooling choice determined by heterogeneous cost andbenefit shifters

I Model suggests a continuous optimal level of schooling E foreach individual

I Individuals complete the last year with positive expected value

I High ranked individuals within bin would advance to next levelif marginal cost/benefit shifted only a little

I Note: this is a descriptive exerciseI We are not trying to estimate causal effects of parent

education

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Overview of Methods

I Assume:

1. There exists a latent education rank, observed in coarseintervals

2. Monotonicity: Expected child rank is weakly increasing inparent rank (Dardanoni 2012)

3. Child CEF has discrete jumps or kinks at major educationboundaries only (if at all)

4. Child rank directly observed (loosened in paper)

I Manski and Tamer (MT 2002)I Bound a CEF E (y |x) with interval-censored xI But bounds are too wide to be meaningful in this case

I Three extensions to MT can get us useful estimates:

1. Use knowledge of the distribution (ranks are uniform)2. Constrain curvature of CEF3. Estimate E (y |x ∈ (a, b)) instead of E (y |x = i)

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An Example for Intuition

I Assume E (y |x ∈ (0, 60)) = 40, E (y |x ∈ (60, 80)) = 55.

I We want to know z = E (y |x ∈ (0, 50)).

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0

20

40

60

80

100

Chi

ld R

ank

0 20 40 60 80 100Parent Rank

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0

20

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60

80

100

Chi

ld R

ank

0 20 40 60 80 100Parent Rank

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0

20

40

60

80

100C

hild

Ran

k

0 20 40 60 80 100Parent Rank

Monotonicity within bin → z ≤ 40

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0

20

40

60

80

100C

hild

Ran

k

0 20 40 60 80 100Parent Rank

Monotonicity with next bin → z ≥ 37 — but suggests desirabilityof curvature constraint.

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Constraining Curvature of the CEF

I Edges of CEFs imply large discrete changes at arbitrary rankintervals

I These are unlikely to occur in real life

I Add assumption Y ′′(x) <= CI Numeric rather than analytic solution (currently) Setup

I Matlab solver calculates bounds on discrete approximation toCEF

I CEF approximation takes the form of 100 values for 100integer ranks

I Permit (but do not impose) sheepskin effects by allowingdiscrete jumps at bin thresholds (e.g. where people attaindegrees)

I Most extreme curvature constraint C = 0 gives us therank-rank gradient

I Curvature-constrained estimation generalizes the standardapproach

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Choosing a Curvature Restriction

How to choose C?

I We found parent-child income rank CEFs for USA, Denmark,Sweden, Norway Chetty et al. (2016), Bratberg et al. (2017)

I Fit splines to each of these and calculate max 2nd derivativeExample Spline

I Conservative C : Double the maximum value of 1.6 to get∼ C = 3

I All results go through without curvature constraint

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CEF Bounds under Interval Data: Manski-Tamer 2002

0

20

40

60

80

100

Par

ent r

ank

0 20 40 60 80 100Child rank

MT Bounds under an Unknown Distribution Bin Means

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CEF Bounds under Interval Data: Uniform X

0

20

40

60

80

100

Par

ent r

ank

0 20 40 60 80 100Child rank

Bounds under Uniform Distribution Bin Means

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CEF Bounds under Interval Data: C = 20

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Some Additional Details

I Validate this approach using fully supported income rank CEFfrom Denmark (Bratberg et al. 2017)

I Interval censor the data using education bin boundaries, andrecover bounds on the original CEF Simulation

I Can assume curvature constraint and loosen monotonicityassumption

I Allows estimation of interval-censored function even withoutmonotonicity assumption

I Get standard errors through bootstrap

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CEF Bounds With Bootstrap Errors: C = 3

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Introducing µba

I Same structure allows us to bound any function of the CEFI We focus on one function of interest µb

a = E (Y |x ∈ (a, b))I e.g., µ25

0 : expected child rank, given a parent in the bottom25%

I a and b can be arbitrary and unrelated to actual binboundaries

I Bounds on µba :

I Trivially point estimated if a and b are boundaries in the dataI Tightest when bin boundaries are close to a, b

I We will use µ500 and µ100

50I µ50

0 is a measure of upward mobility analogous to p25 fromChetty et al.

I p25 is the expected rank of a child born to the median parentin the bottom half

I µ500 is the expected rank of a child born to any parent in the

bottom halfI If the CEF is linear, µ50

0 = p25

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Mobility Statistics: 1960s birth cohort

Bounds on key mobility statistics C = 3:Gradient β: [0.45, 0.63]

Abs. Mobility p25: [31.0, 46.0]Interval Mobility µ50

0 : [36.5, 38.5]

Why are µ500 bounds so much tighter?

I Bin 1 has fathers in ranks 1-57:I µ57

0 is point identified – we observe it in the data

I µX0 is mean of µ1

0, µ21, ..., µ

XX−1

I Given µ570 and monotonicity, narrow set of possible values of

µ500 .

I In paper: proof of analytical bounds for µba given interval data

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Comparison with Other Approaches

Other approaches to dealing with coarse dataI Focus on groups for whom education has not changed very

muchI Useful, but limiting

I Assume linearity of CEFI Canonical approach in intergenerational educational mobilityI But many fully supported CEFs are concave at bottomI Doesn’t distinguish change at top from change at bottomI Identical to our approach with C = 0

I Randomly reassign people across bins to get same bin sizesI Common in the mortality / education literatureI Used in Fair Progress (2018)

I Concludes Ethiopia has almost perfect upward mobility

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Outline

Preview



Data


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Data

Two Data Sources

1. India Human Development Survey

I Household survey, men are asked about fathers’ educationI Because education is static, records mobility going back 30

yearsI Subgroup characteristics: caste and religionI Mothers/Daughters — data limitations, some preliminary

results

2. Socioeconomic and Caste Census (2012)

I Complete enumeration of household demographics and assetsI One of many administrative data sources used internally by

governmentI 31 million sons aged 20-23 who coreside with fathersI Limited subgroup characteristics—but has names

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The SHRUGThe Socioeconomic High-res Rural-Urban Geographic panel forIndia (SHRUG)

I High resolution socioeconomic aggregation of remote sensingand administrative data

I 600,000 villages and 5,000 towns from 1990 to the presentI Version 1.0 release is imminent

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Outline

Preview



Data


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Comparing 1950s to 1980s birth cohort (raw data)

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Comparing 1950s to 1980s birth cohort (preferredestimate)

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Comparing 1950s to 1980s birth cohort (naive estimate)

I Naive estimates suggests small but decisive mobilityimprovement

I Closes 40% of gap with USA, and 17% of gap with DenmarkI Nonparametric graphs show this is driven by decrease in

persistence at the top

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Upward and Downward Mobility over Time: All India

Downward Mobility

Upward Mobility

20

40

60

80

Exp

ecte

d S

on R

ank

1950 1960 1970 1980 1990Birth Cohort

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Upward Mobility: By Subgroup

Forward / Others

Muslims

Scheduled Castes

Scheduled Tribes

25

30

35

40

45

Exp

ecte

d S

on R

ank

1950 1960 1970 1980 1990Birth Cohort

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Downward Mobility: By Subgroup

Forward / Others

Muslims

Scheduled Castes

Scheduled Tribes

50

55

60

65

70

Exp

ecte

d S

on R

ank

1960 1970 1980Birth Cohort

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High School (µ500 , i.e. given Parent in Bottom Half)

Forward / Others

Muslims

Scheduled Castes

Scheduled Tribes0

.05

.1

.15

.2S

hare

Son

s w

ith H

igh

Sch

ool+

1960 1970 1980Birth Cohort

Primary School Middle School University

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Gender and Mobility

I Thus far all results for fathers and sonsI Breaking out results by gender tells a richer story:

I Relative decline in Muslim education does not hold for womenI Same-sex parents matter most for children’s outcomesI Mother’s education cannot explain decline in Muslim mobility

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Educational Attainment by Group and Cohort (FullSample)

Women Men

0

2

4

6

8

Yea

rs o

f Edu

catio

n

1960 1970 1980

Forward / Other Muslim

SC ST

0

2

4

6

8

10

Yea

rs o

f Edu

catio

n

1960 1970 1980

Forward / Other Muslim

SC ST

I All groups gaining education

I Persistent gap between forward castes and others

I Muslim men but not women falling behind SCs

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Mobility by Gender

Mother−Son Mother−Daughter Father−Son Father−Daughter30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

Upw

ard

Mob

ility

(µ−

0−50

)

Upward Mobility by Parent/Child Gender (µ−0−50)

Mother−Son Mother−Daughter Father−Son Father−Daughter

43

43.5

44

44.5

45

Upw

ard

Mob

ility

(µ−

0−80

)

Upward Mobility by Parent/Child Gender (µ−0−80)

I Lower values mean that parent’s low rank matters more forchild outcomes

I Different intervals allow us to make different comparisons

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Mobility by Gender and Group


25

30

35

40

45

50

Upw

ard

Mob

ility

(µ−

0−50

)

Forwards Muslims

Scheduled Castes Scheduled Tribes

Upward Mobility by Parent/Child Gender (µ−0−50) group


35

40

45

50

Upw

ard

Mob

ility

(µ−

0−80

)

Forwards Muslims


Upward Mobility by Parent/Child Gender (µ−0−80) group

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Mother’s Education Does Not Explain Muslim Decline

1960s cohorts 1980s cohorts

0

.2

.4

.6

.8M

othe

r’s E

duca

tion

if F

athe

r in

Bot

tom

50%

Forwards/Others Muslims


I Fertility differences also unable to explain the gap

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How Much Does Geography Explain?

Two extreme hypotheses:

1. The mobility curve exists locally:I Within any location, boys with low-ranked fathers have little

opportunity to advanceI Within any location, mobility is highest for forwards and lowest

for Muslims

2. Group differences are entirely based on geography:I e.g. Maybe everyone does well in AP, and poorly in BiharI In places where Muslims live, everyone has low mobilityI If we control for place fully, group differences will disappear

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Mobility Differences Across Groups

41.2

28.8

36.8

33.0

0

10

20

30

40

Upw

ard

Mob

ility

Unadjusted

Upward Mobility By Group, Unadjusted

Forwards/Others Muslims


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Transform These to Mobility Gaps to Forward/Others

−12.4

−4.4

−8.2

−15

−10

−5

0

Upw

ard

Mob

ility

Gap

with

For

war

ds/O

ther

s

Unadjusted Within−State Mobility Within−District Mobility

Upward Mobility Gaps to Forward/Others, By Group

Muslims Scheduled Castes

Scheduled Tribes

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Mobility Gaps Controlling for State and District

−12.4

−4.4

−8.2

−10.2

−3.6

−6.3

−11.3

−3.8−3.4

−15

−10

−5

0

Upw

ard

Mob

ility

Gap

with

For

war

ds/O

ther

s

Unadjusted Within−State Mobility Within−District Mobility

Upward Mobility Gaps to Forward/Others, By Group

Muslims Scheduled Castes

Scheduled Tribes

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The Local Geography of Intergenerational Mobility

What characteristics of places predict high and low mobility?

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Mobility is Higher in Cities

0

20

40

60

80

100

Son

Edu

catio

n R

ank

0 20 40 60 80 100Father Education Rank

Rural Urban

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The Effect of Cities Depends on Group Identity

−12.3

−4.2

−7.3

−14.9

−4.6

−7.1

Muslims ScheduledCastes

ScheduledTribes Muslims Scheduled

CastesScheduled

Tribes

−20

−15

−10

−5

0

Upw

ard

Mob

ility

Gap

Rural Urban

Upward Mobility Gap Behind Forward / Others

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Regional Variation in Mobility is Substantial

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Local Variation in Mobility is Also Substantial

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Correlates of Rural Mobility

Share Scheduled Caste

SC/ST Segregation

Land Inequality

Consumption Inequality

Manufacturing Jobs Per Capita

Log Rural Consumption

Average Years Education

Average Remoteness

Primary Schools per Capita

High Schools per Capita

Share Villages with Paved Roads

Share Villages with Power

−2 0 2 4 6

Expected Upward Mobility Rank Gain from 1 SD Change

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Correlates of Urban Mobility

Log Population

Population Growth 2001−2011

Share Scheduled Caste

SC/ST Segregation

Consumption Inequality

Manufacturing Jobs Per Capita

Log Urban Consumption

Average Years Education

Primary Schools per Capita

High Schools per Capita

−2 0 2 4 6

Expected Upward Mobility Rank Gain from 1 SD Change

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Conclusions on Mobility in India

I Our method for calculating mobility is valid for comparisonacross subgroups, countries, and time when only educationaldata available for older generation

I Intergenerational mobility gains and growth are notinextricably linked

I Access to opportunity is improving for policy-targetedScheduled Castes, but Muslims are losing ground

I Contrasting political talking points on “Muslim appeasement”

I Substantial regional and local mobility variation

I Ongoing work on mechanisms: discrimination, affirmativeaction

I Long run: understanding barriers to migration, especially ruralto urban

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Appendix Figures

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Choosing a Curvature RestrictionPanel A: U.S.A. Panel B: Denmark

20

30

40

50

60

70

Son

ran

k

0 10 20 30 40 50 60 70 80 90 100Father Rank

2nd derivative in [−.009,.017]

Cubic spline, 4 knots

20

30

40

50

60

70

Son

ran

k

0 10 20 30 40 50 60 70 80 90 100Father Rank



Panel C: Sweden Panel D: Norway

20

30

40

50

60

70

Son

ran

k

0 10 20 30 40 50 60 70 80 90 100Father Rank



20

30

40

50

60

70

Son

ran

k

0 10 20 30 40 50 60 70 80 90 100Father Rank



Back

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Test Case: Simulate Interval Censoring in Danish Data

I We know the full CEF in DenmarkI Create parent bins on intervals from Indian data, and apply

interval censoringI All we will observe is mean child rank in each parent bin

I Calculate bounds using our methodology and compare tooriginal distribution

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Test Case: Raw Danish Data

20

30

40

50

60

70

Son

ran

k

0 10 20 30 40 50 60 70 80 90 100Father Rank



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Test Case: Simulated Interval Censoring in Danish Data

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Test Case: Recovering Bounds from Censored Data

Panel A Panel B

Panel C Panel D

Back

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Implementing the Curvature Constraint

I Numerically calculate set of feasible curvature-constrainedCEFs

I Minimize MSE with respect to data, i.e. match meanoutcome in each coarse bin

I Calculate the min and maximum of the CEF at a given pointthat satifies this minimum MSE

I MSE = 0 is possible

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Numerical Optimization Problem

We seek

Y min(i) = min{Y (i)} (1)

such that

Y (i) is weakly increasing in i (Monotonicity)

|Y ′′(i)| ≤ C , (Curvature)"KX

k=1

ik+1 − ik100

„„1

ik+1 − ik

Z ik+1

ik

Y (i)di

«− rk

«2#

= MSE

(MSE Minimization)

I MSE: Lowest attainable MSE under monotonicity and curvature

constraints

I Could use any desired loss function

Back

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