Tempo distortions in period mortality measures

Tempo distortions in period mortality measures (e.g.,e0) are more controversial. With marriage and fertility, it is easy to understand that the conflation of tempo and quantum changes can distort period measures; with mortality, the quantum is fixed (everyone will die and luckily die only once). This debate is ongoing, and this is not the place to elaborate in detail. However, a simple example developed by Jim Vaupel (2008) illustrates in lucid fashion how tempo changes in mortality can cause “turbulence in life tables”. Table 3a demonstrates life table quantities for a fictitious population where everyone dies at age 3. The quantities shown are the life expectancy (e), the population surviving to each age (P), the deaths at each age (D) and the probability of dying in an age interval (q). In year 4, 30 lives are saved and their death postponed with one year. This implies that 1q0 declines in year 4 and 1q1 increases in year 5. Vaupel refers to this phenomenon as the “delayed gerontological failure of pediatric success”. Under these circumstances, e0 is inflated in year 4 and assumes its new steady values once all the extra survivors have died (here in year 5).

Year
Age Statistic 1 2 3 4 5 6 7
0 e 1.7 1.7 1.70 2.3 2.0 2.0 2.0
  P 100 100 100 100 100 100 100
  D 40 40 40 10 10 10 10
  q 0.4 0.4 0.4 0.1 0.1 0.1 0.1
                 
1 e 1.50 1.50 1.50 1.50 1.17 1.17 1.17
  P 60 60 60 60 90 90 90
  D 20 20 20 20 50 50 50
  q 0.330 0.330 0.330 0.330 0.556 0.556 0.556
                 
2 e 1 1 1 1 1 1 1
  P 40 40 40 40 40 40 40
  D 20 20 20 20 20 20 20
  q 0.5 0.5 0.5 0.5 0.5 0.5 0.5
                 
3 e 0.5 0.5 0.5 0.5 0.5 0.5 0.5
  P 20 20 20 20 20 20 20
  D 20 20 20 20 20 20 20
  q 1 1 1 1 1 1 1
Total deaths   100 100 100 70 100 100 100

Table 3a: Population statistics at different ages and times when 30 lives are saved at age 0 and extended by one year

Source: Vaupel (2008)