Accounting for the E⁄ect of Health on Economic Growth by...

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Accounting for the E/ect of Health on Economic Growth by David Weil (2006) September 2007 () Health September 2007 1 / 15

Transcript of Accounting for the E⁄ect of Health on Economic Growth by...

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Accounting for the E¤ect of Health on EconomicGrowth by David Weil (2006)

September 2007

() Health September 2007 1 / 15

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Basic Framework

Builds on Hall and Jones (1999)

Aggregate production function for country i :

Yi = AiK αi H

1�αi

whereHi = hiviLi

and

hi = educational human capital per worker

vi = health human capital per worker

Li = number of workers

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Decomposition in log per capita terms:

ln yi = lnAi + α ln ki + (1� α) ln hi + (1� α) ln vi

,! given estimates of yi , ki , hi and α, need to construct an index for vi .

Wage per unit of human capital in country i :

wi = (1� α)Ai

�KiHi

�α

Wage earned by individual j in country i , in logs:

lnwij = lnwi + ln hij + ln vij + ηij

where ηij is an individual�speci�c error term.

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Individual health and productivityConsider two workers j = 1, 2 in country i with the same education.The expected di¤erence in log wages is

lnw2 � lnw1 = ln v1 � ln v2,! we can�t observe vj directly, but can observe health indicators, Ij

Suppose zj represents the health of worker j and assume

Ij = α+ γI zj + εIj

ln vj = β+ γv zj + εvj

,! for workers 1 and 2:

lnw2 � lnw1 = γv (z1 � z2)I1 � I2 = γI (z1 � z2)

,! the expected log wage gap is then

lnw2 � lnw1 = ln v1 � ln v2 = ρI (I1 � I2)where ρI = γv/γI denotes the return to health indicator I

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Health Indicators

Average height of adult men

,! a good indicator of the health environment in which a person grew up

,! depends on nutrition and health in utero and childhood

,! non-health determinants of height wash out at the aggregate level

Adult Survival Rate (ASR)

,! fraction of 15 year olds who will survive to 60

,! good measure of health during working years

,! captures impact of AIDS (Figure I and II)

Age of Menarche (onset of menstruation)

,! delayed menarche is a good indicator of malnutrition in childhood

,! data limitations (Figure III)

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Figure IGDP per Worker vs. Adult Survival Rate

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

100 1000 10000 100000

GDP per Worker (1996)

Adu

lt Su

rviv

al R

ate

for M

ales

(19

99)

Botswana

South Africa

Zimbabwe

Guinea

Cote d'Ivore

Zambia

Central Afr. Rep.Rwanda

Uganda

Papua New Guinea

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Figure II Adut Survival Rate

0.56

0.61

0.66

0.71

0.76

0.81

0.86

1960 1970 1980 1990 2000

Year

Mea

n A

SR

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Stan

dard

Dev

iatio

n of

ASR

Mean ASR (left scale)

Standard Deviationof ASR (right scale)

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Figure III

Age of Menarche vs. GDP per Worker

12

12.5

13

13.5

14

14.5

15

15.5

16

1000 10000 100000

GDP per Worker in 1995

Ag

e o

f M

en

arc

he

Nigeria

Haiti

Papua New Guinea

Mozambique

United States

Italy

Ireland

Nicaragua

Algeria

Thailand

Kenya

Zambia

Portugal

Norway

Malaysia

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Estimating the Return to Health Characteristics

Naive approach: regress log wages on the indicator

Problems: estimate would be biased due to

(1) reverse causation

,! a person may have good health because they have high wages

(2) omitted variable bias

,! a person may have good health and high wages for other reasons

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Instrumental Variables (2SLS) MethodologyHypothesized structural model:

log yi = α+ βSi + εi

Si = γ+ δ log yi + θXi + ηi ,

where

yi = dependent variable (e.g. wages)

Si = key explanatory variable (e.g. health)

Xi = vector of exogenous instrumental variables

Reduced form for Si :

Si =γ+ δα+ θXi + δεi + ηi

1� δβ

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If Xi is uncorrelated with εi and ηi then we can estimate the ��rststage regression�

Si = a+ bXi + ui

using OLS where

a =γ+ δα

1� δβand b =

θ

1� δβ

Then run �second-stage regression�

log yi = α+ βSi + εi

using the �tted valueSi = a+ bXi

Estimate of β should re�ect impact of variations in Si that are due toexogenous variation in X 0i s only

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Three key requirements of "good instruments":

,! R2 in �rst stage regression must be reasonably high

,! must clearly be an exogenous determinant of Si,! no other channels through which Xi e¤ects yi (over identifying

restriction)

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Instrumental Variables Approaches to Health Outcomes

Exogenous Variation in Childhood Inputs,! distance to local health facilities; relative price of food in worker�sarea of origin,! estimates in Table I control for schooling,! estimates for ρheight = (0.08, 0.094, 0.078); for ρmen = 0.28

Exogenous variation in birth weights between monozygotic twins (US),! genetically identical and same family environment,! only di¤erence is birth weight,! implied estimates for ρheight = (0.033, 0.035)

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Table I

Structural Estimates of the Effect of Health Indicators on Wages

Health Indicator

(unit)

Effect on

ln(wage)

Sample Country and Year Source

Height (cm)

0.080

(0.0056)

Males 18-60 Colombia (urban),

1991

Ribero and NuZez

(2000)

0.094

(0.025)

Males 25-54 Ghana, 1987-89 Schultz (2002)

0.078

(0.0083)

Males 20-60 Brazil, 1989 Schultz (2002)

Age of Menarche

(yrs)

-0.261

(0.111)

Females 18-54 Mexico, 1995 Knaul (2000)

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Return to health using historical data

Fogel (1997) estimates caloric intake in the UK over 1780-1980 andits impact on labour supply

,! estimates improved nutrition raised labour input by a factor of 1.95

,! given that height increased by 9.1 cm over this period:

ρheight =ln(vt+1/vt )It+1 � It

=ln(1.95)9.1

= 0.073

,! similarly for age of menarche

ρmen = 0.26

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Relating ASR and Height

Problem:

,! ASR is available for many countries, but there is no estimate of ρASRfrom micro studies

,! we have estimates of ρheight, but height data is not available for manycountries

Can take advantage of existing framework to back out relevant proxy

,! regress height on ASR using panel data on 10 countries with country�xed e¤ects (Table II)

,! slope coe¢ cient is a proxy for ρASR/ρheight = 19.2 and so

ρASR = 0.653

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Figure IVData on Height and Adult Survival

400

450

500

550

600

650

700

750

800

850

900

162 164 166 168 170 172 174 176 178 180 182

height (cm)

Adu

lt Su

rviv

al R

ate

(per

thou

sand

)

DenmarkFranceItalyJapanS. KoreaNetherlandsSpainSwedenUKUSA

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The Contribution of Health to Income Di¤erences

Recall that we have

ln yi = lnAi + α ln ki + (1� α) ln hi + (1� α) ln vi

Share of var(ln y) attributable to each factor (Table III)

,! cross country variance decomposition is given by

var( ln y) = var( ln y) + var( lnA) + α2var( ln k) + (1� α)2var( ln h)

+(1� α)2var( ln) + covariance terms

,! eliminating health gaps across countries reduces variance of logincome by 9.9 - 12.3%

,! accounting for health reduces the fraction of var(ln y) coming fromresidual productivity by 7 - 12 %

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Table III

Shares of Variation in Output per Worker Attributable to Each Factor

Sample: ASR (N=92) Menarche (N=42)

Health Indicator Adjusted for: None ASR None Age of

Menarche

ASR

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

var(ln(y)) 1.22 1.22 .888 .888 .888

var( """" ln(k)) / var (ln(y)) .221 .221 .242 .242 .242

var ((1- """")ln(h)) / var(ln(y)) .032 .032 .038 .038 .038

var (ln(A)) / var (ln(y)) .179 .144 .175 .154 .139

cov ("""" ln(k), (1- """")ln(h)) / var(ln(y)) .074 .074 .083 .083 .083

cov (ln(A), """" ln(k)) / var (ln(y)) .161 .137 .150 .111 .123

cov (ln(A), (1- """")ln(h)) / var(ln(y)) .048 .040 .040 .028 .032

var ((1- """") ln(v)) / var(ln(y)) .004 .021 .005

cov ("""" ln(k), (1- """")ln(v)) / var(ln(y)) .024 .039 .027

cov ((1-"""") ln(h), (1- """")ln(v)) / var(ln(y)) .008 .012 .008

cov (ln(A), (1- """")ln(v)) / var(ln(y)) .015 .000 .015

Fraction of Variance in ln(y)

Attributable to Productivity

.598 .529 .555 .431 .480

Proportional Reduction in Variance of

ln(y) from Eliminating Health Gaps

.099 .123 .106

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E¤ect of Eliminating health gaps on income ratios (Table IV)

,! �90/10 ratio� is the ratio of GDP per worker of country at 90thpercentile to that of country at 10th percentile, etc.

,! eliminating health gaps would reduce the 90-10 income ratio by 12.7%

,! most of this comes from the lower half of the distribution

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Table IV

Effect of Eliminating Health Gaps on Income Ratios

Sample Health

Measure

Income Ratio Raw Data Eliminating

Health Gaps

ASR ASR

90/10 20.47 17.88

90/50 3.21 3.08

50/10 6.37 5.80

Menarche ASR

90/10 10.05 9.21

90/50 1.75 1.71

50/10 5.74 5.39

Menarche Menarche

90/10 10.05 7.76

90/50 1.75 1.82

50/10 5.74 4.25

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Broad Conclusions

Health has an economically important e¤ect in determining incomedi¤erences among countries

,! BUT health is less important than human capital from education andphysical capital

,! residual productivity is still the most important determinant ofcross�country income di¤erences

Caveat: accounting approach does not measure health e¤ects actingthrough investment in physical capital, education and populationgrowth

,! i.e. health improvements could cause k = KL and h =

HL to rise or fall

() Health September 2007 15 / 15