A country has a life expectancy at birth of 55 years but a life expectancy at age 5 of 65 years. What explains this apparent paradox?
AThe data are inconsistent — life expectancy should always decrease with age
BHigh infant and child mortality pulls down the average at birth; those who survive early childhood face much lower mortality and can expect to live considerably longer
CLife expectancy at age 5 is calculated differently and is not comparable to life expectancy at birth
DImmigration of healthy adults artificially inflates life expectancy at older ages
Life expectancy at birth is an average across all members of the hypothetical cohort, including those who die in infancy and childhood. When early-life mortality is high, it drags the average down substantially. Conditional on surviving to age 5, the remaining life expectancy (e5) can be considerably higher than e0 because the high-risk early years have been survived. This is why historical populations with e0 of 35-40 years still had many people living into their 60s and 70s.
Question 2 True / False
A period life table predicts how long people born in a given year will actually live.
TTrue
FFalse
Answer: False
A period life table applies the age-specific mortality rates observed in a single year (or period) to a hypothetical cohort, showing what would happen if those rates persisted unchanged for a lifetime. Since mortality rates typically improve over time, period life expectancy at birth usually underestimates how long newborns will actually live. Cohort life tables, which follow a real birth cohort and use the actual mortality rates they experience at each age, provide a better (but retrospective) measure of true longevity.
Question 3 Short Answer
Describe the relationship between qx (probability of dying), lx (survivors), and ex (life expectancy) in a life table, and explain why ex can increase from one age to the next in some populations.
Think about your answer, then reveal below.
Model answer: qx is the probability of dying in the interval starting at age x; it converts age-specific death rates into probabilities. lx tracks how many of the original cohort (typically 100,000) survive to exact age x — each lx is derived by applying the previous age's qx to the previous lx. ex is the average remaining years of life for those who reach age x, computed from cumulative person-years lived (Tx) divided by survivors (lx). ex can increase from birth to age 1 or 5 in populations with high infant/child mortality because surviving the dangerous early years removes a major source of mortality, increasing the conditional expectation of remaining life.
The mathematical structure of the life table makes this counterintuitive result inevitable when early-age mortality is high. The key insight is that ex is conditional on survival to age x — it asks 'given that you made it this far, how much longer can you expect to live?' When the hazard of dying is concentrated in early life, making it past that gauntlet substantially improves your outlook.