INCOME ELASTICITIES OF INTRA-HOUSEHOLD HEALTH GAPS IN INDIA

A THESIS

Presented to

The Faculty of the Department of Economics and Business

The Colorado College

In Partial Fulfillment of the Requirements for the Degree

Bachelor of Arts

By

Venkatasai Ganesh Karapakula

April 2016

ii

INCOME ELASTICITIES OF INTRA-HOUSEHOLD HEALTH GAPS IN INDIA

Venkatasai Ganesh Karapakula

April 2016

Economics

Abstract

This paper examines the relationship between household income and intra-household health gaps in India using a cooperative Nash bargaining model of household behavior, data from a recent nationally representative survey, and control function-based econometric methods. Intra-household health gaps, measured as the heterogeneity in the body mass indices (BMIs) and the average sub-optimality of the BMIs of adult members within a household, seem to be inelastic to increases in household income at the median level. However, for households at the tenth percentile of the income distribution, a one percent increase in household income would decrease intra-household health gaps by more than a half percent; the reduction in health gaps is by more than one-and-a-half percent for households affected by negative income shocks. On the other hand, for households with income at the ninetieth percentile, a one percent increase in household income would lead to an almost proportional increase in intra-household health gaps. Dynamics associated with bargaining power within a household help explain the economic mechanisms underlying these phenomena. These findings suggest that income redistributive policies designed to benefit any households with income at or beyond the median level may be counterproductive. However, systems that protect households against negative income shocks and severe poverty would have high social returns.

iii

ON MY HONOR, I HAVE NEITHER GIVEN NOR RECEIVED UNAUTHORIZED AID ON THIS THESIS

Signature

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TABLE OF CONTENTS

ABSTRACT ii 1 INTRODUCTION

1

2 LITERATURE REVIEW 6 2.1 Absence of the Microeconomic Kuznets Curve............................................. 6 2.2 Intra-household Nutritional Disparities.......................................................... 7 2.3 Nature of the Dual Burden Household........................................................... 8 3 THEORY 10 3.1 Conceptual Framework.................................................................................. 10 3.2 Measures of Intra-household Health Gaps..................................................... 17 3.3 Empirical Design............................................................................................ 25 4 DATA

31

5 RESULTS AND DISCUSSION 37 6 CONCLUSION

45

REFERENCES

47

Introduction

India’s real Gross Domestic Product in trillions of Indian rupees more than tripled

from about 15.2 in 1993–1994 to 49.2 in 2010–11, with 2004-05 as the base fiscal year

(Planning Comission, Government of India, 2014). In addition, the percentage of the

Indian population living below the poverty line decreased from about 45.3% in 1993 to

about 21.9% in 2011 (The World Bank, 2016). However, the Asian Development Bank

(2014) estimates that urban India’s Gini coefficient, a measure of income inequality,

increased from 0.344 in 1993 to 0.393 in 2010, while that of rural India increased from

0.286 to 0.3 in the same period.1 One could argue that the increase in income inequality

hindered poverty reduction to some extent in the last two decades and therefore that

India’s economic growth in the same period was not adequately “inclusive,” according to

the World Bank’s (2009) definition of “inclusive growth.”

A recent survey by the Pew Research Center (2014) indicates that roughly three

quarters of even the most fortunate or high-income Indians express strong unease about

the growing inequality in income and wealth. This is understandable because income

inequality has negative implications not only for poverty reduction but also for economic

1The Gini index equals twice the area between the Lorenz curve and the 45-degree line. It is equal to zero

in the case of perfectly equal income distribution and equals one when the highest income group possesses

all the income. According to the Congressional Budget Office (2015), the Gini index for the United States in

2011 was 0.59.

1

growth. There is some consensus among economists that inequality can hamper the

development of healthy and educated human capital and also cause political and economic

instability, reducing investment (Persson and Tabellini, 1994; Easterly, 2007; Berg, Ostry,

and Zettelmeyer, 2012). Using a recent cross-country panel data set, Ostry, Berg, and

Tsangarides (2014) find a robust correlation between lower net income inequality and

“faster and more durable growth, for a given level of [income] redistribution,” and also

conclude that both the direct and indirect effects of income redistribution are, by and

large, pro-economic growth.

Public spending is one of the means India uses to address its skewed income

distribution. Some of the Indian government’s redistributive fiscal policies, such as cash

transfers to poor pregnant women who need maternal health care services (Ministry of

Health and Family Welfare, Government of India, 2015) are designed to benefit specific

members within households. However, most of India’s major poverty alleviation and

redistributive programs are aimed at the household level. For example, the Public

Distribution System provides subsidized cooking fuel and ingredients to a household

based on its poverty status. In addition, the Mahatma Gandhi National Rural Employment

Guarantee scheme guarantees a hundred days of manual employment to every household

in rural India (The World Bank, 2011).

Inter-household redistribution, aimed at the convergence of incomes across

households, promotes welfare at the individual level only if the redistributed entity is

equally beneficial to all members of every recipient household. However, increases in the

perceived ‘average’ well-being of individuals within a household are not necessarily

accompanied by a decline in intra-household inequality in well-being (Haddad et

2

al., 1995). Many studies, such as those of Sen (1984) and Behrman (1988), document and

examine intra-household inequalities in calorie consumption between men and women

and also among children in rural India and Bangladesh. Accordingly, Haddad and Kanbur

(1990a) argue that neglecting intra-household inequality can lead to underestimation of

aggregate poverty and inequality levels. More recently, Lise and Seitz (2011) explore

consumption inequality in the United Kingdom. Their analysis shows that ignoring

intra-household consumption inequalities leads to underestimation of individual-level

consumption inequality by between 25% and 50%. In addition, Sahn and Younger (2009)

examine various countries, including Brazil, Ghana, and Vietnam, and find that about 50%

of the total inequality in the body mass index (BMI) at the country level is within

households. Thus, if an inter-household redistributive policy also aims to improve

well-being of all individuals, the design of such a policy should take intra-household

inequalities into account.

Since inter-household redistribution increases incomes of relatively poor households,

a basic question arises: how does the level of income of a household affect, if at all, its

intra-household inequality? Kuznets (1955), Bourguignon and Morrison (1990), Anand

and Kanbur (1993), and Barro (2000), among others, attempt to answer the

macroeconomic counterpart of this question: how does the level of national income of an

economy affect its income distribution? Kuznets (1955) hypothesized a long-run

relationship between income inequality and the level of national income: over the course

of a nation’s economic development, income inequality first increases but eventually

decreases with industrialization. Although there is mixed evidence for this hypothesis,

Barro (2000) finds that Kuznets’ hypothesized pattern is a regular feature in a panel of

3

countries. Barro (2000) puts this finding in the context of technological progress of an

economy: technological innovations initially increase income inequality, but this trend

reverses as more economic agents become familiarized with the new technology and go

through a process of re-education. However, there is a paucity of empirical

microeconomic literature on intra-household inequality.

Intra-household inequality is more subtle than inter-household income inequality.

For example, the notion of intra-household inequality in income might not even be

applicable in the case of a household with a family business or a household with income

pooling behavior. Thus, variation among members of a household with respect to some

other measure of individual well-being might be more appropriate in this context.

Intra-household inequality in physical well-being especially deserves concern. Anand

(2002) argues that “we should be more averse to, or less tolerant of, inequalities in health

than inequalities in income . . . [because] . . . health is a special good, which has both

intrinsic and instrumental value. Income, on the other hand, has only instrumental value.

[Health] directly affects a person’s well-being,” and so dealing with inequalities in health

is arguably more urgent.

Human beings are naturally heterogeneous, and so it is very difficult to holistically

and objectively compare the overall health of different people. Nevertheless, the body

mass index (BMI), which is the ratio of weight (in kilograms) to squared height (in square

meters), is one possible measure2 of individual well-being: it not only indicates caloric

consumption relative to the needs of a person but also reflects the individual’s command

2Although the BMI theoretically ranges from 0 to infinity, summary statistics in recent empirical literature

(Dutton and McLaren, 2014; Kline and Tobias, 2013) suggest that most adults have a BMI in the range

[10, 70]. The BMI also has an optimal range that depends on many factors, including ethnicity. For example,

an optimal range for the South Asian adult population is [18.5, 23] (The World Health Organization, 2004).

4

over both food and non-food resources, such as sanitary conditions and labor-saving

resources, within the household (Sahn and Younger, 2009). Thus, the distribution of the

body mass indices (BMIs) of the individuals within a household at the microeconomic

level can be thought of as analogous to the distribution of incomes of households within

an economy at the macroeconomic level.

As mentioned earlier, there is a sizable macroeconomic literature on the dynamics of

income inequality but relatively little microeconomic literature on intra-household

inequality. Although this limited literature (Sen, 1984; Behrman, 1988) examines

intra-household inequalities in caloric consumption in rural India, all of this literature

relates to the twentieth century independent India under the “License Raj,” which was a

system of mostly planned economy. There is a lack of empirical literature on

intra-household inequalities in India after its economic liberalization, which was initiated

in 1991. This study aims to help fill this void by estimating the income elasticities of

various types of gaps in health, or specifically the BMI, among adults within households

in twenty-first century India. If the income elasticities of intra-household health gaps are

negative, then there is a stronger case to be made for inter-household redistribution. On

the other hand, if the responsiveness of intra-household health inequalities to household

income is nil, positive or non-linear, then redistributive policies need to be not only

designed more carefully but also need to be simultaneously accompanied by measures to

reduce intra-household health gaps.

5

Literature Review

Absence of the Microeconomic Kuznets Curve

At the macroeconomic level, Kuznets (1955) analyzed data from the period of

industrialization of currently developed nations and then formulated the following

hypothesis: income inequality at the national level initially increases with economic

growth but eventually decreases. This hypothesis of an inverse-U-shaped relationship

between economic growth and income inequality, which is also referred to as the Kuznets

curve, was first accepted as a stylized fact around the 1970s, based on a number of

cross-sectional studies, such as those of Paukert (1973), Adelman and Morris (1973), and

Ahluwalia et al. (1979), which confirmed the relationship. However, Bourguignon and

Morrison (1990) found a weak association between per capita income and income

distribution in a cross-sectional study of developing countries. In addition, Anand and

Kanbur (1993) suggested that the inverse-U relationship between income and income

inequality weakened over time. However, using panel analysis of about 100 countries

from 1960 to 1995, Barro (2000) has re-established the inverted-U hypothesis of Simon

Kuznets (1955) as a “clear empirical regularity.”

At the microeconomic level, however, there is some theoretical support but weak

empirical evidence for an intra-household Kuznets curve. Kanbur and Haddad (1994) use

6

a Nash cooperative bargaining model and Haddad et al. (1995) use the framework of

household welfare maximization to show that “under certain conditions” bargaining

models predict a Kuznets-type inverse-U relationship between intra-household inequality

and average household well-being. On the basis of empirical evidence on calorie

adequacy from the Philippines, Haddad and Kanbur (1990b) argue in support of an

intra-household Kuznets curve. However, Haddad et al. (1995) later discover that this

relationship is not statistically significant. Sahn and Younger (2009) look for a more literal

version of the Kuznets curve concerning health inequalities; in other words, they ask

whether there is an inverted-U-shaped relationship between a household’s average BMI

and its dispersion in a number of developing countries, which do not include India. The

authors “do not find any evidence to support the idea of an intra-household . . . Kuznets

curve [of BMI inequality versus mean household BMI].” Instead, they find a generally

positive relationship between the two variables. In addition, some of their non-parametric

models indicate that intra-household inequality in BMI usually increases as household

expenditures increase, implying that the expenditure elasticity of intra-household BMI

inequality is mostly positive in the developing countries included in their analysis.

Intra-household Nutritional Disparities

Other studies (Rosenzweig and Schultz, 1982; Sen, 1984; Behrman, 1988; Behrman

and Deolalikar, 1990; Pitt et al., 1990; Thomas, 1990; Sahn and Stifel, 2002; Molini,

Nube, and Boom, 2009; Wittenberg, 2013) do not explicitly look for an inverse-U-shaped

relationship but find significant intra-household disparities in nutrition and food

consumption. Sen (1984) and Behrman (1988) observe significant calorie

7

consumption-related differences between men and women in rural India and Bangladesh.

Behrman and Deolalikar (1990) find that nutrient intakes for women have lower price

elasticities than do those for men, which implies that women are more vulnerable during

food shortages. Pitt et al. (1990) find that households in Bangladesh have significant

intra-household disparities in calorie consumption but are, interestingly, averse to

inequality. Sahn and Stifel (2002) find evidence of different parental preferences for

nutrition of boys and girls in Africa. Molini, Nube, and Boom (2009) find evidence of an

inverse-U-shaped relationship between the human development index (HDI) and female

BMI at the macro (cross-country) level. They also use data from Vietnam to show that a

certain income supplement improved health outcomes for men much more than women.

Wittenberg (2013) finds that “body mass increases with economic resources among most

Southern Africans” and also that unemployed people tend to have lower BMIs than the

employed, even after controlling for household level fixed effects.

Nature of the Dual Burden Household

There is a significant amount of recent research on the nature of the “dual burden”

household, a household with at least one overweight person and one underweight person.

Doak et al. (2002) use data from China and find that the “under/over household,” or dual

burden household, is more urban and has higher income, even after controlling for other

socioeconomic confounders. Doak et al. (2005) also confirm these results for other

countries, including Brazil, Indonesia, Russia, Vietnam, and the United States. Caballero

(2005) argues that the co-existence of underweight children and overweight adults within

the same family is a relatively new phenomenon in developing countries undergoing the

8

“nutrition transition, the changes in diet, food availability, and lifestyle that occur in

countries experiencing a socioeconomic and demographic transition.” Caballero (2005)

also finds that middle-income countries have higher percentages of households with dual

burden than countries with low Gross National Product (GNP) or high GNP. Roemling

and Qaim (2013) find that the phenomenon of dual burden within households is transitory

in Indonesia and that “most households that move out of the dual burden category end up

as overweight.” They also observe the highest prevalence of dual burden households in the

lowest expenditure quintile, implying that the expenditure elasticity of intra-household

BMI inequality in Indonesia is negative. This finding is somewhat in contrast with the

positive expenditure elasticties reported by Sahn and Younger (2009), although their study

pertains to developing countries that do not include Indonesia.

Although the recent studies mentioned above examine nutritional disparities and

health gaps within households in many developing countries, there is a dearth of

contemporary research specifically related to India in this area. Sen’s (1984) and

Behrman’s (1988) studies are the only notable ones that look specifically at India, but

these studies do not relate to contemporary India after its economic liberalization

beginning in 1991. In addition, most of the microeconomic studies mentioned above are

correlational in nature and do not specifically examine the microeconomic relationship

between intra-household health gaps and income. In contrast, this paper develops new

econometric techniques to estimate income elasticities of intra-household health gaps and

attaches economic meaning to these estimates in hope of aiding public policy. Even

though this paper’s geographical scope is limited to India, the econometrics used in this

study is quite broad and applicable to other countries as well.

9

Theory

Conceptual Framework

Although the empirical literature examining intra-household inequality and its

relationship with household income is not extensive, there is a relatively adequate

theoretical framework for analysis of intra-household inequality. The theoretical literature

on the behavior of households is mainly divided into two categories: unitary models and

non-unitary models. The so-called ‘unitary models’ of household behavior assume that a

household with many persons has a set of transitive and stable preferences, but there is an

increasing consensus in the economic literature that unitary models are not generally

practical (Browning, Chiappori, and Lechene, 2006). On the other hand, non-unitary

models3 allow for the possibility that the members of a household may have preferences

that differ from one another. Kanbur (1995) uses non-unitary models, which include

cooperative and non-cooperative models of intra-household resource allocation, within the

‘linear expenditure systems’ framework to theorize intra-household consumption

inequalities. The following non-unitary cooperative model of intra-household BMI

inequality is inspired by the theoretical analysis of Kanbur (1995), although Kanbur’s

(1995) main results are much different from those presented in this section.

3Donni and Chiappori (2011) broadly survey both the theoretical and empirical literature on non-unitary

models of household behavior. In addition, Chiappori and Meghir (2014) discuss some non-unitary models

of intra-household inequality.

10

Suppose that a household comprising n adults, where n ∈ N \ {1}, has resources to

allocate C calories among the adults so that c1 + c2 + · · · + cn = C, where ci is the total

number of calories consumed by the i-th adult. Suppose further that ci is the minimum

number of calories the i-th adult needs or is entitled to, depending on his or her height,

productivity, level of physical activity, basal metabolic rate, altruism, and so on, for all

i ∈ {1, 2, · · · , n}. If the adults engage in Nash bargaining to determine the final

allocation, Theorem 3 of Myerson (1979) guarantees that the outcome is given as the

solution to the following problem:

maxc1,c2,··· ,cn

n∏

i=1

(ci − ci)ai , (3.1)

subject to the following constraints: c1 + c2 + · · · + cn = C; a1 + a2 + · · · + an = 1; and

ci ∈ (ci, ∞) for all i ∈ {1, 2, · · · , n}. In the terminology of game theory, the parameters

c1, c2, · · · , cn are also called threat points or disagreement payoffs, and the parameters

a1, a2, · · · , an indicate the relative bargaining strengths of the adults. Internalizing the

constraint that ci ∈ (ci, ∞) for all i ∈ {1, 2, · · · , n}, the maximization problem (3.1) can

be re-formulated using a Lagrangian multiplier λ:

maxc1,c2,··· ,cn,λ

L =

[

n∑

i=1

ai ln(ci − ci)

]

+ λ

(

C −n∑

i=1

ci

)

. (3.2)

Then, the first-order conditions for problem (3.2) are

∂L∂λ

= 0 =⇒ C −n∑

i=1

ci = 0 =⇒n∑

i=1

ci = C

11

and

∂L∂ci

= 0 =⇒ ai

ci − ci

− λ = 0 =⇒ λci − λci = ai

for all i ∈ {1, 2, · · · , n}, implying that

n∑

i=1

(λci − λci) =n∑

i=1

ai =⇒ λ(C − C) = 1 =⇒ λ = (C − C)−1,

where C = c1 + c2 + · · · + cn. Thus, the set {(c∗1, c∗

2, · · · , c∗n, (C − C)−1)}, where

c∗i =

ai + [(C − C)−1]ci

(C − C)−1= ci + (C − C)ai (3.3)

for all i ∈ {1, 2, · · · , n}, is the set arg maxc1,c2,··· ,cn,λ

L.

Let hi and b∗i represent the i-th adult’s height and BMI in the current time period,

respectively. Further let wi = wi(t−1) − ρiτit, where wi(t−1) is his or her weight in the

previous time period, ρi is the reciprocal of his or her energy density (in calories per

kilogram) of added body tissue (so that ρi is in kilograms per calorie), and τit denotes the

number of calories expended in the current time period. Then, equation (3.3) implies that

b∗i =

ρic∗i + wi

h2i

=⇒ b∗i = (C − C)

ρiai

h2i

+ci + wi

h2i

(3.4)

for all i ∈ {1, 2, · · · , n}, since ρic∗i + wi represents the i-th adult’s weight in the current

time period.

Let b, u, and v be the discrete uniform random variables on the sets {b∗1, b∗

2, · · · , b∗n},

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{

ρ1a1

h2

1

, ρ2a2

h2

2

, · · · , ρnan

h2n

}

, and{

c1+w1

h2

1

, c2+w2

h2

2

, · · · , cn+wn

h2n

}

, respectively. Then, equation (3.4)

implies4 that

E(b2) − [E(b)]2 = (C − C)2{E(u2) − [E(u)]2} + {E(v2) − [E(v)]2}

+ 2(C − C){E(uv) − E(u)E(v)}, (3.5)

where E represents expected value. Accordingly,

var(b) = (C − C)2 var(u) + 2(C − C) cov(u, v) + var(v)

=⇒ σ2b = σ2

u(C − C)2 + 2σuv(C − C) + σ2v , (3.6)

where σ2b = var(b), σ2

u = var(u), σuv = cov(u, v), and σ2v = var(v). Suppose that C is the

number of calories needed to satiate all the members of the household. Then,

{(σ2u, σuv, σ2

v) ∈ R≥0 × R × R≥0 : σ2ud2 + 2σuvd + σ2

v ≥ 0 ∀d ∈ (0, C − C)} is the set

containing all the economically feasible values of σ2u, σuv, and σ2

v , since σ2b ≥ 0 and

C > C > C. Then, for all C ∈ (C, C),

∂σ2b

∂C= 2σ2

u(C − C) + 2σuv, (3.7)

4Note that equation (3.4) implies that bi = (C − C)ui + vi for all i ∈ {1, 2, · · · , n}. It follows that

Pr(u = ui, v = vi) = Pr(b = bi) = 1/n for all i ∈ {1, 2, · · · , n}. In addition, Pr(u = ui, v = vj) = 0for all i 6= j ∈ {1, 2, · · · , n}, implying that

∑

i

∑

j Pr(u = ui, v = vj) =∑

i Pr(b = bi) = n · (1/n) = 1

and that E(uv) =∑

i

∑

j uivjPr(u = ui, v = vj) = (1/n)∑n

k=1vkuk. Hence, E(b2) = (1/n)

∑

i b2

i =

(1/n)∑

i[(C − C)ui + vi]2 =

[

(C − C)2 · (1/n)∑

i u2

i

]

+[

2(C − C)(1/n)∑

i uivi

]

+[

(1/n)∑

i v2

i

]

,

so E(b2) = (C − C)2E(u2) + 2(C − C)E(uv) + E(v2). This result directly leads to equation (3.5), after

observing that [E(b)]2 = [(1/n)∑

i bi]2 = (C − C)2[E(u)]2 + 2(C − C)E(u)E(v) + [E(v)]2.

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which implies that

∂2σ2b

∂C2= 2σ2

u ≥ 0. (3.8)

In other words, a Kuznets curve or, specifically, a concave quadratic curve plotting

intra-household inequality (σ2b ) against calorie consumption is an impossibility in this

particular model. However, if Y represents household income, then5

∂2σ2b

∂Y 2= 2

σ2u

(

∂C

∂Y

)2

+ (C − C) · ∂2C

∂Y 2

+ σuv · ∂2C

∂Y 2

, (3.9)

and so clearly∂2σ2

b

∂Y 2< 0 for all C ∈ (C, C) if

σuv < −σ2u

(

∂C

∂Y

)2

+ (C − C) · ∂2C

∂Y 2

÷ ∂2C

∂Y 2

for all C ∈ (C, C). Hence, this model does not rule out a Kuznets curve of

intra-household BMI inequality with respect to household income. However, the key

insight of this bargaining model is not the possibility of a microeconomic Kuznets curve

but the relationship described by equation (3.6). The equation,

σ2b = σ2

u(C − C)2 + 2σuv(C − C) + σ2v ,

has three implications. First, σ2v , which represents the relative differences in minimum

5Note that∂2σ2

b

∂Y 2 = ∂∂Y

(

∂σ2

b

∂Y

)

= ∂∂Y

(

∂σ2

b

∂C· ∂C

∂Y

)

= ∂∂Y

(

∂σ2

b

∂C

)

· ∂C∂Y

+∂σ2

b

∂C· ∂2C

∂Y 2 , which equals(

∂2σ2

b

∂C2 · ∂C∂Y

)

· ∂C∂Y

+[

2σ2

u(C − C) + 2σuv

]

· ∂2C∂Y 2 = 2σ2

u

(

∂C∂Y

)2

+[

2σ2

u(C − C) + 2σuv

]

· ∂2C∂Y 2 , resulting

in equation (3.9).

14

caloric needs or entitlements, contributes to intra-household BMI inequality without any

dependence on the household’s aggregate caloric consumption.

Second, σuv, which represents the covariance of the relative bargaining powers and

the caloric needs or entitlements of the household members, contributes to BMI inequality

through its interaction with total household caloric consumption. Since σ2u ≥ 0 and

σ2v ≥ 0, a reduction in BMI inequality with an increase in consumption is possible only if

the covariance, σuv, is negative.

Third, since σ2u, which represents the relative variation in the bargaining powers of

the household members, contributes to intra-household inequality through its interaction

with the squared term of consumption, even moderate increases in consumption can

increase BMI inequality considerably if σ2u is high. Equation (3.7) describes the last two

implications more formally.

It is not possible to test the empirical validity of equation (3.6) because σ2u, σuv, σ2

v ,

and (C − C) are all latent variables. Nonetheless, the theoretical insights of this model are

still useful for estimating the income elasticities of intra-household health gaps. Suppose

that the econometrician knows a priori that

C − C = γ1Ψc + γ2, (3.10)

where γ1, γ2, ∈ R are parameters and Ψc is an observable. For example, equation (3.10)

can be thought of as describing an Engel curve, in which case Ψc would be a function of

household income. Then, the right hand side expression of equation (3.6),

σ2u(C − C)2 + 2σuv(C − C) + σ2

v , is equal to

15

(σ2uγ2

1)Ψ2c + (2σ2

uγ1γ2 + 2σuvγ1)Ψc + (σ2uγ2

2 + 2σuvγ2 + σ2v). (3.11)

This provides a non-rigorous reason for modeling intra-household variation in body mass

indices as a linear combination of the observables Ψc, Ψ2c , and a constant.

Suppose that there is an optimal level B of BMI for a healthy adult. Then, E[|b − B|]

represents the household’s average deviation from the optimal BMI level. In other words,

E[|b − B|] represents the overall level of sub-optimality of the body mass indices. Then,

compared to var(b), a more holistic notion of an intra-household health gap is some linear

combination of variation in the BMIs and overall sub-optimality of the BMIs of the adults,

that is, γ3 · var(b) + γ4 · E[|b − B|], where γ3, γ4 ∈ R+ are some constants chosen by the

econometrician. Since equation (3.4) implies that

E[|b − B|] = (C − C)(Eu|b>B[u] − Eu|b<B[u]) + (Ev|b>B[v] − Ev|b<B[v])

− (Eb|b>B[B] − Eb|b<B[B]), (3.12)

it follows from equation (3.10) that γ3 · var(b) + γ4 · E[|b − B|] is equal to

γ3(σ2uγ2

1)Ψ2c + [γ3(2σ2

uγ1γ2 + 2σuvγ1) + γ4(γ1(Eu|b>B[u] − Eu|b<B[u]))]Ψc

+ [γ3(σ2uγ2

2 + 2σuvγ2 + σ2v) + γ4(γ2(Eu|b>B[u] − Eu|b<B[u]))

+ γ4((Ev|b>B[v] − Ev|b<B[v]) − (Eb|b>B[B] − Eb|b<B[B]))]. (3.13)

Again, this provides at least a non-rigorous reason for modeling intra-household health

gaps as a linear combination of the observables Ψc, Ψ2c , and a constant.

16

Measures of Intra-household Health Gaps

As mentioned earlier, the BMI reflects not only a person’s overall health but also his

or her command over both food and non-food resources within the household (Sahn and

Younger, 2009). However, an individual’s body mass index is only a proxy indicator of his

or her excess body fat. At the population level, however, the BMI of an adult is a strong

predictor of his or her body fat and risk of obesity-related illness, although the relationship

between BMI and body fat is uncertain in the case of children (National Obesity

Observatory, 2009).

The index is calculated the same way for both children and adults, but it is

interpreted differently for the two groups. Classifications of BMI depend on age and sex

for children and adolescents but not for adults (Centers for Disease Control and

Prevention, 2011). There exist schemes such as the one based on “BMI-for-age” (The

World Health Organization, 2006), or that of Cole et al. (2007) and, more recently, Cole

and Lobstein (2012) for standardizing the body mass indices of non-adults so as to make

them comparable to those of adults, but many of the standardization schemes may not be

reliable because they do not consider factors such as ethnicity by which the accurate

“BMI-for-age” varies. For example, in a longitudinal study of a population-based cohort

of men and women in Delhi, India, Sachdev et al. (2005) find that many subjects were

considered underweight-for-age as children but overweight or obese as adults. The

researchers also find a strong association between accelerated BMI gain in later childhood

and adolescence and increased adiposity and central adiposity in adulthood.

These findings suggest that the available international schemes for standardization of

17

body mass indices of non-adults may not always adjust the BMI of a non-adult in India

accurately enough for comparability with an adult’s BMI, although they may be useful as

rough measures of general health in an initial clinical examination of a non-adult. Thus,

measures of inequalities in BMI among adults in an Indian household may be more robust

than the measures of inequalities among all household members, justifying the exclusion

of non-adults from the analysis of this paper.

Unlike income, the BMI is practically bounded and also has an optimal range that is

well within the practical bounds. Although the BMI has a theoretical range of (0, ∞), any

BMI outside the range of [10, 70] can be considered an outlier for practical purposes6,

because it is very difficult to survive with such a BMI in the absence of serious medical

attention. For the South Asian adult population, an optimal range of BMI is [18.5, 23]

(The World Health Organization (WHO), 2004), which is smaller than the range [18, 25]

for Caucasian adults, since “South Asians have a muscle-thin but adipose body phenotype

and high rates of obesity-related disease” (Sachdev et al., 2005).

Many income inequality metrics are invariant to relative changes in the distribution

of values of income as opposed to absolute changes. However, such relative invariance

may not be appropriate for metrics that measure variation in variables such as the BMI.

Consider the pairs of values (20, 50), (10, 25), and (20, 45). If these pairs represent body

mass indices of two-person households, it is difficult to argue that the first pair has the

same inequality as the second pair and that the third pair has a lower inequality than the

second pair. For this reason, “invariance with respect to equal absolute changes might

6Dutton and McLaren’s (2014) and Kline and Tobias’ (2013) estimates of the kernel density of BMI

suggest that adults usually have a BMI in the range [10, 70].

18

seem more appropriate” than invariance with respect to equal relative changes while

measuring inequalities in health and the human lifespan (Atkinson, 2013).

In addition, most income inequality metrics require that the variable under

consideration be unbounded, at least from above, and have zero as a possible value, which

is clearly impossible in the case of BMI. Thus, many income inequality measures,

especially the relative ones, may not be appropriate for measuring inequalities in BMI and

other bounded variables with optimal ranges. Therefore, it would be more appropriate to

measure inequalities in BMI using an absolute metric, which is invariant to absolute

changes in the distribution of BMI values.

Another property of an ideal index for measuring BMI is additive decomposability; if

it is possible to divide the population under consideration into mutually exclusive and

completely exhaustive subgroups, additive decomposability would make it possible to

infer the proportion of overall heterogeneity in the BMI values that is due to variation

within each subgroup and the proportion that is due to variation between the subgroups. In

econometric analyses, additive decomposability “offers an opportunity to ‘control’ for

[sources of heterogeneity] that are classifiable when data are collected” (Maasoumi, 1999).

Karapakula (2016) axiomatically derives a unique absolute, additively decomposable

metric for measuring heterogeneity in a variable bounded by two real numbers α and β

such that α < β. This metric, termed the heterogeneity index, is an adjusted version of the

simple variance formula, because the supremum of the variance function of an odd

number of input variables is lower than that of an even number of input variables.

Specifically, the heterogeneity index Vβα of an N -component vector

19

x = (x1, x2, · · · , xN) ∈ [α, β]N is given by7

Vβα(x) =

8N

(β − α)2[2N2 − 1 + (−1)N ]

N∑

i=1

(xi − µ)2, (3.14)

where µ =1

N

N∑

i=1

xi. Although this is an absolute metric, it is invariant to the unit of

measurement used for measuring the components of x; specifically, if y = γ1x + γ21 so

that y ∈ [γ1α + γ2, γ1β + γ2]N for any two numbers γ1 ∈ (0, ∞) and γ2 ∈ R, then

Vγ1β+γ2

γ1α+γ2(y) = Vβ

α(x). In contrast, there exists no meaningful metric of inequality that is

generally unit-invariant in the case of an unbounded variable (Zheng, 1994).

As mentioned earlier, the BMI has a theoretical range of (0, ∞). However, a

practical range would be a bounded one. One such practical range of BMI values is

[10, 70]; this choice for the practical range is based on Dutton and McLaren’s (2014)

kernel density estimates of the BMI distribution. One could also choose a shorter range,

because Kline and Tobias’ (2013) kernel density estimates show a BMI distribution that is

bounded between 15 and 60. However, this paper chooses [10, 70] because

[15, 60] ⊂ [10, 70]. This study treats any outliers as missing values. A key advantage of

the heterogeneity index is that the lower and the upper bounds of the index can be

computed using a linear-time algorithm even when some values in the input vector are

missing (Karapakula, 2016). For these reasons, the heterogeneity index or, simply, the H

index H of a collection of BMI values, some of which may be missing, can be defined as

H = V7010 . This index indicates the extent to which the BMI values of the members of a

7In specific, an index of heterogeneity in bounded outcomes is symmetrical, continuous, twice-

differentiable, strict Schur-concave, has scaled additive subgroup decomposability, quasi-translation

invariance, and the property of comparability if and only if the index equals Vβα times a positive real number,

which in this case is chosen to be 1.

20

household differ from one another. To be specific, a value of zero indicates homogeneity

and a value of one indicates maximum heterogeneity, since 0 ≤ H ≤ 1.

Karapakula (2016) also proposes an index for measuring the sub-optimality of a

collection of values when there exists an optimal range, or, more generally, a set of

optimal values for the bounded variable. Suppose there is a function g that maps each

component xi of the vector x from [α, β] onto [0, 1] such that g ≡ 0 only on the subset of

optimal values in the interval [α, β] and such that g is continuous on (α, β). Then, the

sub-optimality index Sβα of the vector x is given by

Sβα(x; g) =

1

N

N∑

i=1

g(xi). (3.15)

Cao et al. (2014) find that the risk of death for people with a BMI value lower than

18.5 is on average 1.8 times that of a person with an optimal BMI, which for South Asian

adults is in the range [18.5, 23]. The authors also find that the risk of death for overweight

persons, who have a BMI between 23 and 30, and for obese persons, who have a BMI of

30 or more, are 1.2 times and 1.3 times higher on average, respectively, than a person with

an optimal BMI. This justifies the proposition that the sub-optimality of BMIs of South

Asian adults can be roughly measured using the following sub-optimality function g. As

shown in Figure 1, for all x ∈ [10, 70],

g(x) =

18.5 − x

18.5 − 10if 0 ≤ x < 18.5

0 if 18.5 ≤ x ≤ 23

x − 23

70 − 23if 23 < x ≤ 70.

(3.16)

21

Figure 1

The Proposed Sub-optimality Function for the Bounded BMI of South Asian Adults

10 20 30 40 50 60 70

BMI

0.2

0.4

0.6

0.8

1.0

g

Source: author’s calculations.

Then, the sub-optimality index S of a collection of BMI values is given by

S(x) = S7010 (x) = 1

N

∑Ni=1 g(xi) for all x ∈ [10, 70]N , where N ∈ N. This measure

indicates the average level of sub-optimality of the BMI values of the members of a

household.

The sub-optimality index and the heterogeneity index can be combined to form a

hybrid inequality index called the suboptimality-and-heterogeneity index or, simply, an

SH index Ii given by Ii = 4−i4

S + i4H for a chosen number i ∈ {0, 1, 2, 3, 4}. According

to this index, there is no inequality only when the BMI values of a household are

homogeneous (or have no heterogeneity) and are optimal (or have zero sub-optimality). In

other words, the SH indices equal zero for a two-person South Asian household only

when both the BMI values of that household are equal and are optimal, that is, between

22

18.5 and 23.

On a related note, the SH indices achieve their maximum value of one only when the

BMI values of a household have maximum heterogeneity and sub-optimality. For a

two-person household, the SH indices have their maximum value of one only when one of

the household members has a BMI of 10 and the other has a BMI of 70. Just as in the case

of the H index, an SH index can be bounded even when there are missing BMI values.

Figure 2 shows the graph of I2 = 12S + 1

2H for a two-person South Asian household.

Figure 2

The SH Index I2(BMI1, BMI2) for a Two-Person South Asian Household

Source: author’s calculations.

Because 0 ≤ Ii ≤ 1 for all i ∈ {0, 1, 2, 3, 4}, these indices need to be mapped into R

before the econometrician has access to models that depend on continuity of the

dependent variable on the real line. Although there are many choices for such a mapping,

this paper chooses the probit function, because it is much smoother than the alternatives

23

such as the logit function or the complementary log-log function. Thus, the transformed

SH indices Θi are given by

Θi = Φ−1(Ii), (3.17)

where Φ is the standard cumulative normal function, for all i ∈ {0, 1, 2, 3, 4}. In this

paper, the index Θ2, given by

Θ2 = Φ−1(I2) = Φ−1(

1

2S +

1

2H)

, (3.18)

is the main dependent variable of interest, since it weights both heterogeneity in BMIs and

sub-optimality of BMIs equally.

Thus, the index Θ2 represents intra-household health gaps in the rest of the paper,

unless specified otherwise. Nevertheless, Θ1 and Θ2 serve as dependent variables for

robustness checks. Since Φ−1(0) and Φ−1(1) are not finite, they can be winsorized, that is,

they can be set equal to a value that is an order of magnitude below or above the observed

minimum and maximum values of the indices, respectively. Note that these transformed

indices can also be bounded in the case of missing BMI values, because the SH indices

can be bounded.

Therefore, Θ2 serves as the main measure of intra-household health gaps in this

study because it equally informs two dimensions of inequality in BMI within a household,

as Θ2 attaches equal importance to heterogeneity in BMIs and average sub-optimality of

BMIs in a household.

24

Empirical Design

As discussed in Section 3.1, intra-household health inequalities can be modeled as a

linear combination of the functions of the variables that influence household caloric

consumption.

Since the total household income influences total household caloric consumption and

household income can be negative, this paper uses Λ(Y ), where Λ(·) = sinh−1(·) and Y is

the total household income, as an observable that influences caloric consumption of the

household. The inverse hyperbolic sine transformation is useful in estimating the income

elasticity of an intra-household health gap. Consider the following relationship between a

measure of intra-household health gap G and household income Y :

Λ(G) = κ0 + κ1Λ(Y ) + κ2[Λ(Y )]2 + f + e, (3.19)

where κ0, κ1, and κ2 are parameters to be estimated, f is a function of variables other than

Y , perhaps also containing some additional parameters, and e describes the error process

unrelated to Y . Then,

∂Λ(G)

∂Y= κ1 · ∂Λ(Y )

∂Y+ 2κ2 · Λ(Y ) · ∂Λ(Y )

∂Y

=⇒ ∂Λ(G)

∂G· ∂G

∂Y= κ1 · 1√

Y 2 + 1+ 2κ2 · Λ(Y ) · 1√

Y 2 + 1

=⇒√

Y 2 + 1√G2 + 1

· ∂G

∂Y= κ1 + 2κ2 · Λ(Y ), (3.20)

the left hand side term of which is approximately equal to the income elasticity of the

intra-household health gap for income levels that are not too close to zero, since

25

√Y 2 + 1 ≈ |Y | and

√G2 + 1 ≈ |G| for Y and G that are not close to zero. Thus, the left

hand side term of equation (3.20) can be interpreted as an approximation of the percent

change in G for a percent increase in Y . According to this equation, the income elasticity

of the intra-household health gap is κ1 when the level of household income is zero, and the

parameter κ2 describes how the income elasticity changes along the income distribution.

Let xi be the vector containing Λ(Yi) and [Λ(Yi)]2. Then, based on the theoretical

framework developed previously, the main relationship of interest is

Λ(Gi) = β0 + β1x′i + β2s

′i + εi, (3.21)

where Gi is a measure of intra-household health gap, si is a vector of control variables

that are assumed to be uncorrelated with εi, which is the household-specific error term,

and β0, β1, and β2 are scalar and vector parameters to be estimated. The vector si could

be a subset of the following variables: a binary variable indicating whether the

household’s location is urban or rural; a measure of household’s assets; average age and

education of the adult household members; the fraction of women within the household;

and regional controls.

The main parameters of interest in equation (3.21) are in the vector β1, which

indicates the direction and magnitude of income elasticity of the intra-household health

gap. If xi and εi are uncorrelated, the parameters can be estimated using a maximum

likelihood method under the assumption that εi ∼ N (0, σ2). Ordinary Least Squares

estimation is feasible only when Gi is a point datum for all the households. In general,

only the interval [Gil, Giu] in which Gi belongs is observed, especially when there is a lot

26

of missing data as in the case of large-scale household surveys; note that Gil is the lower

bound and Giu the upper bound of Gi so that Gil = Giu whenever point datum is

available. Therefore, the parameters in the equation (3.21) can be estimated by

maximizing the sum∑

i Li of log-likelihood functions Li, where

Li =

−ri

2

(

Λ(Gil) − β0 − β1x′i − β2s

′i

σ

)2

+ ln(2πσ2)

if Gil = Giu

ri ln

{

Φ

(

Λ(Giu) − mi

σ

)

− Φ

(

Λ(Gil) − mi

σ

)}

if Gil < Giu,

(3.22)

where ri is the sampling weight of the i-th household and mi = β0 + β1x′i + β2s

′i. This

maximum likelihood approach is known as the interval regression method.

Although Λ(Gi), which is a function of the anthropometric measurements taken ex

post, cannot statistically influence any of the independent variables, ruling out reverse

causality, the equation (3.21) is not identified because of the problem of endogeneity of

xi. In specific,

εi = βgΛ(G∗i ) + νi, (3.23)

where G∗i represents the level of intra-household inequality in the previous time period

and βg is a parameter that represents the intertemporal persistence of the intra-household

inequalities in health. However, G∗i clearly influences the economic outcomes of the

household, since health gaps are mostly inefficient and have negative effects on total

household labor supply or production. In other words, xi and Λ(G∗i ) are not independent.

Thus, identification of the parameter vector β1 depends on finding valid instruments that

27

influence Λ(Gi) through xi but are independent of εi. Although it is not possible to

objectively test the validity of any instrument, this paper uses functions of the following

variables to instrument for xi: natural log of rainfall in the district of the household, and

an indicator variable for major exogenous incidents, such as accidents, fire, drought, or

crop failure.

It is reasonable to assume that rainfall influences the intra-household health gaps in

the current time period mainly through or perhaps only through its effects on the total

household income. Although Sarsons (2015) criticizes the indiscriminate use of rainfall as

an instrument and analyzes how the exclusion restriction is often violated when using

rainfall as an instrument for income, this criticism applies mainly in the context of

macroeconomic studies. Since this paper is concerned with phenomena within

households, rainfall can be used as an exogenous source of variation in household income.

Then, the following system identifies the income elasticity of the intra-household

health gap:

Λ(Gi) = β0 + β′1xi + β′

2si + εi

xi = Π1zi + Π2si + ξi, (3.24)

where zi is the vector containing one (the constant) and statistically appropriate

instruments from the following set: {ln(R1), ln(R2), [ln(R1)]2, [ln(R2)]

2, M}, where R1

and R2 represent rainfall (in millimeters) in the household’s district in the two calendar

years which contain the current fiscal year, respectively; and M is an indicator variable for

major exogenous incidents, such accidents, fire, drought, or crop failure. In addition, Π1

28

and Π2 are matrices of reduced-form parameters such that Π1 has a full row rank, and ξi

is the vector of errors with mean zero such that E[z′iξi] = 0 and εi = ρ′ξi + ei, where ρ is

a parameter vector to be estimated, and the vector ξi and the error term ei are independent.

Since εi ∼ N (0, σ2), it follows that ei, conditional on ξi, is also normally distributed with

some variance σ2e .

This paper uses an adaptation of the “control function” method (Wooldridge, 2015)

to estimate the parameters in equation (3.24). Suppose Π1 and Π2 are the estimates of Π1

and Π2, obtained via Ordinary Least Squares regression of each variable in xi on the

variables in the vectors zi and si. Let ξi = xi − Π1zi − Π2si, since ξi is unobserved and

can only be estimated. Hence, estimating the equation

Λ(Gi) = β0 + β′1xi + β′

2si + ρ′ξi + ei, (3.25)

which is obtained by substituting ρ′ξi + ei for εi in equation (3.24), provides more reliable

estimates of β1 than those obtained by estimating equation (3.21). The interval regression

method can be used again for the purpose of estimating equation (3.25). Specifically, the

parameters in the equation (3.25) can be estimated by maximizing the sum∑

i Li of

log-likelihood functions Li, where

Li =

−ri

2

(

Λ(Gil) − mi

σe

)2

+ ln(2πσ2e)

if Gil = Giu

ri ln

{

Φ

(

Λ(Giu) − mi

σe

)

− Φ

(

Λ(Gil) − mi

σe

)}

if Gil < Giu,

(3.26)

where ri is the sampling weight of the i-th household and mi = β0 + β′1xi + β′

2si + ρ′ξi.

29

This procedure is essentially a control function approach, where inclusion of the “control

function” or “control vector” ξi ≡ xi − Π1zi − Π2si in equation (3.25) makes the

problem of endogeneity of xi less severe for producing estimates of β1 that are more

reliable than those produced by an ordinary interval regression.

In summary, the main parameters of interest are the coefficients of Λ(Yi) and

[Λ(Yi)]2 in the vector β1, because these parameters inform the econometrician how elastic

intra-household health gaps are at each level of income distribution; the parameters in β1

are also rooted in the economic theory of intra-household bargaining, as the equation

(3.13) shows. Using the assumption that district-level rainfall and major household-level

exogenous incidents (such as accidents, fire, and crop failure) influence intra-household

health gaps only through their effects on household income, it is possible to obtain reliable

estimates of the parameters in β1 using the control function method, as explained above.

Finally, reliable inference of income elasticities of intra-household health gaps at various

levels of household income distribution is important for designing public policies that

affect the income distribution.

30

Data

This study uses data from the second wave a longitudinal survey called the India

Human Development Survey (IHDS), the first round of which was conducted in 2004–05

and the second in 2011–12 by the National Council of Applied Economic Research and

the University of Maryland. The IHDS is a nationally representative, multi-topic survey of

more than forty thousand households in 1,503 villages and 971 urban neighborhoods

across India. The first round, IHDS-I, collected information on 41,554 households.

Approximately 85 percent of these households were re-interviewed in 2011–12; the

IHDS-II also collected information on some additional households, making the total

sample size of the second round 42,152. The IHDS-I and IHDS-II are available online for

public use (Desai and Vanneman, 2015). The data have sampling weights for each

household and also information on the primary sampling unit (PSU) out of the 2,462

PSUs each household is located in. In addition, each PSU is located in one of the 373

districts, which comprise the strata, and each district is located in one of the 33 states or

union territories, which do not include the Andaman/Nicobar and Lakshadweep islands.

There are 3,089 households among the 42,152 interviewed in 2011–12 with one or no

adult members. Thus, the sub-sample used for this analysis comprises 39,063 households,

of which 13,805 households are located in urban regions and the rest in rural areas. (The

31

sampling weights of the mentioned 3,089 households are taken into account in calculating

the cluster-robust standard errors in the analyses of the sub-sample of 39,063 households.)

The IHDS collects detailed information about each household’s sources of income to

calculate its total income, and so there should be no significant measurement errors in the

total income figures in the IHDS. In addition, measurement error in the anthropometric

data is also not a major concern because the survey data contains multiple measures of

height and weight of the household members who were available for such measurements.

One main limitation of IHDS in the context of this study is that anthropometric

information of at least some members is missing for many households. In specific, the

weights and heights of all adult household members are available for only 12,720

households. Although this implies that the intra-household health gaps cannot be precisely

calculated for the remaining 26,343 households, this study uses available information to

estimate the lower and upper bounds of the health inequalities for these households. Table

1 presents the estimated means and variances of the measures of intra-household health

gaps proposed earlier.

Table 1

Means and Variances of Intra-household Health Gaps

Intra-household health gap Mean (95% CI) Variance (95% CI)

Θ1 = 0.75S + 0.25H −1.178 ± 0.009 0.422 ± 0.006

Θ2 = 0.50S + 0.50H −1.268 ± 0.008 0.365 ± 0.006

Θ3 = 0.25S + 0.75H −1.394 ± 0.006 0.292 ± 0.005

Source: author’s calculations. Note: the 95% confidence intervals (95% CI) for

means and variances of Θ1, Θ2, and Θ3 are obtained by estimating a constant-

only model, that is, equation (3.21) without any regressors but with Θ1, Θ2, and

Θ3 as regressands, respectively, using the interval regression method.

32

Estimates in Table 1 suggest that intra-household health gaps appear larger when the

measure of the health gaps places more weight on the overall sub-optimality of BMIs of

adult household members than on the heterogeneity in the BMIs.

The control variables in the main models of this paper include average age and

education of adult members within households, an asset index that indicates a household’s

ownership of real estate and other property, including appliances, and the fraction of

women within a household, in addition to geographical indicator variables. Figure 3

shows the kernel density estimates of the asset index, average education and age of

households, while Figure 4 shows the kernel density of the fraction of women among

adult members within households.

Figure 3

Kernel Densities of Assets, Average Age, and Average Education of Households

0.0

2.0

4.0

6.0

8D

ensit

y

0 20 40 60 80 100Variable

Asset index (0 - 33)Average number of years of education (0 - 16)Average age of adult household members (21 - 100)

Source: author’s calculations. Note: estimates are based on a Gaussian kernel and a bandwidth of 1.

33

The asset index is integer-valued and ranges from 0 to 33. Although this index

indicates a household’s wealth to a certain extent, it does not quantify the value of the

household’s assets. This limitation of the asset index is quite pronounced in its kernel

density, which is far from a bell shaped curve. Nevertheless, the asset index is an essential

control in the econometric models of this study, because there is usually an association

between a household’s income and its wealth. In addition, as Figure 3 shows, the average

number of years of education of adult members of a household is also bounded between 0

and 16, since the IHDS censors the number of years of education at 16. Furthermore, the

average level of education in most households is very low. Additionally, since this study

focuses on adult members within households, the average age is between 21 and 100.

Figure 4

Kernel Density of the Fraction of Women within a Household

05

1015

2025

Den

sity

0 .2 .4 .6 .8 1Fraction of women among the adult household members

Source: author’s calculations. Note: estimates are based on a Gaussian kernel and a bandwidth of 0.01.

34

Gender composition of a household is generally related to intra-household bargaining

power structure. Thus, the fraction of women within a household is an important control

variable. Figure 4 suggests that the gender composition in most households is balanced.

Symmetry is another notable feature of the kernel density in Figure 4.

The main explanatory variable of this study is household income. Statistics

summarizing household income in ten thousands of Indian National Rupees (INR) at the

2011–12 nominal level are presented in Table 2.

Table 2

Summary Statistics of Household Income (in Ten Thousands of INR)

Statistic Value

10th percentile 1.973

First quartile 3.800

Median 7.000

Mean 11.907

Third quartile 13.476

90th percentile 25.400

Standard deviation 20.294

Skewness 18.506

Source: author’s calculations.

Next section presents estimates of income elasticities of intra-household health gaps

at the mean level and various percentiles of the household income distribution. Note that

the household income does not directly enter the estimating equations. Instead, the inverse

hyperbolic sine of income and its square are used as regressors. Figure 5 shows the kernel

35

density estimate of the inverse hyperbolic sine transform of household income. It seems to

follow a smooth bell curve.

Figure 5

Kernel Density of Inverse Hyperbolic Sine of Household Income0

.1.2

.3.4

Den

sity

-5 0 5 10Inverse hyperbolic sine of household income (in ten thousands of INR)

Source: author’s calculations. Note: estimates are based on a Gaussian kernel and a bandwidth of 0.1.

Additionally, district-wise rainfall data are obtained from the Indian Meteorological

Department, Ministry of Earth Sciences, Government of India (2016), since district-wise

rainfall is used as an instrument in the control function approach outlined in Section 3.3.

Thus, merging these rainfall data with the IHDS data creates a rich dataset that is adequate

for estimating income elasticities of intra-household health gaps in India.

36

Results and Discussion

Using data from the India Human Development Survey, this section implements the

empirical design developed in Section 3.3 and discusses the results. In other words, the

following models try to gauge the responsiveness of intra-household health gaps to

changes in the level of household income. Table 3 presents the parameter estimates of the

coefficients of Λ(Y ), the inverse hyperbolic sine of income, and its square obtained using

the specification given by equation (3.21), which ignores the endogeneity of Λ(Y ).

Table 3

Interval Regression Models of Intra-household Health Gaps

Regressand Λ(Θ2) Λ(Θ2) Λ(Θ2) Λ(Θ1) Λ(Θ3)

Regressors Model IR2a Model IR2b Model IR2 Model IR1 Model IR3

Λ(Y ) 0.00215 0.00107 0.00627 0.00823 0.00466

(0.00712) (0.00715) (0.00682) (0.00774) (0.00557)

[Λ(Y )]2 0.0112* 0.00964* 0.00852* 0.00888* 0.00712*

(0.00142) (0.00146) (0.00138) (0.00152) (0.00114)

Controls A† No Yes Yes Yes Yes

Controls B†† No No Yes Yes Yes

Source: author’s calculations. Note: cluster-robust standard errors, which are clustered at the

primary sampling unit level, are in parentheses. A star (*) indicates statistical significance at

the 1% level. †Controls A include the asset index and a binary variable indicating whether the

household’s location is urban or rural. ††Controls B include the following variables: average age

and average education of the adult household members; the fraction of women among the adult

household members; and a categorical variable indicating which zone (northern, southern, western,

eastern, northeastern, or central zone of India) the household belongs to.

37

The main model in Table 3 is model IR2. The other models, namely, IR2a, IR2b,

IR1, and IR3, serve as robustness checks. Assuming that Λ(Y ) is exogenous, the

estimates of IR2 seem to be robust to specification and also to the measure of

intra-household health gaps used. The coefficient of [Λ(Y )]2 is statistically significant and

positive. Within the conceptual framework in Section 3.1, this means that intra-household

variation in the bargaining powers interacts with household income and causes the health

gaps to increase when the level of already positive income increases, while the same

mechanism reduces health gaps when negative income shocks become less severe.

Figure 6

Interval Regression-based Income Elasticities of Intra-household Health Gaps

-.1-.0

50

.05

.1In

com

e el

astic

ity o

f int

ra-h

ouse

hold

hea

lth g

aps

-10 0 10 20 30Income (in ten thousands of INR)

IR2a IR2b IR2IR2 (95% CB) IR1 IR3

Source: author’s calculations. Note: the 95% confidence band (95% CB) is based on model IR2.

However, Figure 6, which uses the models in Table 3 to estimate the extent to which

38

health gaps respond to increases in household income, shows that the income elasticity of

health gaps for households with incomes between the 10th and the 90th percentiles

(between 19.73 thousand INR and 254 thousand INR), is less than 0.1 although positive.

In other words, for these households, a one percent increase in household income would

increase the intra-household health gaps by less than 0.1 percent. Therefore, model IR2,

as well as the other models in Table 3, suggest that intra-household health gaps are, by and

large, rather “inelastic” to changes in household income.

However, models in Table 3 possibly suffer the problem of endogeneity, as discussed

in Section 3.3, and are thus not very reliable. Thus, control function-based regression

models in which the issue of endogeneity of Λ(Y ) is less severe are presented in Table 4.

Table 4

Control Function Regression Models of Intra-household Health Gaps

Regressand Λ(Θ1) Λ(Θ2) Λ(Θ3)

Regressors Model CF1 Model CF2 Model CF3

Λ(Y ) −1.703* −1.554* −1.329*

(0.519) (0.470) (0.396)

[Λ(Y )]2 0.341* 0.313* 0.269*

(0.106) (0.096) (0.081)

Controls† Yes Yes Yes

Source: author’s calculations. Note: the above estimates are obtained

by instrumenting Λ(Y ) and its square using the log of district-level

rainfall in 2012, its square, and an indicator variable for major household-

specific exogenous incidents such as any accidents, fire, drought or crop

failure. Cluster-robust standard errors, which are clustered at the primary

sampling unit level, are in parentheses and are based on 1000 bootstrap

replications. A star (*) indicates statistical significance at the 1% level.†Controls include the following variables: the asset index; a binary

variable indicating whether the household’s location is urban or rural;

average age and average education of the adult household members;

the fraction of women among the adult household members; and a

categorical variable indicating which zone (northern, southern, western,

eastern, northeastern, or central zone of India) the household belongs to.

39

All three models in Table 4 use the specification given by equation (3.25) with three

instruments: ln(R2012), [ln(R2012)]2, where ln(R2012) represents district-level rainfall (in

millimeters) in 2012, and M , which is an indicator variable for major household- specific

exogenous incidents, such as any accidents, fire, drought or crop failure. Note that rainfall

in 2012 is used instead of rainfall in 2011 because most of the India Human Development

Survey was carried out during 2012 (Desai and Vanneman, 2015).

If the chosen instruments explain the variation in endogenous variables only

“weakly,” the final control function regression model(s) would produce inconsistent

estimates of the parameters of interest and may sometimes be more biased than the

interval regression models. However, the models in Table 4 do not suffer the problem of

weak instruments because Sanderson and Windmeijer’s (2016) test rejects the null

hypothesis of weak identification. In specific, the Sanderson–Windmeijer conditional

F -statistics for Λ(Y ) and [Λ(Y )]2 are 10.08 and 10.89, respectively. The null hypothesis

of weak identification is rejected because both the test statistics are greater than 9.08,

which is the appropriate 5% critical value computed by Stock and Yogo (2005) for a 10%

“maximal IV size.” Note that using any strict subset of {ln(R2012), [ln(R2012)]2, M} as a

set of instruments would lead to weak identification, because Sanderson and Windmeijer’s

(2016) test fails to reject the null hypothesis in this case. This justifies the choice of

ln(R2012), [ln(R2012)]2, and M as instruments for the control function-based regression

models CF1, CF2, and CF3.

In the models CF1, CF2, and CF3, the coefficients of both Λ(Y ) and [Λ(Y )]2 are

statistically significant at the 1% level. These models provide more insight into the

underlying process behind the generation of intra-household health gaps. Compared to the

40

models in Table 3, the magnitude of the coefficient of [Λ(Y )]2 is much larger in Table 4.

Again within the conceptual framework in Section 3.1, this means that bargaining powers

within an average Indian household are much more unequal than models in Table 3

suggest. These intra-household inequalities in bargaining power widen intra-household

health gaps as the household becomes more prosperous beyond a certain income level. On

the other hand, households with incomes below this threshold experience a reduction in

intra-household health gaps as their economic situation improves, despite any

intra-household inequalities in bargaining powers. In other words, inequalities in

bargaining powers work in reverse when a household is in severe poverty. As a household

moves out a state of severe negative income shock or severe poverty, members with the

most bargaining power perhaps utilize their bargaining power in reducing the overall level

of sub-optimality of health outcomes in the household. A comparison of models CF1,

CF2, and CF3 supports this observation. Specifically, the magnitude of the coefficient of

[Λ(Y )]2 in model CF1, which places more weight on sub-optimality of heath outcomes, is

0.341, which is higher than the magnitude 0.269 in model CF3, which places more weight

on heterogeneity in health outcomes.

The coefficient of Λ(Y ) in all models in Table 4 is negative and statistically

significant at the 1% level. In model CF2, which has Λ(Θ2) as the regressand, the value of

the coefficient is −1.554 (with a standard error of 0.470). In other words, this is the “base

level” of income elasticity of intra-household health gaps. If the coefficient of [Λ(Y )]2

were zero, that is, if the effect of inequality in intra-household bargaining power were

negligible, then a one percent increase in household income would be expected to

decrease intra-household health gaps by about one-and-a-half percent. However, the

41

coefficient of [Λ(Y )]2 is positive and significant, meaning that the magnitude and the sign

of the income elasticity usually differs from the base level, depending on the household

income level, as Figure 7 shows.

Figure 7

Control Function Regression-based Income Elasticities of Intra-household Health Gaps

-6-4

-20

2In

com

e el

astic

ity o

f int

ra-h

ouse

hold

hea

lth g

aps

-10 0 10 20 30Income (in ten thousands of INR)

CF1 CF2 CF2 (95% CB) CF3

Source: author’s calculations. Note: the 95% confidence band (95% CB) is based on model CF2.

The contrast between Figure 6 and Figure 7 is quite stark. Although the lower end of

the 95% confidence band (CB) shown in Figure 7 has some overlap with the 95% CB in

Figure 6 at positive income levels, the control function-based regression models imply

income elasticities that are generally higher in absolute value. This is especially true for

households affected by negative income shocks. For example, if a household with a

negative income shock of a hundred thousand INR were to experience a one percent

42

improvement in its economic situation, its intra-household health gaps would be expected

to decrease by at least about two percent, as Figure 7 shows. Thus, the models seem to

suggest that protecting households, especially those in severe poverty, against negative

income shocks reduces intra-household health gaps. For example, a well-designed

weather insurance scheme would not only protect agricultural households against crop

failures and negative income shocks but would also bring the household ‘together’ and

closer to the optimal levels with respect to health in the mean process.

Most households however do not experience negative income shocks, as the

summary statistics in Table 2 indicate. Nevertheless, Figure 7 shows that income

elasticities of intra-household health gaps are still negative at low levels of non-negative

income but become positive after a certain point on the income distribution. Table 5 paints

a more specific and useful picture of this observation.

Table 5

Income Elasticities of Intra-household Health Gaps

Income level Elasticity of Θ2 [95% confidence interval]

10th percentile −0.6597 −1.0859 −0.2336

First quartile −0.2763 −0.5475 −0.0050

Median 0.0982 −0.1689 0.3653

Mean 0.4282 0.0358 0.8205

Third quartile 0.5053 0.0756 0.9349

90th percentile 0.9008 0.2603 1.5414

Source: author’s calculations. Note: the results are based

on model CF2 and thus on 1000 bootstrap replications.

43

At the tenth percentile of the household income distribution, the income elasticity of

the intra-household health gaps, as measured by Θ2, is estimated at about −0.66 in the

95% confidence interval [−1.09, −0.23]. In other words, a one percent increase in

household income at the tenth percentile reduces intra-household health gaps by about

0.66%. The magnitude of this negative income elasticity is lower at the twenty fifth

percentile. At the first quartile, a one percent increase in household income is expected to

reduce health gaps by about 0.28%. However, intra-household health gaps seem to be

inelastic to an increase in household income at the median level, because the

corresponding 95% confidence interval for the income elasticity is approximately

[−0.17, 0.37], which contains 0.

Intra-household health gaps do not remain inelastic to changes in household income

beyond the median level. At the mean level, the third quartile, and the ninetieth percentile

of the household income distribution, the income elasticities of health gaps are positive

and are estimated at about 0.43, 0.51, and 0.90, respectively, and the corresponding 95%

confidence intervals are approximately [0.04, 0.82], [0.08, 0.93], and [0.26, 1.54],

respectively.

Therefore, the level of household income has a non-linear effect on intra-household

health gaps. If an inter-household income redistributive policy, involving tools such as

subsidies, tax benefits, or direct cash transfers, intends to reduce intra-household health

gaps, such a policy should be targeted at households with income below the median level.

Because implementing income redistribution can be costly, redistributive policies should

be aimed at the poorest households, perhaps those with income below the tenth percentile,

for the greatest impact.

44

Conclusion

Using conceptual framework from a game theoretic household bargaining model,

data from a recent large-scale household survey in India, and control function-based

econometric techniques, this paper finds that the level of household income has a

non-linear effect on intra-household health gaps, which encompass both the variation in

the BMIs and the average suboptimality of BMIs of adult household members. For

households affected by negative income shocks, a one percent increase in total household

income would reduce intra-household health gaps by more than one-and-a-half percent.

Within the conceptual framework of this paper, the reduction occurs as the household

members with the most bargaining power utilize their power to reduce the overall

suboptimality of the household’s health outcomes.

For households with positive incomes, a different economic mechanism seems to be

at play. There is a base level of income elasticity, which is about −1.55 and thus negative.

From one angle, income is a positive force that reduces intra-household health gaps by

about 1.6% for a one percent increase in household income. From another angle, income

is also a negative force: for households that are unaffected by negative income shocks, the

income elasticity itself increases as income increases, counteracting the base level of

income elasticity. In particular, a one percent increase in the income of a household at the

45

tenth percentile reduces intra-household health gaps by about 0.66%, whereas the

reduction is only by about 0.28% for a household at the first quartile of the household

income distribution. At the median level, the health gaps are inelastic to increases in

household income. Within the conceptual framework of this study, this trend is due to the

following economic mechanism: household members with the most bargaining power

disproportionately benefit from the household’s relative prosperity, and this not only

increases the sub-optimality of their BMIs and thus the overall sub-optimality but also

increases the heterogeneity in the BMIs of all household members. Consequently, for

households at the third quartile and the ninetieth percentile of the income distribution, a

one percent increase in household income increases intra-household health gaps by about

0.5% and 0.9%, respectively. These results are consistent with two findings: Sahn and

Younger’s (2009) finding that intra-household inequalities in BMI increase as household

expenditures increase; and Doak et al.’s (2002, 2005) finding that dual burden households,

which have large intra-household health inequalities, tend to have higher incomes.

Therefore, inter-household redistributive policies, involving subsidies, tax benefits,

direct cash transfers, and so on, are counterproductive if they are designed to benefit any

households at or beyond the median level of income distribution, where income

elasticities of intra-household health gaps are positive and high. Redistributive policies

that are designed to benefit the poorest households, say, those with income below the tenth

percentile, would help reduce not only poverty but also intra-household health gaps.

Finally, systems that protect households against negative income shocks, such as a

well-designed weather insurance scheme, would significantly reduce intra-household

health gaps within households affected by such shocks and thus have high social returns.

46

References

Adelman, Irma, and Cynthia Taft Morris. Economic growth and social equity in

developing countries. Stanford University Press, 1973.

Ahluwalia, Montek S., Nicholas G. Carter, and Hollis B. Chenery. “Growth and poverty in

developing countries.” Journal of Development Economics 6, no. 3 (1979): 299-341.

Anand, Sudhir, and Ravi Kanbur. “The Kuznets process and the inequality—development

relationship.” Journal of Development Economics 40, no. 1 (1993): 25-52.

Anand, Sudhir. “The concern for equity in health.” Journal of Epidemiology and

Community Health 56, no. 7 (2002): 485-487.

Asian Development Bank. ADB’s support for inclusive growth: thematic evaluation study.

Metro Manila: Asian Development Bank, 2014.

Atkinson, Anthony B. “Health inequality, health inequity and health spending.”

Inequalities in Health: Concepts, Measures, and Ethics, edited by Nir Eyal, Samia

A. Hurst, Ole F. Norheim, and Dan Wikler, 27-36. New York: Oxford University

Press, 2013.

Barro, Robert J. “Inequality and growth in a panel of countries.” Journal of Economic

Growth 5, no. 1 (2000): 5-32.

Behrman, Jere R. “Nutrition, health, birth order and seasonality: Intrahousehold allocation

among children in rural India.” Journal of Development Economics 28, no. 1 (1988):

43-62.

Behrman, Jere R., and Anil B. Deolalikar. “The intrahousehold demand for nutrients in

rural south India: Individual estimates, fixed effects, and permanent income.”

Journal of Human Resources 25, no. 4 (1990): 665-696.

Berg, Andrew, Jonathan D. Ostry, and Jeromin Zettelmeyer. “What makes growth

sustained?” Journal of Development Economics 98, no. 2 (2012): 149-166.

Bourguignon, Francois, and Christian Morrisson. “Income distribution, development and

foreign trade: A cross-sectional analysis.” European Economic Review 34, no. 6

(1990): 1113-1132.

47

Browning, Martin, Pierre-Andre Chiappori, and Valerie Lechene. “Collective and unitary

models: A clarification.” Review of Economics of the Household 4, no. 1 (2006):

5-14.

Caballero, Benjamin. “A nutrition paradox–underweight and obesity in developing

countries.” New England Journal of Medicine 352, no. 15 (2005): 1514-1516.

Cao, Sissi, Rahim Moineddin, Marcelo L. Urquia, Fahad Razak, and Joel G. Ray.

“J-shapedness, an often missed, often miscalculated relation: The example of weight

and mortality.” Journal of Epidemiology and Community Health 68, no. 7 (2014):

683-690.

Centers for Disease Control and Prevention. “Body mass index: Considerations for

practitioners.” Atlanta: U.S. Department of Health and Human Services, 2011.

Chiappori, Pierre-Andre, and Costas Meghir. Intrahousehold inequality. No. w20191.

National Bureau of Economic Research, 2014.

Cole, Tim J., Katherine M. Flegal, Dasha Nicholls, and Alan A. Jackson. “Body mass

index cut offs to define thinness in children and adolescents: International survey.”

British Medical Journal 335, no. 7612 (2007): 194-197.

Cole, Tim J., and T. Lobstein. “Extended international (IOTF) body mass index cut-offs

for thinness, overweight and obesity.” Pediatric Obesity 7, no. 4 (2012): 284-294.

Congressional Budget Office. The distribution of household income, federal taxes, and

government spending. Washington, D.C.: Congressional Budget Office, 2015.

Desai, Sonalde, and Reeve Vanneman. India Human Development Survey-II (IHDS-II),

2011-12. ICPSR 36151, version 3. Ann Arbor, MI: Inter-university Consortium for

Political and Social Research, 2015. doi:10.3886/ICPSR36151.v3.

Doak, Colleen, Linda Adair, Margaret Bentley, Zhai Fengying, and Barry Popkin. “The

underweight/overweight household: An exploration of household sociodemographic

and dietary factors in China.” Public Health Nutrition 5, no. 1a (2002): 215-221.

Doak, Colleen, Linda Adair, Margaret Bentley, Carlos Monteiro, and Barry Popkin. “The

dual burden household and the nutrition transition paradox.” International Journal of

Obesity 29, no. 1 (2005): 129-136.

Donni, Olivier, and Pierre-Andre Chiappori. “Nonunitary models of household behavior:

A survey of the literature.” In Household Economic Behaviors, edited by Jose

Alberto Molina, 1-40. New York: Springer, 2011.

Dutton, Daniel J., and Lindsay McLaren. “The usefulness of ‘corrected’ body mass index

vs. self-reported body mass index: comparing the population distributions,

sensitivity, specificity, and predictive utility of three correction equations using

Canadian population-based data.” BMC Public Health 14, no. 1 (2014): 1-11.

48

Easterly, William. “Inequality does cause underdevelopment: Insights from a new

instrument.” Journal of Development Economics 84, no. 2 (2007): 755-776.

Haddad, Lawrence, and Ravi Kanbur. “How serious is the neglect of intra-household

inequality?” The Economic Journal 100, no. 402 (1990a): 866-881.

Haddad, Lawrence, and Ravi Kanbur. Is there an intra-household Kuznets curve? Office

of the Vice President, Development Economics, The World Bank, 1990b.

Haddad, Lawrence, John Hoddinott, and Harold Alderman. Intrahousehold resource

allocation in developing countries: Models, methods, and policy. Johns Hopkins

University Press, 1997.

Haddad, Lawrence, Ravi Kanbur, and Howarth Bouis. “Intrahousehold inequality at

different welfare levels: Energy intake and energy expenditure data from the

Philippines.” Oxford Bulletin of Economics and Statistics 57, no. 3 (1995): 389-409.

Indian Meteorological Department, Ministry of Earth Sciences, Government of India.

“Customized Rainfall Information System (CRIS).” 2016. Accessed April 10, 2016.

http://hydro.imd.gov.in/hydrometweb/(S(3g0gco45ceiyrsul5jgcec55))/DistrictRaifall.aspx.

Kanbur, Ravi, and Lawrence Haddad. “Are better off households more unequal or less

unequal?” Oxford Economic Papers 46, no. 3 (1994): 445-458.

Kanbur, Ravi. “Children and intra-household inequality: A theoretical analysis.” In

Choice, Welfare and Development, edited by Kaushik Basu, Prasanta Pattanaik, and

Kotaro Suzumura, 242-252. Oxford: Clarendon Press, 1995.

Karapakula, Venkatasai Ganesh. “Axiomatic measurement of heterogeneity and

sub-optimality in bounded variables.” Unpublished manuscript, 2016.

Kline, Brendan, and Justin L. Tobias. “Explaining trends in body mass index using

demographic counterfactuals.” Econometric Reviews 33, no. 1-4 (2014): 172-196.

Kuznets, Simon. “Economic growth and income inequality.” The American Economic

Review 45, no. 1 (1955): 1-28.

Lise, Jeremy, and Shannon Seitz. “Consumption inequality and intra-household

allocations.” The Review of Economic Studies 78, no. 1 (2011): 328-355.

Maasoumi, Esfandiar. “Multidimensioned approaches to welfare analysis.” In Handbook

of Income Inequality Measurement, edited by Jacques Silber, 437-484. Netherlands:

Springer, 1999.

Ministry of Health and Family Welfare, Government of India. National health policy. New

Delhi: Government of India, 2015.

Molini, Vasco, Maarten Nube, and Bart van den Boom. “Adult BMI as a health and

nutritional inequality measure: Applications at macro and micro Levels.” World

Development 38, no. 7 (2010): 1012-1023.

49

Myerson, Roger B. “Incentive compatibility and the bargaining problem.” Econometrica

47, no. 1 (1979): 61-74.

National Obesity Observatory. “Body mass index as a measure of obesity.” London:

Public Health England, 2009.

Ostry, Jonathan David, Andrew Berg, and Charalambos G. Tsangarides. Redistribution,

inequality, and growth. International Monetary Fund, 2014.

Paukert, Felix. “Income distribution at different levels of development: A survey of

evidence.” International Labor Review 108 (1973): 97-125.

Persson, Torsten, and Guido Tabellini. “Is inequality harmful for growth?” The American

Economic Review (1994): 600-621.

Pew Research Center. Indians reflect on their country and the world. Washington, D.C.:

Pew Research Center, 2014.

Pitt, Mark M., Mark R. Rosenzweig, and Nazmul Hassan. “Productivity, health, and

inequality in the intrahousehold distribution of food in low-income countries.” The

American Economic Review 80, no. 5 (1990): 1139-1156.

Planning Commission, Government of India. GDP at factor Cost at 2004–05

Constant/Current prices by Industry of Origin, Share to GDP for Each Sector, and

Percentage Rate of Growth: 71–72 to 13–14. New Delhi: Government of India, 2014.

Roemling, Cornelia, and Matin Qaim. “Dual burden households and intra-household

nutritional inequality in Indonesia.” Economics and Human Biology 11, no. 4 (2013):

563-573.

Rosenzweig, Mark R., and T. Paul Schultz. “Child mortality and fertility in Colombia:

individual and community effects.” Health Policy and Education 2, no. 3 (1982):

305-348.

Sachdev, Harshpal S., Caroline HD Fall, Clive Osmond, Ramakrishnan Lakshmy, Sushant

K. Dey Biswas, Samantha D. Leary, Kolli Srinath Reddy, David JP Barker, and

Santosh K. Bhargava. “Anthropometric indicators of body composition in young

adults: relation to size at birth and serial measurements of body mass index in

childhood in the New Delhi birth cohort.” The American Journal of Clinical

Nutrition 82, no. 2 (2005): 456-466.

Sahn, David E., and David C. Stifel. “Parental preferences for nutrition of boys and girls:

Evidence from Africa.” Journal of Development Studies 39, no. 1 (2002): 21-45.

Sahn, David E., and Stephen D. Younger. “Measuring intra-household health inequality:

Explorations using the body mass index.” Health Economics 18, no. 1 (2009):

S13-S36.

50

Sanderson, Eleanor, and Frank Windmeijer. “A weak instrument F-test in linear IV models

with multiple endogenous variables.” Journal of Econometrics 190, no. 2 (2016):

212-221.

Sarsons, Heather. “Rainfall and conflict: A cautionary tale.” Journal of Development

Economics 115 (2015): 62-72.

Sen, Amartya K. “Family and food: Sex bias in poverty.” In Resources, Values, and

Development, edited by Amartya K. Sen, 346-368. Cambridge: Harvard University

Press, 1984.

Stock, James H., and Motohiro Yogo. “Testing for weak instruments in linear IV

regression.” In Identification and Inference for Econometric Models, edited by

Donald W. K. Andrews, and James H. Stock, 80-108. New York: Cambridge

University Press, 2005.

The World Bank. What is inclusive growth?. Washington, D.C.: The World Bank, 2009.

The World Bank. Social protection for a changing India, vol. 2. Washington, D.C.: The

World Bank, 2011.

The World Bank. “Poverty headcount ratio at national poverty lines (percentage of

population).” 2016. Accessed April 10, 2016.

http://data.worldbank.org/indicator/SI.POV.NAHC.

The World Health Organization, Expert Consultation. “Appropriate body-mass index for

Asian populations and its implications for policy and intervention strategies.” Lancet

363, no. 9403 (2004): 157-163.

The World Health Organization. “WHO child growth standards: length/height-for-age,

weight-for-age, weight-for-length, weight-for-height and body mass index-for-age.”

Geneva: The World Health Organization, 2006.

Thomas, Duncan. “Intra-household resource allocation: An inferential approach.” Journal

of Human Resources 25, no. 4 (1990): 635-664.

Wittenberg, Martin. “The weight of success: the body mass index and economic

well-being in southern Africa.” Review of Income and Wealth 59, no. S1 (2013):

S62-S83.

Wooldridge, Jeffrey M. “Control function methods in applied econometrics.” Journal of

Human Resources 50, no. 2 (2015): 420-445.

Zheng, Buhong. “Can a poverty index be both relative and absolute?” Econometrica 62,

no. 6 (1994): 1453-1458.

51