For countries that have a GDP per capita in the initial year of less than $15,000 an elasticity factor with health spending ( elhlmortspn ) of -0.06 will affect mortality of children under 5.  That is, each 1 percent change in health spending as a percentage of GDP will lower mortality by 0.06 percent; an increase of 100 percent (doubling) would produce an automatic reduction of 6 percent in mortality. We have implemented a limit on the reductions to be at most 80 percent of mortality.

The GBD project’s distal driver formulation does not take public health spending into account.  However, we add a term to the basic GBD distal driver formulation to incorporate public health spending as a proximate driver to account for the relatively consistent inverse relationship between total public health expenditures and child mortality rates in poor countries (Anand and Ravallion 1993; Bidani and Ravallion 1997; Jamison et al. 1996; Nixon and Ulmann 2006; Wagstaff 2002). For countries having a GDP per capita (at PPP) of $15,000 or less, our model applies a simple elasticity for the effects of government health expenditure as a percentage of GDP on all-cause mortality (except HIV/AIDS) for the age 0-4 group from the distal driver formulation (the base calculation that health expenditures adjust): 

where  is the mortality rate for age 0-4.

In IFs this formalized version becomes

where

where

where

GDS is government expenditure; elhlmortspn is the elasticity of mortality with health spending, j is age category; r is country/region; d is cause (1 is other communicable); t is time step.

In this calculation we use health expenditure as a percentage of GDP, rather than health expenditure per capita, to avoid any confounding with the distal driver for GDP per capita. We established this coefficient for all-cause mortality in the 0-4 age category on the basis of multivariate regressions using the GBD distal driver specifications as a base.