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Accounting for the E¤ect of Health on EconomicGrowth by David Weil (2006)
September 2007
() Health September 2007 1 / 15
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
() Health September 2007 2 / 15
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.
() Health September 2007 3 / 15
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
() Health September 2007 4 / 15
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)
() Health September 2007 5 / 15
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
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)
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
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
() Health September 2007 6 / 15
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
() Health September 2007 7 / 15
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
() Health September 2007 8 / 15
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)
() Health September 2007 9 / 15
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)
() Health September 2007 10 / 15
50
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)
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
() Health September 2007 11 / 15
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
() Health September 2007 12 / 15
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
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 %
() Health September 2007 13 / 15
52
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
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
() Health September 2007 14 / 15
53
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
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