Questions: Demographic Estimation Techniques

Question 1

The Brass P/F ratio method compares cumulative fertility from two different data sources. What are the two sources, and what does their ratio reveal?

• A. P comes from vital registration and F from survey data; the ratio measures registration completeness
• B. P (parity) comes from census questions on children ever born (a cohort measure) and F (current fertility) comes from census or survey questions on recent births (a period measure); the ratio reveals whether recent fertility data are consistent with lifetime fertility, allowing adjustment of current fertility estimates
• C. Both P and F come from the same survey; the ratio is a reliability check on individual responses
• D. P measures paternal fertility and F measures female fertility; the ratio reveals sex-based reporting differences

Answer: (B)

The P/F method exploits the fact that censuses often collect both 'children ever born' (lifetime parity, a cohort measure) and 'births in the past 12 months' (a period measure). Cumulating the period ASFRs up to each age group gives F; actual average parity at each age gives P. In a stable population with constant fertility, P/F should equal 1. Deviations suggest reference-period errors (women reporting too many or too few recent births) or actual fertility change. The P/F ratio for older women is used to adjust period fertility estimates — a correction that has proven remarkably robust across many populations.

Question 2

Model life tables assume that all populations experience mortality in the same pattern, just at different levels.

• T. True
• F. False

Answer: False

Model life tables recognize distinct mortality patterns across populations. The Coale-Demeny system (1966, revised 1983) identifies four regional families — West, North, East, South — each with a different age pattern of mortality (e.g., the South pattern has high infant mortality relative to adult mortality). The UN model life tables (1982) identify five patterns based on geographic clusters. Users choose the family that best matches their population's observed mortality pattern and then use the model to interpolate age-specific rates from limited data. The flexibility of multiple families is precisely what makes model life tables useful — they accommodate real variation in how mortality is distributed across ages.

Question 3

Explain why the assumption of a stable or quasi-stable population is important for many indirect estimation methods, and what happens when the assumption is violated.

Model answer: Many indirect methods derive vital rates from age distributions, exploiting the mathematical relationship between vital rates and age structure in a stable population. In a stable population, the age distribution is uniquely determined by fertility and mortality rates, so the age distribution can be 'read backward' to infer those rates. When the stability assumption is violated — due to recent fertility change, mortality shocks, or large migration flows — the observed age distribution reflects a mixture of past conditions, not current rates. Methods that assume stability will produce estimates that are biased toward historical rather than current conditions. Extensions like quasi-stable methods relax the assumption to allow slowly changing rates, and some methods (e.g., the variable-r method) explicitly model changing growth rates.

The stability assumption is the theoretical foundation that makes indirect estimation possible but also its principal limitation. In practice, no population is truly stable, but many change slowly enough that quasi-stable approximations work well. Populations experiencing rapid fertility decline, HIV epidemics, or mass displacement require more sophisticated methods that do not rely on stability — an active area of methodological development in demography.