Accounting for the Eect of Health on Economic Growth by David Weil - - PowerPoint PPT Presentation

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

September 2007

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Basic Framework

Builds on Hall and Jones (1999) Aggregate production function for country i: Yi = AiK α

i H1α i

where Hi = 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 = ln Ai + 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 Ki Hi α Wage earned by individual j in country i, in logs: ln wij = ln wi + ln hij + ln vij + ηij where ηij is an individual–speci…c error term.

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Individual health and productivity

Consider two workers j = 1, 2 in country i with the same education. The expected di¤erence in log wages is ln w2 ln w1 = 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 + γvzj + εvj , ! for workers 1 and 2: ln w2 ln w1 = γv (z1 z2) I1 I2 = γI (z1 z2) , ! the expected log wage gap is then ln w2 ln w1 = 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 I GDP 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) Adult Survival Rate for Males (1999) 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 Mean ASR

• 0.1
• 0.05

0.05 0.1 0.15 0.2 Standard Deviation of ASR Mean ASR (left scale) Standard Deviation

• f 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 Age of Menarche 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

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Instrumental Variables (2SLS) Methodology

Hypothesized 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 “…rst stage regression” Si = a + bXi + ui using OLS where a = γ + δα 1 δβ and b = θ 1 δβ Then run “second-stage regression” log yi = α + β ˆ Si + εi using the …tted value ˆ Si = ˆ a + ˆ bXi Estimate of β should re‡ect impact of variations in Si that are due to exogenous variation in X 0

i 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’s area 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 Nuez (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 and its 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 ρASR from micro studies , ! we have estimates of ρheight, but height data is not available for many countries 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 IV Data 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) Adult Survival Rate (per thousand) Denmark France Italy Japan

• S. Korea

Netherlands Spain Sweden UK USA

The Contribution of Health to Income Di¤erences

Recall that we have ln yi = ln Ai + 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( ln A) + α2var( ln k) + (1 α)2var( ln h) +(1 α)2var( ln) + covariance terms , ! eliminating health gaps across countries reduces variance of log income by 9.9 - 12.3% , ! accounting for health reduces the fraction of var(ln y) coming from residual 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

E¤ect of Eliminating health gaps on income ratios (Table IV) , ! “90/10 ratio” is the ratio of GDP per worker of country at 90th percentile 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

Broad Conclusions

Health has an economically important e¤ect in determining income di¤erences among countries , ! BUT health is less important than human capital from education and physical capital , ! residual productivity is still the most important determinant of cross–country income di¤erences Caveat: accounting approach does not measure health e¤ects acting through investment in physical capital, education and population growth , ! i.e. health improvements could cause k = K

L and h = H L to rise or fall

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