The Equality of Opportunity for Health in the U.S.: An

Analysis using NLSY

Yvonne Jie Chen ∗

April 14, 2015

Abstract

We define a measure of equality of opportunity (EOp) for health and test the existence of health in-

equity in the Unite States using data from the National Longitudinal Survey of Young 1979 (NLSY79).

Two decomposition methods are used to study the channels through which inequality of opportunity

arises. We simulate counterfactual health distributions and compute equity indices for various policy

states. Policy simulations suggest that the most effective way to reduce inequality of opportunity for

health is through interventions on income condition on education attainment.

1 Introduction

It has long been recognized that the social economic circumstances of an individual are closely re-

lated to her health (Wilkinson and Marmot 2003). These determinants, which include social economic

status (SES)1, early life health endowment, access to health care and physical and mental stress, 2 are

usually referred to as the social determinants for health. Education and income are the best studied

social determinants in the literature. A large body of evidence shows that wealthier and more educated

individuals live longer and healthier lives (Lleras-Muney 2005, CDC 2011, Meara et al. 2008). This posi-

tive correlation holds throughout the entire income and education distribution and persists throughout

an individual’s course of life (Case et al. 2002, Currie and Stabile 2003, Chen et al. 2006).

Recent research suggests that the socio-economic disparity in health is substantial and keeps grow-

ing. Meara et al. 2008 found that the education gap in life expectancy has been rising since the early

1980s in the U.S.. Almost all gains in life expectancy happen in the higher education groups. Cross-

country evidence indicates that the large social economic gradient, meaning that individuals with lower

∗National University of Singapore, sppcj@nus.edu.sg1Such as race, gender, income, education and social classes etc.2For a complete review please see (Wilkinson and Marmot 2003, CDC 2011)

1

SES have poorer health, is a universal phenomenon in high-income countries (Crimmins et al. 2011).

Both British White Hall studies I and II revealed reverse association between employment grade (social

class) and the prevalence of a variety of diseases (Marmot et al. 1991).

The relationship between SES and health provides motivation for research presented in this paper.

Let’s consider two types of SES. First type includes SES that individuals were endowed with and over

which they have little or no control. Examples include race, gender and parental social classes. A

second type of SES includes things that are jointly determined by individual choices and endowment,

such as education attainment and income. The question I’m interested in answering is how to partition

individuals when estimating health inequality? Shall we use SES from the first type or the second?

In order to answer these questions, I first discuss a measurement of health equity based on the equal

opportunity theory. I then examine empirical evidence of equality of opportunity for health using the

NLSY79 data. This paper is most closely related to empirical works on inequality of opportunity in the

labor market and health (Betts and Roemer 2007, Llavador and Roemer 2001, Jones et al. 2012, Trannoy

et al. 2010, Roemer et al. 2003). This paper adds to the current literature by providing empirical evidence

of inequality of opportunity for health in the context of the U.S. population.

2 Theories of Inequality of Opportunity for Health

In this section I provide a formal model to analyze equal opportunity for health. The goal of this

section is to set the theoretical ground for empirical analysis in this paper. In the social justice and phi-

losophy literature, the question under constant scrutiny is: what do we want to equalize? Utilitarianism

was in dominance before the publication of John Rawls’s A Theory of Justice in 1971. The utilitarianism’s

objective is to maximize the sum of utilities, which requires the equality of the marginal utility. Rawls

replaced the aggregation of equality and welfare with primary goods. Following Rawls’s work, Sen

proposed the concept of basic capability equality in his Tanner Lecture series in 1979 (Sen 1979). Sen

sees the new concept as a combination of Rawlsian equality and equality under the welfarist concep-

tions, namely utilitarian equality and total utility equality. In his view, the notion of ”basic capabilities”

are the goods that allow a person to do certain basic things. These views on equality were later syn-

thesized and extended by Dworkin (Dworkin 1981a,b). In these articles, Dworkin proposed the idea

that people should be responsible for the choices they make, but need to be compensated for the arbi-

trary distribution of resources in society. His theory, namely differentiating inequalities by their origins,

provides the theoretical foundation for research on equality of opportunity.

Dworkin’s concept of equality was formalized in the social science literature by Roemer, Fleurbaey

and many others (Roemer 1998, Fleurbaey 2008). All scholars retain the key ingredient of the theory:

that there are two types of inequality - one that individuals should be held accountable for and the

other for which they should not. The theory of inequality of opportunity has attracted much attention

2

in health economic research. A series of works by Roemer and Fleurbaey extend the equal opportu-

nity model to the demand and production of health (Roemer 2002a, Fleurbaey and Schokkaert 2009).

Similar to the general concept of equal opportunity, the theories hold that individuals should be held

responsible for some of the inequality in health outcomes and that the policy objective is to compensate

individuals for the part that they should not be held responsible for.

As Roemer [2002a] points out, the concept of the responsible factors is key to equal opportunity the-

ory. Theorists have presented many different forms of the concept. In this section I adopt the framework

proposed by Roemer [1998] and explicitly model two channels of inequality - circumstances and effort.

The Roemer model as I discuss below distinguishes these two sources of inequality. This formulation of

equal opportunity (EOp) was first proposed by Roemer [1998]and was later applied to the health care

delivery market in Roemer [2002b]. The standard approach for health-related policy evaluation maxi-

mizes the average health status in a given population. EOp, on the other hand, evaluates a policy by

maximizing the sum of the minimum health statuses across groups of individuals. The optimal policy

under EOp sets out to minimize the gaps of health statuses among individuals who have expended the

same degree of effort.

Consider a population partitioned into T types based on individuals’ socioeconomic status (SES).

The fraction of type t agent in the population is θt. Suppose there is a policy set P 3. The EOp approach

focuses on equalizing opportunities for health status for people with different SES4 Assume there is a

continuous distribution of individual effort et for type t. Possible effort measures include behaviors

such as smoking, alcohol usage and regular exercise. Suppose individuals are set out to maximize their

total health stock.

Let the cumulative distribution of effort for each type t be Fet . Define a new term called the degree

of effort π as the effort of an individual who’s at the π − th quantile of the effort distribution. Denote

this term as et(π).

π =

� et(π)

0

dF (et)⇔ et(π) = F−1et (π) (1)

Suppose a given policy P ensues a distribution of effort Fet(.) for each type t. Therefore et(π) is a

function of π and policy P . Write it as et(π, P ). We consider two individuals to have expended the same

degree of effort if, for a given policy set P , they sit at the same ranking in the effort distribution of their

own types.

Suppose within type t, health is determined by degree of effort et(π, P ) and P . Denote the health

3In constructing this measurement, I focus on distributional issues and assume that policy variables are exogenous.4There are several notions of efficiency used by researchers. One popular objective is to maximize the average life expectancy

among all individuals, a.k.a. the Utilitarian approach. Let λti(P ) be the health status of individual i in type t, who receives

spending P . Then the utilitarian approach sets out to maximize∑T

1θt( 1

Nt

∑Nt

i=1λti(P )), where Nt is the number of people in

type t and θt = Nt∑T

j=1Nj

is the fraction of people in type t.

3

status associated with degree of effort π and policy P as Λt(et(π, P ), P ). The goal of EOp policy is

to make individuals expend the same degree of effort e(π, P ) achieve similar health outcomes across

types t. Because degree of effort is defined by individual’s rank within type, EOp objective function

will involve comparisons of individuals sit at different position of the health distribution across types.

The remaining question is to find a measure that can rank these outcome distributions. This seem-

ingly simple question has involved considerable debate over the years. The most controversial issue

whether to use a cardinal or ordinal measure. A cardinal measure is a summary index such as the

Gini coefficient. The ordinal measure comparable to the Gini coefficient is the Lorenz curve, which di-

rectly depicts the distributional characteristics of income. In the Roemer model, a cardinal measure to

construct an index for health equity. The advantage of a cardinal measure is that it offers straightfor-

ward estimation of policy effect and is easier to compute empirically. In addition to this measure, I will

also discuss a stochastic dominance test that directly compares distributions with and without policy

treatment in the next section.

If we assume there’s a continuum of individuals in each type, then the EOp welfare function for

each type is defined as

� 1

0

mint

Λt(et(π, P ), P )dπ. (2)

This measure of health equity calculates the total health stock for individuals of the worst-off type

across π. It is clear that instead of maximizing the expected health status of the society, the EOp policy

maximizes the average health status of those individuals that are in the worst circumstances for a given

degree of effort. What matters here is the degree of effort, a relative measure, rather than the absolute level

of lifestyle quality. At any given policy state P , value of equation (2) constitutes a measure of health

equity index, which will be referred to as the “EOp value” hereafter.

3 Empirical Evidence of Inequality of Opportunity for Health in the

United States

The Roemer model outlined above can be illustrated with Figure (1). As shown in the graph, cir-

cumstance affects health outcomes either directly or indirectly through its effect on effort. In order to

make effort comparable across types, we need a measure of effort that is independent of circumstances.

This new measure is referred to as the ”degree of effort” in the previous section.

Two approaches are commonly used in the literature to determine degree of effort. One approach,

as discussed in the previous section, is to define degree of effort of an individual as the rank of her

effort within her own type. Another method, as outlined by Lefranc et al. [2009], is to define degree of

4

Figure 1: Effort, Circumstances and Health

effort as the component of effort orthogonal to circumstances, denoted as eR = e⊥C 5. Lefranc et al.

[2009] shows that equal opportunity implies that for C 6= C ′, FH|C,eR = FH|C′,eR . This means that

for individuals with the same eR, her probability of achieving health level H = h should be the same

whether she has circumstances C or C ′. Lefranc et al. [2009] proves that inequality of opportunity can

be tested using the conditional distribution of FH|C and FH|C′ , where F is the cumulative distribution

of the outcome variable and C is circumstance.

In this section I discuss the use of stochastic dominance test as a nonparametric approach to esti-

mate the level of inequality of opportunity. This method was first proposed by Lefranc et al. [2009]

and later applied in many empirical works (Trannoy et al. 2010, Rosa-Dias 2009). Based on Lefranc

et al. [2009], inequality of opportunity can be tested by comparing the cumulative distributions of the

outcome variable across types.

Recall that our goal is to compare the cumulative distributions FH|C and FH|C′ for C 6= C ′. Hence

we have the proposition as follows

Definition 3.1 There is inequality of opportunity if for C 6= C ′, FH|C 6= FH|C′

where C and C ′ are circumstances. This proposition holds under scenarios in which effort is not

observable and/or C is partially observable.

4 Data

Data from NLSY79 are used for the empirical analyses in this section. NLSY79 is a longitudinal

survey conducted by the National Bureau of Labor Statistics since 1979. The survey covers a nationally

representative sample of 12,686 individuals who were 14 to 21 years of age when first interviewed

in 1979. The interviews were conducted annually through 1994 and every two years afterward. The

5The notation is short handed for eR ≡ e− L(e|C), where L(.) is the projection of effort on circumstances

5

NLSY79 provides detailed information on education history and labor market participation as well as

other aspects of life including marriage, fertility, income and health. In addition, the survey collects data

on parental education and household characteristics when individuals were 14 years old. Incidence of

health shocks such as disability and health limitations are collected during each survey round. I use

the full sample of NLSY79, which over-sampled minority and disadvantaged individuals. This over-

sampling provides more data for the disadvantaged groups hence allows more accurate estimation of

the outcome distribution.

Health Variables A general health survey is administered when sample individuals turn 40. Three

health measures are reported in the survey - the self-rated health status (SAH), the physical component

score (PAH) and the mental component score (MAH). SAH are reported on a 1 to 5 scale with 5 being

excellent and 1 being poor6 PAH and MAH are indexes constructed on 12 questions specifically de-

signed for the panel. The component indexes are calculated on a 0 to 100 basis. If an individual scores

50 it means his health is better than 50% of the general population.

I use both self-reported health and the physical/mental component scores as the measure of health

condition. There is ongoing debate in the literature about using self-rated health as an objective mea-

sure of health. Some authors believe that the variable can capture aspects that are difficult to measure

by ”objective” variables (Case et al. [2002]). However, self-rated health is associated with reporting er-

ror and other psychological measurement issuesButler et al. 1987. Therefore as a double check, I also

use measures including the physical component score and mental component score, and birth weights

whenever possible. Another issue is that social norms used to rate health vary over time, hence the

measure captures a time effect. However, this is less of a concern because majority of my analyses

throughout this dissertation focus on a specific cohort of individuals and do not attempt to compare the

self-rated health for individuals that were born many years apart.

Circumstance In order to determine the circumstance variables, I need to find a partition variable

that is closely associated with adult health but over which individuals have little or no control. Many

theories have been proposed to explain the links between SES and health7. Two popular models in the

literature, the pathway model and the latency model, both attribute SES gradient in health to early life

experiences. The latency model emphasizes the importance of early life events and attributes dispari-

ties in adult health entirely to early experiences. The pathway model, on the other hand, underscores

the cumulative effect of SES over the life course, especially the interaction between SES and psycholog-

ical effectsAnderson et al. 2004, Asthana and Halliday 2006. Supporting evidence finds that parental

education level and parental income are significantly correlated with overall child health and onset of

chronic diseases. This positive correlation persists in children from infancy to early adulthood (Case

6The original survey reports the self rated health using a 5-1 scale with 5 being poor and 1 being excellent. I reverse the scale ofSAH so that it is consistent with other two health measures. It also makes the interpretation of inequality measure more intuitive.

7Please see ? for review

6

et al. 2002, Currie and Stabile 2003). Channels that link parental SES and child health include prenatal

nutrition, pregnancy health status, parental attention to young children and availability of consumption

of medical products Goldman 2001.

Based on discussions above, I classify the data into four types by individual race and parental ed-

ucation. The classification of types strictly follow the definition in the Roemer model. The chosen

circumstance variables in the analysis satisfy two conditions: First, they have direct or indirect effect on

adult health. Second, individuals have little or no control over these variables. Race and parental edu-

cation apparently satisfy both conditions. I recode race into white and minority based on the ethnicity

information collected during the initial round of interview. Parental education is coded into a binary

number based on the years of schooling of parents. I classify the parental schooling as ”high school”

if either parent received a high school degree and ”non-high school” if neither of the parent is a high

school graduate.

Effort In reality, effort is a multi-dimension variable that includes everything resulted from a per-

sonal choice that contributes to a healthy life. Effort would include choices of education, marriage, time

to exercise etc. In addition, it also includes any efforts made by the parents that enhance individual

health. Hence in this framework, I am not able to differentiate effort expended by the individual or by

her parents.

Summary statistics are presented in Table (1). Table (2) reports the average health by type. Average

health varies significantly across types. Type 7 (low parent education minority females) has the lowest

health status across all types. Type 4 (high parent education males) has the highest average health.

Standard deviation of health measures are similar across types.

Differences between average health are tested using the high parent education minority (type 1) as

the reference group. T-tests for each type-pair are presented in Table (3). The sample t-statistics reveal

that all three health measures are statistically different across types. Average health for the high parent

education groups (types 1, 3 and 2, 4) are statistically higher than that of the low parent education

groups (types 5, 7 and 6, 8). This holds for both men and women. Among the high parent education

types, minorities are less healthy than than whites.

However, comparing the average health across types does not tell us much about the distributional

differences and cannot be used to measure inequality of opportunity. Because FH|C �FSD FH|C′ ⇒

EH|C′ > EH|C8, comparisons between average health in fact constitutes a weaker test for inequality

of opportunity. In the next section, I will proceed with a direct test of distribution difference between

types.

8EH|C is the conditional mean of health given circumstances C

7

Table 1: Summary Statistics - Circmany empirical worksumstances by Gender

Females

Variable Obs Mean Std. Dev. Min Max

Self Rated Health (SAH) 3505 3.58 1.02 1 5

Physical Component Score (PAH) 3505 51.4 8.69 11.2 66.6

Mental Component Score (MAH) 3505 51.9 88.5 7.54 71.4

High School Graduate - Father 3068 0.57 0.50 0 1

High School Graduate - Mother 3415 0.54 0.50 0 1

Minority 3505 0.49 0.50 0 1

Males

Variable Obs Mean Std. Dev. Min Max

Self Rated Health (SAH) 3314 3.74 1.00 1 5

Physical Component Score (PAH) 3314 52.8 7.00 11.6 67.2

Mental Component Score (MAH) 3314 54.3 73.4 15.7 72.0

High School Graduate - Father 2950 0.58 0.49 0 1

High School Graduate - Mother 3210 0.58 0.49 0 1

Minority 3314 0.49 0.50 0 1

8

Tabl

e2:

Sum

mar

ySt

atis

tics

ofN

LSY

79-B

yTy

pe

SAH

*PA

H**

MA

H**

*Ty

peIn

dex

Mea

nSt

dFr

eq.

Mea

nSt

dFr

eq.

Mea

nSt

dFr

eq.

Hig

hPa

rent

Edu

Min

orit

yFe

mal

e1

3.51

1.00

802

51.0

8.70

802

51.9

9.20

802

Hig

hPa

rent

Edu

Min

orit

yM

ale

23.

780.

9282

252

.96.

7482

254

.77.

4882

2H

igh

Pare

ntEd

uW

hite

Fem

ale

33.

820.

9614

5352

.38.

4214

5352

.18.

2114

53H

igh

Pare

ntEd

uW

hite

Mal

e4

3.87

0.88

1394

53.6

5.96

1394

54.4

6.36

1394

Low

Pare

ntEd

uM

inor

ity

Fem

ale

53.

341.

0390

050

.98.

3990

051

.79.

0890

0Lo

wPa

rent

Edu

Min

orit

yM

ale

63.

551.

0679

451

.68.

2179

454

.07.

9579

4Lo

wPa

rent

Edu

Whi

teFe

mal

e7

3.37

0.99

350

49.4

9.92

350

50.8

9.89

350

Low

Pare

ntEd

uW

hite

Mal

e8

3.44

1.01

304

51.5

7.90

304

52.7

9.04

304

Tota

l3.

650.

9968

1952

.07.

9368

1953

.08.

2368

19*S

AH

-Sel

f-R

ated

Hea

lth;

**PA

H-P

hysi

calC

ompo

nent

Scor

e;**

*MA

H-M

enta

lCom

pone

ntSc

ore

9

Table 3: Type-wise Test of Equality of Mean

Type Type Index SAHa PAHb MAHc

Female

High Parent Edu Minor Female 1 - - -

High Parent Edu White Female 3 0.311 *** 1.226*** 0.215

Low Parent Edu Minori Female 5 -0.161*** -0.181 -0.154

Low Parent Edu White Female 7 -0.133 ** -1.645*** -1.037*

Male

High Parent Edu Minor Male 2

High Parent Edu White Male 4 0.091** 0.722*** 0.294

Low Parent Edu Minori Male 6 -0.231*** -1.296*** -0.679*

Low Parent Edu White Male 8 -0.344*** -1.362*** -0.198***a Self-reported Healthb Physical Component Scorec Mental Component Score

5 Results

I first plot the cumulative distributions of physical/mental component score and self-reported health

status by type in figure (2), (3) and (4). Graphs are plotted separately for men and women. The graphs

show significant difference in the cumulative distributions across the eight types. The cdf of the low

parent education types (yellow and green) lie above that of the high education groups (blue and red),

which means that the probability of reaching a certain level of health is higher for the latter group.

Therefore the low parent education types have not only a lower average health, but also an inferior

distribution of health.

In order to quantify the results, I perform the Kolmogorov-Smirnov test for equality of distributions

between the cumulative distributions of the eight types. The empirical distribution functions for F tH

can be computed as follows

F t(h) =1

n

n∑i=1

1(Ht,i ≤ h) (3)

I perform the test between every type-pair as defined in Table (2). The test statistic for the two-

sample Kolmogorov-Smirnov test is defined as

D1n = (

n1n0n1 + n0

)1/2suph∈R|Fn1,r(h)− Fn0,r(h)| (4)

10

Figure 2: Cumulative Distribution of Health - Physical Component

(a) Male

(b) Female

11

Figure 3: Cumulative Distribution of Health - Mental Component

(a) Male

(b) Female

12

Figure 4: Cumulative Distribution of Health - Self-Reported Health

(a) Male

(b) Female

13

Results of the tests are presented in Table (4). The upper panel contains tests for females and the

lower panel for males. I report the test statistics for all three measures of health: self-reported, physical

component and mental component.

The null hypothesis of the Kolmogorov-Smirnov test is that Fn1 and Fn0 are drawn from the same

distribution. D statistics reported in the table are the absolute value of the largest difference between

the two empirical distributions. Therefore a statistically significant D-value indicates that we can reject

the null hypothesis that samples were drawn from the same distribution. Under definition (??), there is

inequality of opportunity if for t 6= t′, F tH 6= F t′

H . Hence a statistically significant D-value indicates the

existence of inequality of opportunity between the two types tested.

As shown in Table (4), 24 out of the 36 pair-wise comparisons produce statistically significant D-stat

at 10% significant level. Hence the hypothesis that there is no inequality of opportunity for health can be

rejected. A close examination of the results show that the inequality of opportunity is more significant

for females than males. The average D-stat (indicating the absolute value of gaps between the two

distribution) is larger for the female group and more at the 10% level significance. Take the physical

component score measure as an example, for females, the type-pair with the largest difference is high

parent education white vs. low parent education minority (D-stat = 0.191). For males, the largest gap

is also observed for this type-pair (D-stat = 0.102). However, the D-stat is much larger for the female

group than the male group.

14

Tabl

e4:

Kol

mog

orov

-Sm

irno

vTe

sts

for

Equa

lity

ofD

istr

ibut

ion

-NLS

Y79

K-S

mir

nov

Test

SAH

PAH

MA

HFe

mal

esD

-sta

tP-

Val

ueD

-sta

tP-

Val

ueD

-sta

tP-

valu

eH

igh

Pare

ntEd

u,M

inor

ity

vs.W

hite

0.14

40.

000*

**0.

145

0.00

0***

0.06

00.

063*

Min

orit

y,H

igh

Pare

ntEd

uvs

.Low

0.06

40.

064*

0.07

90.

011*

*0.

075

0.01

6**

Hig

hPa

rent

Edu

Min

orit

yvs

.Low

Pare

ntEd

uW

hite

0.01

91.

000

0.11

60.

001*

**0.

075

0.09

0*H

igh

Pare

ntEd

uW

hite

vs.L

owPa

rent

Edu

Min

orit

y0.

201

0.00

0***

0.19

10.

000*

**0.

072

0.00

6***

Whi

te,H

igh

Pare

ntEd

uvs

.Low

0.16

30.

000*

**0.

178

0.00

0***

0.04

80.

420

Low

Pare

ntEd

u,M

inor

ity

vs.W

hite

0.04

50.

592

0.05

20.

389

0.06

50.

163

Mal

es:

Hig

hPa

rent

Edu,

Min

orit

yvs

.Whi

te0.

065

0.02

8**

0.06

40.

029*

*0.

111

0.00

0***

Min

orit

y,H

igh

Pare

ntEd

uvs

.Low

0.03

60.

646

0.06

00.

100*

0.03

90.

552

Hig

hPa

rent

Edu

Min

orit

yvs

.Low

Pare

ntEd

uW

hite

0.05

50.

451

0.05

90.

371

0.13

10.

000*

**H

igh

Pare

ntEd

uW

hite

vs.L

owPa

rent

Edu

Min

orit

y0.

101

0.00

0***

0.10

20.

000*

**0.

117

0.00

0***

Whi

te,H

igh

Pare

ntEd

uvs

.Low

0.07

10.

129

0.08

40.

043*

*0.

088

0.02

8**

Low

Pare

ntEd

u,M

inor

ity

vs.W

hite

0.04

60.

687

0.04

50.

712

0.14

10.

000*

**SA

H-S

elfR

epor

ted

Hea

lth;

PAH

-Phy

sica

lCom

pone

ntSc

ore;

MA

H-M

enta

lCom

pone

ntSc

ore

15

6 Distribution Decomposition

In this section I use the decomposition method to study the mechanisms through which educational

policy affects inequality of opportunity. I illustrate the method using NLSY79. The goal is to estimate

inequality of health generated via two pathways - education attainment and lifestyle-income pair. De-

composition allows easy construction of counterfactual distributions under different policy states. By

comparing the actual and counterfactual distributions, I can estimate the policy effect on equality of

opportunity based on our equity measure. I can also use the comparison to identify the gainers and

losers of potential policy change, both across types and within type.

NLSY79 constitutes a great data source for the purpose of our analysis because: (1) All individuals

were born within a cohort, which ruled out time variant policy effects on health. (2) NLSY has rich in-

formation on income and lifestyle choices such as cigarette consumption. Two decomposition analyses

are performed. First, by replacing the fraction of schooling in each type by the average fraction of the

sample, I calculate the policy effect through the education attainment channel. The second analysis re-

placed the individual income and lifestyle, condition on education, by the average income and lifestyle

across types. This analysis shows the portion of inequality that is attributed to the income-lifestyle

channel.

6.1 Data

The NLSY79 provides detailed information on education history, labor market participation and

activities as well as other aspects of life including marriage, fertility, income and health. Information

on parental education and occupation are also available. A general health survey is administered when

sample individuals turn 40. Self-rated health status are reported in this survey. Physical and mental

component indexes were calculated based on 12 questions specifically designed for the panel. The

component indexes are calculated on a 0 - 100 scale. An individual scores 50 means her health is better

than 50% of the general population. Physical component score is standardized to have mean 0 and

standard devision of 1.

Individuals are classified into eight types by circumstances. The types are determined by gender

x race x parental education. I recode race into white and minority based on the ethnicity information

collected during the initial round of interview. Parental education is coded into a binary number based

on their years of schooling. Parental schooling is classified as ”high” if either parent received a high

school degree and ”low” if neither of the parent is a high school graduate.

In addition to health and parental background data, lifestyle choices and income data are also

needed for the decomposition analysis. Questions on smoking behaviors were asked in survey year

1994 and 1998. Information on timing of smoking initiation, duration, current and past number of daily

cigarette consumption was gathered in these interviews. Income is divided into two categories: above

16

Table 5: Summary Statistics for NLSY79 Sample

Male SAHa PAHb Log Incomec Smokerde College Freq

High Parent Edu Minority 3.788 -0.123 10.757 0.456 0.196 825

High Parent Edu White 3.871 0.318 11.166 0.448 0.343 1402

Low Parent Edu Minority 3.553 -0.145 10.437 0.444 0.071 799

Low Parent Edu White 3.446 -0.330 10.732 0.593 0.052 305

Total 3.735 -0.085 10.857 0.462 0.215 3331

Female SAH PAH Log Income Smoker College Freq

High Parent Edu Minority 3.509 0.108 10.614 0.368 0.236 804

High Parent Edu White 3.818 0.198 11.071 0.487 0.358 1456

Low Parent Edu Minority 3.347 -0.056 10.283 0.338 0.095 903

Low Parent Edu White 3.377 -0.065 10.576 0.574 0.066 350

Total 3.582 0.090 10.722 0.430 0.233 3513a Self-Reported Health collected when individuals turn 40. It is rated with 1 being worst and 5 being best.b Physical Component Score. A number > 50 means the health of the individual is above the average

populationc 2006 household total income. Income is divided into 5 types by matching the value from the 2006 Current

Population Surveyd Binary indicator. A person is considered as a smoker if 1. She is smoking daily OR 2. She ever smoked dailye The smoking rate in our sample is higher than the national average. This could be explained by two reasons.

First, any one that had ever smoked cigarette regularly in the past is considered as a smoker, which is a morestrict classification. Second, the overall prevalence of smoking decreased sharply over the past three decades.Considering that majority of the individuals in my sample were born in the 1960s, the higher prevalence rateis reasonable.

and below median based on salary surveyed in 2006. The median salary is taken from the current pop-

ulation survey in 2006, which is a national benchmark for earnings in that year. Education attainment

is divided into two categories - college and none-college. Summary statistics are presented in table (5).

6.2 Decomposition with Discrete Health Outcomes

The first method follows Jones et al. [2014], in which the authors propsed a method to decompose

the health distribution via the income and education channel. Let t be the type, s be the educational

attainment, j income quantiles, and λ a life-style quality. Let σt(s) be the fraction of individuals of type t

who attain education level s under given policy. gs,t(λ, j) is the fraction of people in category (s, t) who

attain the income-lifestyle pair (λ, j). N t is the number of people of type t and N is the total number

of people. Assume type affects health through two pathways. First, type t affects education attainment

σ(s)t. Second, conditional on education attainment, type affects income-lifestyle g(λ, j)s,t

Let Hλ,j(.) be the cdf of health of the group that has life-style level λ and income j, which can

be calculated as the fraction of that group’s members whose health status is less than or equal to h.

17

Define F t(.) as the cumulative distribution function of health in type t. Then we can construction the

cumulative distribution of health as follows

F t(h) =1

N t

∑λ,j

Hλ,j(h)∑s

gs,t(λ, j)σt(s) (5)

In this specification, circumstance affects health through its impact on both gs,t(.) and σt(.). By the

decomposition, we are able to calculate the effect of the two separate channels: the education attainment

channel and the income-lifestyle channel (condition on education attainment). In order to quantify the

effect of these two channels, counterfactual distributions can be easily generated by replacing σt(s) (di-

rect effect) and replacing gs,t(λ, j) (indirect effect) with averages across types. LetNs,t be the number of

individuals obtain education level s in type t. Define σ(s) = 1N

∑s

∑tN

s,tσt(s). And let Nλ,j,t be the

number of individuals with income-lifestyle pair (λ, j) in type t. Define gs(λ, j) = 1N

∑s

∑tN

λ,j,tgs,t.

Then the counterfactual distribution by eliminating inequality through the education attainment chan-

nel is

F t1(h) =1

N t

∑λ,j

Hλ,j(h)∑s

gs,t(λ, j)σ(s) (6)

And the counterfactual distribution by eliminating inequality through the income-lifestyle channel is

F t2(h) =1

N t

∑λ,j

Hλ,j(h)∑s

gs(λ, j)σt(s) (7)

In order to analyze the effect of the two pathways through which inequality of opportunity arise,

I present three sets of results. First, Figure (5) shows three counterfactual cumulative distributions for

each type. The curve labeled ”Education” is calculated by replacing education level with the average

across all types. By doing this, the inequality of opportunity resulting from disparities in education

attainment is eliminated. The ”Lifestyle-Income” curve is calculated by replacing the income-lifestyle

pair with the average across all types so that the income-lifestyle channel of inequality is blocked. And

finally, the ”EOp” curve is when both education and income-lifestyle effects are eliminated.

These graphs show that first, the simulated policy has little or no impact on the high parent edu-

cation minority groups and the low parent education white. This holds for both men and women. By

replacing the education and income-lifestyle pairs, there is no significant change in health distributions

for these groups. The second observation is that health of the low parent education minority groups,

which are the least advantaged, becomes better. This is shown by the fact that the cdf is shifted to

the right under EOp policy (the red curve is to the right of the blue curve). Meanwhile, the health

of the most advantaged group, i.e. high parent education white, becomes worse if the education and

income-lifestyle inequality had been reduced (the red curve is to the left of the blue curve).

18

Table 6: Counterfactual Analysis of EOp policy values

Female Male

Eop Valueb Diff Eop Value Diff

Actual 3.323 - 3.446 -

(0.035)a (0.046)

Education 3.368 0.045 3.510 0.065

(0.035) (0.015) (0.064) (0.044)

Lifestyle-Income 3.454 0.131 3.516 0.070

(0.050) (0.042) (0.046) (0.021)

Eop Value 3.459 0.136 3.551 0.105

(0.039) (0.031) (0.059) (0.040)a Bootstrap standard errors based on 500 repetitionsb Health equity calculated based on equation

To further quantify these effects, I calculate the EOp value defined by equation (2). Results are pre-

sented in table (6). The columns labeled as EOp value calculates the health equity measure. The values

computed by EOp criteria is largest under the Equal Opportunity policy when both the education and

income-lifestyle inequalities are muted (3.459 for female and 3.551 for male). This means health of the

worst-off type is better under the EOp policy. The result is consisted with our hypothesis that a policy

that can eliminate these channels of inequality would be opportunity enhancing.

For both males and females, inequality arising from the income-lifestyle channel is larger than that

arising from the education channel. For females, the lifestyle-income channel contributes a lot more to

the total inequality of opportunity. When the education attainment channel is muted, the EOp value

increases by 0.045 (=3.368-3.323). The value increases by 0.131 (=3.454 - 3.323) when lifestyle-income is

equalized. The pattern also holds for males, although the effect arising from the income-lifestyle chan-

nel is less significant comparing to females. Our calculation indicates that for males, education channel

contributes 0.065 to the overall health inequality and income-lifestyle channel contributes 0.070. These

findings have interesting policy implications. In order to effectively reduce inequality of opportunity,

gender specific policies are needed. Enhancing the income-lifestyle opportunity is key to improving the

equality of opportunity for females. While for males, both education and income-lifestyle channels are

important.

6.3 Weighted Kernel Estimation

In this section I extend the decomposition analysis in previous section to a continuous health vari-

able. I use the weighted kernel estimation method proposed by DiNardo et al. [1996] (hereafter, DFL).

The DFL procedure determines how much of the change in health distribution can be explained by

19

Figure 5: Cumulative Distributions by Type - Smoking

(a) High Parent Education Minority Fe-male (b) High Parent Education Minority Male

(c) High Parent Education White Female (d) High Parent Education White Male

(e) Low Parent Education Minority Fe-male (f) Low Parent Education Minority Male

(g) Low Parent Education White Female (h) Low Parent Education White Male

20

Figure 6: Counterfactual Analysis of Equal Opportunity - Actual vs. EOp Policy

(a) Female

(b) Males

21

observed individual attributes. Two decomposition analyses are performed using the NLSY79 dataset.

Similar to the discrete method discussed in the previous section, I use the DFL procedure to study

inequality of opportunity arising from the education attainment, lifestyle and income channels.

Let h be a continuous variable of health outcome and x be a set of individual attributes. Let fH|X

denote the conditional distribution of health. If the distribution functions differ by type, then denote

the conditional pdf of type t as f tH|X . The distribution function of health for type t can be written as

f tH(h) =

�x

f tH|X(h|x)f tX(x)dx (8)

The counterfactual distribution when the distribution of X , f tX , is replaced by that of another type t′

can be written as

�x

f tH|X(h|x)f t′

X(x)dx (9)

Define the above counterfactual distribution as fH(h; tH|X = t, tX = t′). I will refer to tH|X as the

structure of health equation and tX as the structure of attributes. Therefore fH(h; tH|X = t, tX = t′)

denotes the distribution that would prevail if type t retained their own structure of health equation but

had the same attributes as t′. The counterfactuals when the distribution of education is equivalent to

that of the marginal distribution of education across all types can be generated as follows

fH(h; tH|S,I,E = t, tI,S|E = t, tE = avg)

=

�e

�i

�s

f tH|S,I,EftI,S|Ef

tE ∗

favgE

f tEds di de (10)

where favgE is the distribution of education attainment of a randomly chosen individuals from all types

(pooled). The weights favgE

ftE

can be calculated as

θE =favgE

f tE=

favgE

Pr(type = t|E) ∗ favgE

Pr(type=t)

=Pr(type = t)

Pr(type = t|E)(11)

Similarly, we can write the counterfactual distributions when education return to income and lifestyle

is held at the marginal distribution of the population as

fH(h; tH|S,I,E = t, tS|I,E = t, tI|E = avg, tE = t) (12)

=

�e

�i

�s

f tH|S,I,EftS|I,Ef

tI|E ∗

favgI|E

f tI|Ef tEds di de (13)

22

θI =favgI|E

f tI|E=

Pr(I,E)Pr(E)

Pr(type = t|I, E) Pr(I,E)Pr(E,type=t)

(14)

=Pr(E, type = t)

Pr(type = t|I, E)Pr(E)=

Pr(type = t|E)

Pr(type = t|I, E)(15)

The distribution of health can be written in two ways as fH =�(i,s,e)

fH|I,S,EfI|S,EfS|EfE or fH =�(i,s,e)

fH|I,S,EfS|I,EfI|EfE . Therefore equation (12) can also be written as

fH(h; tH|S,I,E = t, tS|I,E = t, tI|E = avg, tE = t)

=

�e

�i

�s

f tH|S,I,EftI|S,E ∗

favgI|S,E

f tI|S,Ef tS|Ef

tEds di de (16)

where

θI2 =Pr(type = t|S,E)

Pr(type = t|I, S,E)(17)

In order to consider both scenarios, I take the average of θI and θI2 in the empirical estimation. Similarly,

counterfactual by muting the lifestyle channel can be calculated as the average of the two weights

θS =favgS|E

f tS]E=

Pr(type = t|E)

Pr(type = t|S,E)(18)

θS2 =favgS|I,E

f tS|I,E=

Pr(type = t|I, E)

Pr(type = t|I, S,E)(19)

Data

Types are partitioned based on parental education level x gender x race. Figures (7) plots the dis-

tributions of physical component scores for each type. The figures show a significant difference in

the distributions of physical health across types, especially between individuals with different parental

education. The low parental education types not only have a lower average health, but also a larger dis-

persion. These graphs provide an intuitive evidence that the distributions of health look very different

across types. Therefore individuals sit at the same position of the health distribution (expend the same

degree of effort) would achieve very different health outcomes depending on her circumstances (or the

type that she belongs to). This difference indicates that there is inequality of opportunity for health.

Summary statistics are shown in table (5). All health measures are standardized to have mean zero and

standard deviation of one.

Direct Effect - Education Attainment Channel

I first calculate the counterfactual distributions when the direct effect of education is eliminated. This

is done by weighting the actual health distribution by θE as defined in equation (14). The probability of

23

Figure 7: Distribution of Physical Component Score - By Type

(a) Females

(b) Males

24

an individual belonging to a certain type, i.e. Pr(tx = type 1|x) is computed using a probit regression9.

The fraction of individuals for each type is directly computed from the sample fraction. Bandwidth for

kernel estimations are selected using the Silverman(1986) algorithm. All estimations use a Gaussian

kernel functions.

Figures (8) plot the actual and counterfactual distributions for females by type. Difference between

the two distributions are plotted on the right panel of figure (8). The most significant changes are

observed for individuals around the mean. For the two high parental education types, the density dif-

ference is positive from approximately -2 to 0, then becomes negative. This suggests that the counter-

factual policy shifts the distribution of these advantaged types to the left. It implies that the probability

of reaching certain health dropped for these types. The biggest distributional gains are observed for the

low parent education white type as shown in figure (8h). The difference is negative to the left of 0 and

becomes positive after 0. This suggests that the counterfactual distribution has shifted to the right for

this type. The maximum difference happens near the physical component score of about 0.5, where the

density increased by almost 4%. These evidence suggests that muting the education channel leads to

improvement health equity by equalizing the health distribution between the high parental educaiton

and low parental educaiton types.

Figure (9) present the same analysis for males. The low parent education white type also gains the

most from the counterfactual analysis. The probability of reaching health level of 0.5 increased almost

8% for this type.

Above evidence indicates that eliminating the direct effect of education through education attain-

ment is opportunity equalizing. It reduces the gap between the high parental educaiton and low

parental educaiton types by shifting the distribution to opposite directions. The most significant im-

pact happens for individuals around the mean.

Indirect Effect - Income and Lifestyle Channel

Counterfactual distributions simulated by equalizing opportunities through the income and lifestyle

channels are presented in Figures(10)-(13). Counterfactual distributions are calculated by weighting

the actual distributions by θI and θS as defined in equations (14) and (18). Difference between the

counterfactual and actual are plotted on the right panel of the figures. For females, when inequality

through the income channel is muted, the low parent minority type has a definitive gain. The entire

distribution is shifted to the right under the counterfactual policy. This can be seen in figure (10f),

where the difference is negative to the left of zero and becomes positive after zero. The effect is not as

significant for the low parent education white type. As shown in figure (10h), the difference is negative

between -4 to -2, becomes positive from -2 to 0 and falls negative after 0. This mixed pattern indicates9 According to the partition summarized in table (5), type 1 is minority male with high parental education.

25

that, for this specific type, the counterfactual policy improves the health for individuals on the left tail

of the distribution (worse health) but hurts individuals that are just above the average. Interestingly,

the pattern is reversed for males. As shown in figure (11e) - (11h), the low education white type has

a definitive gain under the counterfactual policy while the low education minority type experienced

mixed effect.

The counterfactual distributions simulated by muting the smoking channel are presented in figures

(12) and (13). The two low parental education types gained from the counterfactual policy for both

male and female. As shown in figures (12f) (12h)(13f)(13h), eliminating inequality through the smoking

channel shifts the distributions to the right. 10

Parametric Results

Figures presented above characterize the distributional changes with respect to three counterfac-

tual policies. However, it is difficult to access the statistical significance from these graphs. I therefore

present the parametric results from the weighted kernel estimation. I summarize the changes in dis-

tributions (counterfactual minus actual) by deciles for each policy experiment. Results are presented

in table (10) and (11). For example, for the first column of table (10), I first simulate the counterfactual

distribution by weighting the actual distribution by θE . Then I compute the difference of physical com-

ponent score between the actual and the weighted distribution at each decile. The results in the first

column first row is -0.026. This means health of individuals at 10th percentile of the actual distribution

is -0.026 less than that of the counterfactul distribution. If a policy is opportunity equalizing, we expect

to see negative differences below the median (50-percentile) and positive differences above the median

for the low parental education types (columns (7) - (12)). Standard errors are reported in parentheses.

The results indicate that the low parental education types benefit more from the policy changes. For

example, for the low parental education females (columns 7 - 12), the counterfactual policies reduce

percentage of individuals at the bottom 20% of the health distribution and increase percentage in all

other deciles. This means that the counterfactual policies shift the overall distribution towards the right

and these changes are considered as a distributional improvement for these types. Similar pattern holds

for the policy simulations for males. On the contrary, negative changes for the high parental education

types (columns (1) - (6)) can be seen at 50-th and 60-th percentiles.

Distribution comparisons presented in this section illustrate a method to estimate the distributional

effect of a policy changes. When counterfactual distributions are simulated under various policy states,

we can compare the difference between the actual and counterfactual distribution to identify the gain-

ers and losers for the policy shift. The three counterfactual policies I examined all lead to favorable

changes for the low parental education types. The distributions of health shifted to the right under

10For robustness checks, I simulated counterfactuals calculated by equations (17) and (19). There is not significant differencebetween these two measures. Figures available upon request

26

Table 7: Policy Simulation - Females

Policy Physical Component Score Diff (with Original)

Actual 49.338 -

Equal Lifestyle 49.563 0.225

Equal Education 49.673 0.336

Equal Income 49.770 0.432

Table 8: Policy Simulation - Males

Policy Physical Component Score Diff (with Original)

Actual 51.062 -

Equal Lifestyle 51.424 0.362

Equal Education 51.423 0.362

Equal Income 51.572 0.510

these opportunity equalizing policies for these types.

EOp Value

To quantify the distributional effect of the policy experiments, I calculate the EOp value for each

counterfactual distribution. The results are presented in Tables (7) and (8). Health equity improved

under all opportunity equalizing policy simulations. For females, muting the income channel produce

the largest gain in terms of health equity. The EOp value increased by 0.432, followed by the education

attainment channel and lifestyle channel. Similar pattern holds for males, although the education and

lifestyle channel contribute equally to the inequality of opportunity for health.

7 Changes in Average Health under EOp Policy

One of the major criticisms for the equal opportunity theory is equity efficient trade off. Some

opponents argue that a policy that focuses on increasing equality might reduce the ”size of the pie”.

Although understanding the complete picture of efficient-equality trade off in health is beyond the

scope of this paper, it is certainly one of the future research directions. In order to address this issue, I

compare the average health under the Status Quo versus the EOp policy. Counterfactuals are simulated

using NLSY79 data and decomposition models discussed in section (3.4). Results are presented in table

(9). Two measures are reported in the table. Column (4) calculates the difference in average health

between the actual and counterfactual policy. Column (6) computes the ratio of the two.

The results indicate that for females, average health is reduced only under the scenario where the

education attainment channel is muted. The average health decreased by 0.019 comparing to actual.

27

Table 9: Efficiency Comparison - By Gender

(1) (2) (3) (4) (5) (6)

Policy Average Health Std Errorc Diff a Std Error c Fraction b

Female

Actual 3.582 0.018 -

Education 3.563 0.018 -0.019 0.006 0.99

Lifestyle-Income 3.625 0.025 0.043 0.017 1.01

Eop Policy 3.591 0.022 0.009 0.014 1.00

Male

Actual 3.736 0.017 -

Education 3.732 0.018 -0.004 0.006 1.00

Lifestyle-Income 3.742 0.024 0.007 0.016 1.00

Eop Policy 3.716 0.023 -0.019 0.015 0.99a Average health (column 1) of actual minus counterfactualb Ratio of average health between actual and counterfactuala [c]Bootstrapped standard errors based on 500 repetitions

All other equality enhancing policies lead to improved average health. For males, decrease in average

health happens under two of the equality enhancing policies. However, none of the differences are

statistically significant. These evidence does not suggest that there is loss of efficiency for opportunity

equalizing.

28

Tabl

e10

:Diff

eren

cein

Hea

lth

Dis

trib

utio

nD

ecile

s-F

emal

es

Hig

hPa

rent

Edu

Min

orit

yH

igh

Pare

ntEd

uW

hite

Low

Pare

ntEd

uM

inor

ity

Low

Pare

ntEd

uW

hite

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

Edu

Inco

me

Life

styl

eEd

uIn

com

eLi

fest

yle

Edu

Inco

me

Life

styl

eEd

uIn

com

eLi

fest

yle

10-0

.026

-0.0

45-0

.023

-0.0

24-0

.026

-0.0

27-0

.003

-0.0

10-0

.011

-0.0

12-0

.009

-0.0

06

(0.0

04)a

(0.0

04)

(0.0

03)

(0.0

02)

(0.0

02)

(0.0

02)

(0.0

03)

(0.0

04)

(0.0

03)

(0.0

04)

(0.0

06)

(0.0

05)

20-0

.024

-0.0

38-0

.014

-0.0

22-0

.026

-0.0

22-0

.001

-0.0

05-0

.009

-0.0

05-0

.004

-0.0

03

(0.0

05)

(0.0

08)

(0.0

05)

(0.0

03)

(0.0

05)

(0.0

04)

(0.0

04)

(0.0

08)

(0.0

05)

(0.0

09)

(0.0

08)

(0.0

06)

30-0

.022

-0.0

25-0

.012

-0.0

18-0

.014

-0.0

190.

000

0.00

2-0

.005

0.00

00.

004

0.00

0

(0.0

07)

(0.0

09)

(0.0

06)

(0.0

05)

(0.0

07)

(0.0

05)

(0.0

07)

(0.0

11)

(0.0

07)

(0.0

12)

(0.0

13)

(0.0

12)

40-0

.022

-0.0

14-0

.010

-0.0

10-0

.012

-0.0

090.

001

0.01

8-0

.002

0.00

30.

007

0.00

2

(0.0

09)

(0.0

09)

(0.0

09)

(0.0

08)

(0.0

11)

(0.0

08)

(0.0

10)

(0.0

13)

(0.0

09)

(0.0

09)

(0.0

10)

(0.0

07)

50-0

.015

-0.0

03-0

.006

-0.0

02-0

.005

-0.0

020.

002

0.02

30.

000

0.01

10.

010

0.00

4

(0.0

12)

(0.0

13)

(0.0

13)

(0.0

11)

(0.0

16)

(0.0

11)

(0.0

10)

(0.0

14)

(0.0

10)

(0.0

15)

(0.0

20)

(0.0

15)

60-0

.006

0.00

1-0

.002

0.00

0-0

.002

0.00

10.

005

0.03

00.

002

0.02

50.

017

0.00

6

(0.0

13)

(0.0

16)

(0.0

13)

(0.0

14)

(0.0

17)

(0.0

12)

(0.0

11)

(0.0

19)

(0.0

12)

(0.0

20)

(0.0

26)

(0.0

20)

700.

000

0.00

40.

001

0.00

10.

000

0.00

20.

007

0.03

60.

005

0.03

10.

026

0.01

1

(0.0

13)

(0.0

17)

(0.0

12)

(0.0

19)

(0.0

24)

(0.0

17)

(0.0

13)

(0.0

22)

(0.0

13)

(0.0

25)

(0.0

33)

(0.0

25)

800.

004

0.00

70.

003

0.00

30.

003

0.00

30.

009

0.04

70.

007

0.03

40.

034

0.01

4

(0.0

16)

(0.0

22)

(0.0

15)

(0.0

18)

(0.0

22)

(0.0

16)

(0.0

14)

(0.0

22)

(0.0

13)

(0.0

30)

(0.0

41)

(0.0

30)

900.

007

0.01

00.

007

0.00

50.

006

0.00

40.

010

0.05

10.

008

0.03

40.

037

0.01

5

(0.0

19)

(0.0

26)

(0.0

17)

(0.0

18)

(0.0

24)

(0.0

17)

(0.0

15)

(0.0

26)

(0.0

14)

(0.0

32)

(0.0

45)

(0.0

33)

aBo

otst

rapp

edst

anda

rder

rors

29

Tabl

e11

:Diff

eren

cein

Hea

lth

Dis

trib

utio

nD

ecile

s-M

ales

Hig

hPa

rent

Edu

Min

orit

yH

igh

Pare

ntEd

uW

hite

Low

Pare

ntEd

uM

inor

ity

Low

Pare

ntEd

uW

hite

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

Edu

Inco

me

Life

styl

eEd

uIn

com

eLi

fest

yle

Edu

Inco

me

Life

styl

eEd

uIn

com

eLi

fest

yle

10-0

.020

-0.0

25-0

.013

-0.0

03-0

.005

-0.0

04-0

.007

-0.0

10-0

.012

-0.0

09-0

.007

-0.0

03

(0.0

03)a

(0.0

05)

(0.0

03)

(0.0

03)

(0.0

03)

(0.0

03)

(0.0

02)

(0.0

05)

0.00

20.

005

0.00

60.

006

20-0

.017

-0.0

25-0

.008

0.00

0-0

.002

-0.0

01-0

.003

-0.0

04-0

.006

-0.0

06-0

.003

-0.0

01

(0.0

07)

(0.0

10)

(0.0

08)

(0.0

07)

(0.0

08)

(0.0

07)

(0.0

10)

(0.0

10)

(0.0

09)

(0.0

12)

(0.0

15)

(0.0

10)

30-0

.016

-0.0

19-0

.007

0.00

20.

000

-0.0

010.

000

0.00

3-0

.002

-0.0

01-0

.001

0.00

1

(0.0

12)

(0.0

16)

(0.0

12)

(0.0

09)

(0.0

11)

(0.0

09)

(0.0

08)

(0.0

12)

(0.0

08)

(0.0

15)

(0.0

17)

(0.0

13)

40-0

.015

-0.0

10-0

.006

0.00

40.

005

0.00

10.

003

0.01

00.

000

0.00

80.

005

0.00

4

(0.0

11)

(0.0

20)

(0.0

11)

(0.0

10)

(0.0

13)

(0.0

10)

(0.0

11)

(0.0

17)

(0.0

10)

(0.0

13)

(0.0

19)

(0.0

13)

50-0

.012

-0.0

05-0

.005

0.00

40.

005

0.00

20.

020

0.03

90.

003

0.01

70.

018

0.00

8

(0.0

13)

(0.0

20)

(0.0

12)

(0.0

12)

(0.0

13)

(0.0

12)

(0.0

13)

(0.0

21)

(0.0

12)

(0.0

18)

(0.0

24)

(0.0

19)

60-0

.008

0.00

0-0

.003

0.00

70.

009

0.00

60.

029

0.05

00.

010

0.03

80.

036

0.01

0

(0.0

15)

(0.0

25)

(0.0

14)

(0.0

20)

(0.0

20)

(0.0

22)

(0.0

17)

(0.0

21)

(0.0

13)

(0.0

24)

(0.0

31)

(0.0

25)

70-0

.002

0.00

50.

001

0.01

30.

015

0.01

00.

032

0.05

40.

018

0.05

60.

047

0.01

5

(0.0

18)

(0.0

32)

(0.0

19)

(0.0

19)

(0.0

21)

(0.0

20)

(0.0

18)

(0.0

23)

(0.0

16)

(0.0

33)

(0.0

44)

(0.0

33)

800.

002

0.01

30.

003

0.02

00.

016

0.02

30.

034

0.06

60.

022

0.07

70.

065

0.02

1

(0.0

21)

(0.0

32)

(0.0

22)

(0.0

19)

(0.0

23)

(0.0

20)

(0.0

20)

(0.0

26)

(0.0

18)

(0.0

48)

(0.0

63)

(0.0

46)

900.

005

0.02

20.

008

0.02

30.

017

0.03

10.

038

0.06

90.

030

0.08

20.

071

0.02

4

(0.0

23)

(0.0

37)

(0.0

25)

(0.0

26)

(0.0

33)

(0.0

28)

(0.0

21)

(0.0

28)

(0.0

20)

(0.0

51)

(0.0

68)

(0.0

50)

aBo

otst

rapp

edst

anda

rder

rors

30

8 Conclusion

In this paper I proposed an index to estimate the equality of opportunity for health. The equity

measure is constructed based on the Roemer model of equal opportunity. The equal opportunity the-

ory introduced a second dimension into the social welfare function: individual circumstances. The

distributive justice philosophy behind this social welfare function is that individuals should be com-

pensated for factors over which they have little or no control of.

The health equity measure constructed based on the equal opportunity theory captures the under-

lying distribution characteristics of health. This supplements the current research on social economic

status and health, which largely focuses on the social economic differentials of health. The equity mea-

sure provides an easy-to-compute decisions rules for policy makers to compare various outcome distri-

butions.

I apply the equity measure on the NLSY79 dataset. I first test the existence of inequality of oppor-

tunity for health. My results indicate that we can reject the hypothesis that there is no inequality of

opportunity for health in the United States. By comparing the cdf of health across types, I show that the

cdf for the advantaged types are statistically different from the disadvantaged types. The pattern holds

for both men and women.

I then use two decomposition methods to study the mechanisms through which policy interventions

affect health inequality. Counterfactual distributions are generated based on these models. The coun-

terfactual analysis allows us to directly estimate the distributional changes due to policy shifts. Policy

simulations suggest that the most effective way to reduce health inequity is through interventions on

income condition on education attainment. Statistically significant improvement in health equity is

found when inequality through these channels is muted. My calculation does not reveal significant loss

of efficiency as a result of opportunity equalization.

I intend to provide tools that can be applied to evaluate inequality of opportunity for health. There-

fore theoretical models and objective functions proposed here are considered as what can be done rather

than what should be done. The evaluation framework proposed can be extended to other measures of

health equity in the future.

31

Figure 8: Actual and Counterfactual Distribution - Education Channel, Female

(a) High Parent Edu Minority (b) Difference

(c) Low Parent Edu Minority (d) Difference

(e) High Parent Edu White (f) Difference

(g) Low Parent Edu White (h) Difference

32

Figure 9: Actual and Counterfactual Distribution - Education Channel, Male

(a) High Parent Edu Minority (b) Difference

(c) Low Parent Edu Minority (d) Difference

(e) High Parent Edu White (f) Difference

(g) Low Parent Edu White (h) Difference

33

Figure 10: Actual and Counterfactual Distribution - Income Channel, Female

(a) High Parent Edu Minority (b) Difference

(c) Low Parent Edu Minority (d) Difference

(e) High Parent Edu White (f) Difference

(g) Low Parent Edu White (h) Difference

34

Figure 11: Actual and Counterfactual Distribution - Income Channel, Male

(a) High Parent Edu Minority (b) Difference

(c) High Parent Edu White (d) Difference

(e) Low Parent Edu Minority (f) Difference

(g) Low Parent Edu White (h) Difference

35

Figure 12: Actual and Counterfactual Distribution - Smoking Channel, Female

(a) High Parent Edu Minority (b) Difference

(c) High Parent Edu White (d) Difference

(e) Low Parent Edu Minority (f) Difference

(g) Low Parent Edu White (h) Difference

36

Figure 13: Actual and Counterfactual Distribution - Smoking Channel, Male

(a) High Parent Edu Minority (b) Difference

(c) High Parent Edu White (d) Difference

(e) Low Parent Edu Minority (f) Difference

(g) Low Parent Edu White (h) Difference

37

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