DISEASE AND DEVLOPMENT: THE EFFECT OF LIFE EXPECTANCY ON ECONOMIC GROWTH
D. Acemoglu & S. Johnson
Journal of Political Economy, Vol. 115 No. 6 (2007) pp. 92585
Principal Research Question and Key Result  Have the 21^{st} century’s increases in life expectancy translated into increased economic growth? No statistically significant effect on growth is found and in fact per capita indicators show significant negative association with life expectancy, indicating that any aggregate growth gains are more than offset by increases in population and birth rates.

Theory  In neoclassical growth theory increased life expectancy raises that population which initially reduced capital to labour ratios thus depressing income per capita. This may be compensated for in the medium/long run by higher output as more people enter the labour market and more capital is accumulated. This compensation may eventually exceed the initial per capita measures is there are significant productivity benefits from longer life expectancy. This may not occur however if some factors of production are supplied inelastically (not sure I get this last bit). None of this should be taken as an indication that welfare will not be greatly increased from increased life expectancy, only that there is no discernible relationship with GDP.

Motivation  There is a growing consensus that improving health outcomes can have indirect payoffs through accelerating economic growth. Whilst Marco studies of these effects are plagued by problems of comparability and also that countries characterized by ill health are also disadvantaged in other ways, micro studies (which show positive effects of health outcomes on growth) cannot account for general equilibrium effects. The most important of these would be that as there are diminishing returns to effective units of labour, micro studies that cannot account for the effect of population growth pursuant to improvements in health, will tend to overstate the economic returns from doing so. This paper takes a novel approach by instrumenting fairly successfully for life expectancy by exploiting what they term the international epidemiological transition that occurred in the 1940s which was essentially the development and diffusion of curative and preventative medicine.

Data  
Strategy  There is a long differences strategy (primarily to look at effects of life expectancy on other demographic variables), and an IV strategy (to look at effects of life expectancy on wealth variables).
The long differences strategy compares variables in 1940 (prior to the transition) with 1980 (being prior to HIV). By taking differences they are excluding all the country fixed components of the growth model ( technology, initial human capital etc.), with an additional vector of controls. The dependent variables of interest are GDP, population, births, and age composition of the country. The primary explanatory variable is life expectancy. The IV strategy uses potential mortality to instrument for life expectancy. They collect data comparable data for 15 of the most important infectious diseases, and create time dummies for when interventions in that disease started to occur at the medicinal frontier. The instrument is constructed as follows: M_{it} = ∑[(1I_{dt})M_{di40} + IdtM_{dFt}] Mdit denotes mortality in country I from disease d at time t. Idt is a dummy for intervention for disease d at time t (and thus equla to 1 for all dates after the intervention). Mdi40 is the preintervention mortality from disease d in country I, and MdFt is the mortality form disease d at the technological frontier after the intervention. (1I_{dt})M_{di40} – this part of the expression will equal the mortality rate in the country before there is an intervention as I only equals 1 when there has been an intervention, and so when there is no intervention 1I = 1 and 1*Mdi40 equals the mortality rate pre intervention. Then when there is an intervention I turns on to equal 1, and this part of the expression will equal zero. IdtM_{dFt} – this part of the expression will equal zero in the preintervention period, and the mortality rate at the frontier after the intervention turns the dummy to 1. Critically the value of the predicted mortality derived is in no way dependent upon how successful a country is at implementing the intervention. The dummy switches to one for all countries at the same time, which strengthens the exclusion restriction, as variations in predicted mortality are in no way correlated with the country specific error. Additionally, the Mdft is set to zero such that predicted mortality from a disease equals zero after the intervention, and so is uncorrelated with the error. They show that there is a strong first stage relationship between the predicted mortality and life expectancy, and this is the case even excluding the richer countries from the sample 
Results  Long difference: the 194080 estimate of the effect of life expectancy on population is 1.6 which suggests that a 1% increase in life expectancy causes a 1.6% increase in the population. The coefficient on births is 2.35 and the on the % of population under 20 is 0.94. These are robust to using longer time windows (19402000). When the GDP measures are the dependent variable, there is a 0.85% increase in GDP associated with 1% increase in life expectancy, but this is insufficient to compensate for the population effects, so GDP per capita and GDP per working age population are both significant and negative. These results are only tentative, as there are endogeneity problems i.e. richer countries may invest more in health.
The first stage yields a coefficient implies that improving predicted mortality will improve life expectancy by 21% and this is significant at the 1% level. This is the case then shorter time windows are used also. The run the 2SLS IV estimate with different dependent variables:

Robustness 

Problems 

Implications  Increasing life expectancy increases the population, and birth rates did not decline sufficiently for there to be any meaningful compensation in terms of increased productivity. Overall this has led to a decrease in income per capita. This would seem to suggest that for economic (as opposed to simply welfare) benefits to be felt from improved health outcomes, there needs to be concurrent efforts to improve productivity such that capital can be accumulated at a faster rate than the population growth diminished capital per worker. Naturally none of this means that promoting health outcomes does not have its own intrinsic value. 