1. Accounting for the Effect of Health on Economic Growth David N. Weil Proponent/Presenter Section

2. Goals To quantitatively asses the role that health differences play in explaining income differences between rich and poor countries; To calculate the income gain that would result from an improvement in the health of people living in poor countries; To examine the broader question of what determines a country’s level of income. 2

3. Basic Framework (1/2) Builds on Hall and Jones “Why Do Some Countries Produce So Much More Output per Worker than Others?” (1999) Cobb-Douglas aggregate production function for country i: (1) where labor composite H i, is determined by (2) and h i = educational human capital per worker v i = health human capital per worker L i = number of workers 3

4. Basic Framework (2/2) Decomposition in log per capita terms: lny i = lnA i + αlnk i + (1-α)lnh i + (1-α)lnv i (3) 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: (4) Wage earned by individual j in country i, in logs: lnw i,j = ln(w i ) + ln(h i,j ) + ln(v i,j ) + η i,j (5) where η i,j is an individual-specific error term. 4

5. Individual Health and Productivity Consider two workers j = 1, 2 in country i with the same education. The expected difference in log wages is lnw 2 – lnw 1 = lnv 1 – lnv 2 (6) 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 (7) lnv j = β + γ v z j + ε vj (8) -for workers 1 and 2: lnw 2 – lnw 1 = γ v (z 2 – z 1 )(9) I 2 – I 1 = γ I (z 2 – z 1 )(10) The expected log wage gap is then lnw 2 – lnw 1 = lnv 1 – lnv 2 = ρ I (I 2 – I 1 ) where ρ l = γ v /γ l denotes the return to health indicator I 5

6. 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) for men – 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) for women – delayed menarche is a good indicator of malnutrition in childhood – data limitations (Figure III) 6

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10. 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 10

11. Instrumental Variables (2SLS) Methodology Hypothesized structural model: log y i = α + βS i + ε i (11) S i = γ + δlogy i + θX i + η i,(12) 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 : 11

12. If X i is uncorrelated with ε i and η i then we can estimate the “first stage regression” S i = a + bX i + u i using OLS where Then run ”second-stage regression” log y i = α + βŜ i + ε i using the fitted value Ŝ i = â + X i Estimate of β should reflect impact of variations in S i that are due to exogenous variation in only 12

13. What makes “good instruments”? Three key requirements of "good instruments": – R 2 in first stage regression must be reasonably high – must clearly be an exogenous determinant of S i – no other channels through which X i effects y i (over identifying restriction) 13

14. 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 difference is birth weight – implied estimates for ρ height = (0.033, 0.035) 14

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16. Return to Health Using Historical Data Fogel (1997) estimates caloric intake in the UK over 1780-1980 and its impact on labor supply – estimates improved nutrition raised labor input by a factor of 1.95 – given that height increased by 9.1 cm over this period: – similarly for age of menarche ρ men = 0.26 16

17. Relating ASR and Height Problems: – 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 17

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19. The Contribution of Health to Income Differences Recall that we have ln y i = ln A i + a ln k i + (1 – a) ln h i + (1 – a) 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 y) + var(ln A) + a 2 var(ln k) + (1 – a) 2 var(ln h) + (1 – a) 2 var(ln v i ) + 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 % 19

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21. Effect of eliminating health gaps on income ratios (Table IV) – “90/10 ratio” is the ratio of GDP per worker of country at 90 th 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 21

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