Irving Fisher and the contribution of improved longevity to living standards

American Journal of Economics and Sociology, The,  Jan, 2005  by William D. Nordhaus

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Figure 2 shows the survival rates for three years: 1900, 1950, and 2000. The most dramatic change came in the early part of this century--the probability of surviving the first year rose from 85% in 1900 to 97% in 1950. Figure 3 shows life expectancy at different ages. Figure 4 shows the change in life expectancy at different ages over the last century. Gains in life expectancy have been substantial throughout the entire century.

To calculate the value of improved health status, we use the life-years approach outlined above (an alternative, using the mortality approach, can also be done and gives similar answers). Under the life-years approach, the economic value of improved health is equal to the increase in life expectancy times the value of an additional life-year. The estimates are weighted by the share of the population that is experiencing the greater life expectancy, where we use the 1950 equilibrium population weights for all years.

C. Simple Calculations

It may be helpful to work through a simple example to illustrate the methodology. For the period 1975 through 2000, the undiscounted increase in weighted life-years was 2.53 years. Raising life expectancy by one LY is estimated to be the equivalent of raising the consumption annuity at each age by 10.3% of income. Therefore, the gains over that quarter-century were equal to 2.53 x 10.3 = 26.1%, or 1.05% per year. Per capita real income grew by 1.98% per year over that period, so the value of health increases was 53% as the growth in conventional measured per capita real income.

D. Actual Calculations

The central results of this paper, showing calculations on the economic contribution of health and nonhealth consumption, are shown in Table 2 and Figure 5. For these estimates, we use only estimates based on changes in life expectancy. These estimates differ from the simple calculations in the last section because they use actual survival rates and population distributions rather than the simplified ones assumed above.

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The major result that comes through using all techniques is that the value of improvements in life expectancy improvements is about as large as the value of all other consumption goods and services put together. For example, over the two decades from 1975 to 2000, conventionally measured per capita income grew at an average rate of 2.0% per year. Over this period, the annual average improvements in life expectancy had an economic value between 1.0 and 2.1% of income, depending upon the discount rate. (14) Over the entire period from 1900 to 2000, the value of improved health or health income grew at between 1.2 and 2.5% of consumption, whereas income grew at a rate of about 2.0% of consumption.

Looking at the entire 20th century, the contribution of the increase in life expectancy was between 59% and 126% of the contribution of income from all sources combined.

E. Qualifications

How robust are the estimates provided here? The underlying mortality data are among the most reliable of our social statistics. The most fragile estimates concern mortality and life-year valuation, as discussed above. One assumption on which there is little evidence is that the premium on reduced mortality is a constant fraction of per capita consumption over the entire period. More precisely, we assume that the value of a reduction in the mortality rate of 0.001 per year is $3,000 at 1990 income levels and in 2000 prices, and we scale that value over time to the ratio of the given year's per capita income to 1990 per capita income. There are no comprehensive studies of the mortality premium over time, although movements in the wage of risky occupations (such as coal mining) are consistent with this assumption. I suspect, however, that the premium has risen over time. This would be consistent with the rising share of health care expenditures in total consumption. If the premium were indeed increasing over time, then the contribution of health to economic welfare would be relatively smaller in the earlier period and relatively larger in the later period.