Two population projections differ only in their fertility assumption: one uses a TFR of 2.1 and the other uses 1.6. After 50 years, the populations differ by billions. What explains this extreme sensitivity?
AThe projection models are mathematically unstable and produce unreliable results over long time horizons
BCompounding: each generation born under different fertility assumptions produces a differently-sized next generation, and the difference grows exponentially over multiple generations
CThe TFR difference of 0.5 is unusually large; smaller differences would produce negligible divergence
DMortality and migration assumptions cancel out the fertility difference, so the divergence must be due to a modeling error
A TFR of 2.1 produces replacement-level growth (roughly stable population), while 1.6 produces each generation 24% smaller than the last. Over 50 years (roughly two generations), the smaller generation produces an even smaller next generation, and the gap compounds. A 0.5 TFR difference is not unusual — the gap between the UN's high and medium variants is often this magnitude — yet it produces fundamentally different population futures. This is why long-range projections must be understood as scenarios, not forecasts.
Question 2 True / False
The UN's medium-variant population projection represents the most likely future population path.
TTrue
FFalse
Answer: False
The medium variant is the central scenario in a range of projections, not a probability-weighted best estimate. It assumes fertility will converge toward replacement level in most countries, but this assumption could prove too high (if below-replacement fertility persists or deepens) or too low (if fertility rebounds in low-fertility countries). The UN uses probabilistic methods to generate prediction intervals, but the medium variant itself is not a 'most likely' forecast — it is the middle of a distribution of possible outcomes.
Question 3 Short Answer
Describe the cohort-component method and explain why fertility assumptions matter more than mortality assumptions for long-range projections.
Think about your answer, then reveal below.
Model answer: The cohort-component method starts with the current population disaggregated by age and sex. For each projection interval, it: (1) applies age-specific survival rates to advance each cohort to the next age group, (2) applies age-specific fertility rates to women of childbearing age to generate new births, and (3) adds or subtracts net migrants by age and sex. Fertility assumptions matter more for long-range projections because they determine how many new people enter the population, and each cohort of newborns generates the next generation. Small fertility differences compound across generations. Mortality assumptions matter less because most of the variation in mortality improvement affects life expectancy at older ages, which changes population size less than differences in the number of births.
This asymmetry is counterintuitive — students often expect mortality to matter more. But adding 10 years of life expectancy at age 70 adds person-years without adding new births. Changing TFR by 0.5 children per woman changes the entire future population because each generation's size determines the next generation's size. The compounding effect of fertility differences is the single most important fact about long-range population projections.