Disease and Development:The Effect of Life Expectancy

on Economic GrowthDaron, Acemoglu & Johnson

Proponent Section

Does increasing life expectancy accelerate economic growth?

• Improving global health is an important social objective, but is it also an economic objective?

• There is a growing consensus among academics and NGOs that improving health can accelerate economic growth– Eliminating malaria in sub-Saharan Africa could increase

GDP/capita growth rate by 2.6%/yr (Gallup & Sachs 2006)

• However, the only conclusive evidence shows correlation and not causation.

Health interventions appear to have clear microeconomic benefits, but…

• Micro studies have demonstrated improved health’s positive effect on individual productivity

• Yet no general equilibrium study has shown that these micro effects extend to increasing economic growth rates.– Weil (2007) finds positive returns to health, but studies only constant

population scenarios– Young (2005) finds positive GDP per capita returns to one specific disease, the

HIV/AIDS epidemic, as it thinned the population

• Two confounding effects in general equilibrium could be countering the benefits to increasing productivity:– Diminishing returns to individual productivity given capital constraints– Increasing competition in labor market as population increases

Acemoglu & Johnson test the macro effect of health on economic growth

• Experimental setup:– Proxy for health: life expectancy at birth– Exogenous shock to health: the international

epidemiological transition occurring in the 1940s– Instrumental variable: predicted mortality, based on the

interaction of two variables:• Intervention dates for specific diseases• Baseline cross-country disease burden for each disease

• Data obtained from UN, WHO and League of Nations records for burdens of 15 major diseases, fertility rates and life expectancy across 75 countries

Exogenous shock: international epidemiological transition

• Pre-1940 few places aside from western Europe and the United States made significant public health efforts.

• Then a 3-part transition:– New treatments available

• Antibiotics (e.g. penicillin, streptomycin)• Vaccines (e.g. yellow fever)• Chemicals (e.g. DDT)

– New organizations spread tech and practices• e.g. World Health Organization, United Nations International Children’s

Emergency Fund

– Globalization of international values

• Post-1950 most new developments had already been universally implemented.

Exogenous shock: log life expectancy at birth over time

Exogenous shock: log GDP per capita over time

Hypothesis: increased population and limited resources stunts growth

• Increasing population depresses capital-to-labor ratio temporarily (with rebound possible as more capital is accumulated)

• Increasing population depress land-to-labor ratios permanently (land supply is inelastic)

Hypothesis: closed-economy neoclassical growth model

For economy i at time t, a closed-economy neoclassical growth model (essentially a Cobb-Douglas production function) gives:– Yit = (AitHit)αKit

βLit1 - α - β , for α + β ≤ 1

• Ait is a fixed function of cross-country baseline differences

• Kit is the supply of capital

• Lit is the supply of land

• Hit is the effective supply of labor: Hit = hitNit

– Nit is total population (employed and unemployed)

– hit is total human capital per person

Applying the model to health shocks

• To capture these effects in a reduced-form manner (writing production Y as a function of life expectancy X), we assume:– Ait = AiXit

γ, hit = hiXitη, Nit = NiXit

λ

• Xit is life expectancy in country i at time t

• Āi , hi , and Ni designates baselines differences across countries

• Then substitution gives:– Yit = [(AiXit

γ)(hiXitη )(NiXit

λ)]αKitβLit

1 - α – β

• Taking logs:– yit = βlogKit0 + αlogAi + αloghi - (1-α)logNi + [α(γ+η)-(1-α)λ]xit

Applying the model to health shocks

• yit = βlogKit0 + αlogAi + αloghi - (1-α)logNi + [α(γ+η)-(1-α)l]xit

– The increase in log life expectancy xit will raise income per capita yit if• the positive effects of health on total factor productivity

(TFP, measured by α[γ+η]) exceed the potential negative effects arising from the increase in population because of fixed land and capital supply, (1-α) λ.

– Otherwise, increases in log life expectancy will reduce income per capita.

Applying the model to health shocks

• To accommodate the elasticity of the capital supply: – Suppose that country i has a constant saving rate

equal to si ϵ (0, 1) and that capital depreciates at the rate δi ϵ (0, 1)

• Then the capital stock in country i at time t is given by Kit+1 = siYit +(1- δi)Kit, and we find:

Applying the model to health shocks

• Then the condition for a positive correlation between x and y is that TFP be greater than the negative effects arising from the increase in population because of fixed land supply, (1-α-β) λ.

• Because fixed land supply is only a major concern for agriculture-dominated economies, the term (1-α-β) λ approaches zero for developed nations and has a significant detrimental effect in developing nations.

Applying the model to health shocks

• Estimation equation:

• π is the parameter of interest

• ζi denotes the set of fixed effects that are functions of Ai, hi, Ni, si

• µi is set of time-variant factors common across all countries

• Z’i is a vector of other controls

Instrumental variable: predicted mortality

• Predicted mortality M at time t in country i after intervention I for disease d:

• MdFt is the mortality at the “health frontier of the world”, assumed to be 0 in this paper.

• First-stage equation:

• Exclusion restriction: M is not correlated with ε

Change in log life expectancy over change in predicted mortality

Change in log life expectancy over change in predicted mortality

What effect did health shock have?

Main results: health shock did not change GDP/cap growth

• The predicted mortality instrument did have a large & robust effect on changes in life expectancy after 1940 (and not before)

• The instrumented changes in life expectancy did have an effect on population (1.7-2% increase in population per 1% increase in life expectancy) because the increase in life expectancy was only partly compensated for in fertility

Main results: health shock increased population

Main esults: exogenous shock did not change GDP/cap growth

• The predicted mortality instrument did have a large & robust effect on changes in life expectancy after 1940 (and not before)

• The instrumented changes in life expectancy did have an effect on population (1.7-2% increase in population per 1% increase in life expectancy) because the increase in life expectancy was only partly compensated for in fertility

• There was no statistically significant effect on GDP, but two standard error range was so large this result is inconclusive.

Final result: health shock had negligible effect on total GDP