Accounting for the E¤ect of Health on Economic Growth 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 : Y i = A i K α i H 1 � α i where H i = h i v i L i and h i = educational human capital per worker v i = health human capital per worker L i = number of workers () Health September 2007 2 / 15
Decomposition in log per capita terms: ln y i = ln A i + α ln k i + ( 1 � α ) ln h i + ( 1 � α ) ln v i , ! given estimates of y i , k i , h i and α , need to construct an index for v i . Wage per unit of human capital in country i : � K i � α w i = ( 1 � α ) A i H i Wage earned by individual j in country i , in logs: ln w ij = ln w i + ln h ij + ln v ij + η ij where η ij is an individual–speci…c error term. () Health September 2007 3 / 15
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 w 2 � ln w 1 = ln v 1 � ln v 2 , ! we can’t observe v j directly, but can observe health indicators, I j Suppose z j represents the health of worker j and assume I j = α + γ I z j + ε Ij ln v j = β + γ v z j + ε vj , ! for workers 1 and 2: ln w 2 � ln w 1 = γ v ( z 1 � z 2 ) I 1 � I 2 = γ I ( z 1 � z 2 ) , ! the expected log wage gap is then ln w 2 � ln w 1 = ln v 1 � ln v 2 = ρ I ( I 1 � I 2 ) where ρ I = γ v / γ 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 I GDP per Worker vs. Adult Survival Rate 1 0.9 Adult Survival Rate for Males (1999) 0.8 0.7 Papua New Guinea 0.6 Guinea 0.5 Cote d'Ivore Zimbabwe 0.4 South Africa Zambia 0.3 Rwanda Central Afr. Rep. Botswana Uganda 0.2 100 1000 10000 100000 GDP per Worker (1996)
Figure II Adut Survival Rate 0.86 0.2 0.81 0.15 Standard Deviation of ASR (right scale) Standard Deviation of ASR 0.76 0.1 Mean ASR 0.71 0.05 0.66 0 Mean ASR (left scale) 0.61 -0.05 0.56 -0.1 1960 1970 1980 1990 2000 Year
Figure III Age of Menarche vs. GDP per Worker 16 Papua New Guinea 15.5 Haiti Nigeria 15 14.5 Age of Menarche Algeria Malaysia Nicaragua Kenya 14 Zambia Ireland 13.5 Norway Mozambique 13 United States 12.5 Thailand Italy Portugal 12 1000 10000 100000 GDP per Worker in 1995
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) Methodology Hypothesized structural model: log y i = α + β S i + ε i S i = γ + δ log y i + θ X i + η i , where = y i dependent variable (e.g. wages) S i = key explanatory variable (e.g. health) X i = vector of exogenous instrumental variables Reduced form for S i : S i = γ + δα + θ X i + δε i + η i 1 � δβ () Health September 2007 7 / 15
If X i is uncorrelated with ε i and η i then we can estimate the “…rst stage regression” S i = a + bX i + u i using OLS where a = γ + δα θ 1 � δβ and b = 1 � δβ Then run “second-stage regression” log y i = α + β ˆ S i + ε i using the …tted value ˆ a + ˆ S i = ˆ bX i Estimate of β should re‡ect impact of variations in S i that are due to exogenous variation in X 0 i s only () Health September 2007 8 / 15
Three key requirements of "good instruments": ! R 2 in …rst stage regression must be reasonably high , , ! must clearly be an exogenous determinant of S i , ! no other channels through which X i e¤ects y i (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’s area of origin , ! estimates in Table I control for schooling , ! estimates for ρ height = (0.08, 0.094, 0.078); for ρ men = 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 ρ height = (0.033, 0.035) () Health September 2007 10 / 15
Table I Structural Estimates of the Effect of Health Indicators on Wages Health Indicator Effect on Sample Country and Year Source (unit) ln(wage) Ribero and Nu � ez 0.080 Males 18-60 Colombia (urban), (0.0056) 1991 (2000) Height (cm) 0.094 Males 25-54 Ghana, 1987-89 Schultz (2002) (0.025) 0.078 Males 20-60 Brazil, 1989 Schultz (2002) (0.0083) -0.261 Females 18-54 Mexico, 1995 Knaul (2000) Age of Menarche (yrs) (0.111)
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: ρ height = ln ( v t + 1 / v t ) = ln ( 1 . 95 ) = 0 . 073 I t + 1 � I t 9 . 1 , ! similarly for age of menarche ρ 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 ρ ASR from micro studies , ! we have estimates of ρ height , 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 ρ ASR / ρ height = 19 . 2 and so ρ ASR = 0 . 653 () Health September 2007 12 / 15
Figure IV Data on Height and Adult Survival 900 850 800 Adult Survival Rate (per thousand) 750 700 650 Denmark France 600 Italy Japan S. Korea 550 Netherlands Spain 500 Sweden UK 450 USA 400 162 164 166 168 170 172 174 176 178 180 182 height (cm)
The Contribution of Health to Income Di¤erences Recall that we have ln y i = ln A i + α ln k i + ( 1 � α ) ln h i + ( 1 � α ) ln v i Share of var(ln y ) attributable to each factor (Table III) , ! cross country variance decomposition is given by var( ln y ) + var( ln A ) + α 2 var( ln k ) + ( 1 � α ) 2 var( ln h ) var( ln y ) = +( 1 � α ) 2 var( 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 % () Health September 2007 13 / 15
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 ASR Menarche (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 .179 .144 .175 .154 .139 var (ln(A)) / var (ln(y)) 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 .598 .529 .555 .431 .480 Fraction of Variance in ln(y) Attributable to Productivity Proportional Reduction in Variance of .099 .123 .106 ln(y) from Eliminating Health Gaps
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 () Health September 2007 14 / 15
Table IV Effect of Eliminating Health Gaps on Income Ratios Sample Health Income Ratio Raw Data Eliminating Measure Health Gaps 90/10 20.47 17.88 ASR ASR 90/50 3.21 3.08 50/10 6.37 5.80 90/10 10.05 9.21 Menarche ASR 90/50 1.75 1.71 50/10 5.74 5.39 90/10 10.05 7.76 Menarche Menarche 90/50 1.75 1.82 50/10 5.74 4.25
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