“Accounting for the E¤ect of Health on Economic Growth” by David Weil (2007) January 2011 () Health January 2011 1 / 12
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 January 2011 2 / 12
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 January 2011 3 / 12
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 January 2011 4 / 12
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 January 2011 5 / 12
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 January 2011 6 / 12
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 January 2011 7 / 12
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) 50
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 January 2011 8 / 12
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 January 2011 9 / 12
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)
Table II Regression of Height on Adult Survival Rate (1) (2) (3) (4) Constant 156.0 157.5 166.2 165.2 (1.0) (0.8) (2.2) (2.1) Adult Survival Rate 21.1 26.4 16.6 19.2 (2.8) (1.0) (2.5) (2.4) Year .0292 -.0057 (.0068) (.0123) Year × ASR .0719 (.0216) Country Fixed no yes yes yes Effects R 2 .377 .953 .961 .966 Standard errors in parentheses. N=93 for all regressions. Height is measured in cm. Year is normalized to be zero in 2000. In regressions with country fixed effects, the United States is the reference group. 51
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 January 2011 10 / 12
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 52
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 January 2011 11 / 12
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 53
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 () Health January 2011 12 / 12
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