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Population Aging
Cultural Organization statistics (UNESCO 2009). Gross enrollment rates for preprimary, primary, secondary, and tertiary education were taken as coverage rates. b(x,t) was derived from total public expenditure on each education level divided by the number of students. Since the underlying data for education expenditures are tabulated in terms of primary, secondary, and tertiary, and the age ranges associated with each level vary from country to country, it was necessary to standardize the age ranges. Also, owing to the categorization of education into levels, expenditures over ages within a single category do not vary and neither can the ratio of public-to-private expenditure. Since we know only the total public and private expenditures on secondary education for a given country, we must assume that public (private) expenditure per enrolled 12-year-old is the same as that for each enrolled 16-year-old. Health Care: Initial b(x,t) values for health care are available for countries that participate in the NTA project. For the non-NTA countries, however, it was necessary to estimate these initial values. To do so, we used a singular value decomposition (SVD). SVD can be thought of as a way of simultaneously interpolating all of the b(x,t = 2005) values for a non-NTA country based on the shape of the b(x,t = 2005) of the NTA countries and on the country’s GDP per working-age population relative to those of the NTA counties.2 The results of the SVD estimations and the NTA derived b(x,t = 2005) curves are shown in figure 7.7. The strong U-shaped pattern is evident in all the curves. Not surprisingly, those taken from the NTA are less smooth than those that are estimated using SVD. For the five non-NTA countries (Argentina, Colombia, Cuba, Nicaragua, and Peru) it was necessary to use aggregate expenditure data to apportion estimated spending between public and private sources. So while the public share of total expenditure on health care varies by age in the NTA countries, the available data do not allow us to model that aspect of health care expenditures for non-NTA countries. Consequently, each non-NTA country has a constant share of public expenditure across all ages. Pensions: The same SVD procedure described above was used to estimate the initial b(x,t) values for pension programs in non-NTA countries.
Three Scenarios for Expenditure Trajectories We consider three scenarios for the age-specific patterns of expenditures as summarized in table 7.5.