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Transcript of Accounting for the E⁄ect of Health on Economic Growth by ...qed.econ. · PDF...

Accounting for the Eect 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 i H1i

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 + ln ki + (1 ) ln hi + (1 ) ln vi

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

Wage per unit of human capital in country i :

wi = (1 )AiKiHi

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

lnwij = lnwi + ln hij + ln vij + ij

where ij is an individualspecic 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 dierence in log wages is

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

Suppose zj represents the health of worker j and assume

Ij = + I zj + Ijln vj = + v zj + vj

,! for workers 1 and 2:lnw2 lnw1 = v (z1 z2)

I1 I2 = I (z1 z2),! the expected log wage gap is then

lnw2 lnw1 = ln v1 ln v2 = I (I1 I2)where I = v/I 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 = + Si + iSi = + log yi + Xi + i ,

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 =+ + Xi + i + i

1

() Health September 2007 7 / 15

If Xi is uncorrelated with i and i then we can estimate the rststage regression

Si = a+ bXi + ui

using OLS where

a =+

1 and b =

1

Then run second-stage regression

log yi = + Si + i

using the tted valueSi = a+ bXi

Estimate of should reect 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 eects 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 workersarea of origin,! estimates in Table I control for schooling,! estimates for height = (0.08, 0.094, 0.078); for men = 0.28

Exogenous variation in birth weights between monozygotic twins (US),! genetically identical and same family environment,! only dierence is birth weight,! implied estimates for height = (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:

height =ln(vt+1/vt )It+1 It

=ln(1.95)9.1

= 0.073

,! similarly for age of menarche

men = 0.26

() Health September 2007 11 / 15

Relating ASR and Height

Problem:

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

,! we have estimates of height, 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 countryxed eects (Table II)

,! slope coe cient is a proxy for ASR/height = 19.2 and so

ASR = 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 Dierences

Recall that we have

ln yi = lnAi + ln ki + (1 ) ln hi + (1 ) 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) + 2var( ln k) + (1 )2var( ln h)+(1 )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

Eect 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 ga