Preston-Coale Method
Also known as: Synthetic extinct generations method, SEG method, Preston-Coale death distribution method, Preston-Coale Yöntemi
The Preston-Coale method, also called the synthetic extinct generations method, estimates the completeness of death registration by rebuilding a population from the very deaths it records. Introduced by Samuel Preston and Ansley Coale in 1982, it uses the variable-r relations of a non-stable population to project each age group's future deaths forward, growth-adjust them, and accumulate them into the number of people who must currently be alive at each age. Comparing this implied population with the observed census count reveals what fraction of deaths the vital system actually captures.
Key highlights
- Relaxes the stability assumption through the variable-r relations, making it usable in populations with changing growth where the growth balance method fails.
- Requires only an age distribution of deaths plus growth information, data obtainable even without complete vital registration.
- Produces an age profile of completeness C(a) that doubles as a diagnostic of where and how registration or age reporting breaks down.
- Generalizes the intuitive extinct-generations idea, giving it a rigorous, broadly applicable foundation for adult mortality estimation.
Intuition
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How it works
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When to use it
Use the Preston-Coale synthetic extinct generations method to estimate adult death registration completeness and correct mortality in populations with a usable age distribution of deaths but deficient vital registration. Its key advantage over the Brass growth balance method is that it does not require the population to be stable: through the variable-r relations it accommodates changing growth. It does assume the population is closed to migration over the ages analyzed, that registration completeness is constant across adult ages, and that age reporting is reasonably accurate. It should not be used where migration is appreciable at the analyzed ages, where age misstatement is severe, or where the deaths and population refer to inconsistent populations. Because the death distribution methods rest on different assumptions, running Preston-Coale alongside Brass growth balance and the Bennett-Horiuchi variant and comparing results is standard practice.
Strengths & limitations
- Relaxes the stability assumption through the variable-r relations, making it usable in populations with changing growth where the growth balance method fails.
- Requires only an age distribution of deaths plus growth information, data obtainable even without complete vital registration.
- Produces an age profile of completeness C(a) that doubles as a diagnostic of where and how registration or age reporting breaks down.
- Generalizes the intuitive extinct-generations idea, giving it a rigorous, broadly applicable foundation for adult mortality estimation.
- Assumes the population is closed to migration over the analyzed ages; migration corrupts the reconstructed population and biases completeness.
- Assumes registration completeness is constant across adult ages, so age-varying coverage tilts the C(a) profile and complicates the choice of a single factor.
- Sensitive to age misreporting, especially exaggeration at the oldest ages, which distorts both the deaths and the implied population.
- Needs an accurate growth rate (or age pattern of growth); errors in the assumed growth propagate directly into the completeness estimate.
Common pitfalls
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Applications
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Frequently asked
What does 'synthetic extinct generations' mean?
An extinct generation is a birth cohort that has fully died out, so summing its deaths over the years recovers exactly how many were alive at any earlier age. Waiting for real cohorts to go extinct is impractical, so Preston and Coale build a synthetic version: they take the current cross-section of deaths by age and growth-adjust it to represent the future deaths of today's population, reconstructing the living population without waiting a lifetime.
How is the Preston-Coale method different from the Brass growth balance method?
Both are death distribution methods that estimate registration completeness, but the Brass growth balance method assumes a stable population with a single growth rate, whereas the Preston-Coale method uses the variable-r relations to handle non-stable populations with changing growth. Preston-Coale reconstructs the population implied by the deaths and compares it with the census, while Brass exploits the partial-birth-versus-partial-death balance. Comparing the two is a routine robustness check.
Why must the population be closed to migration?
The reconstruction assumes that everyone alive above an age will eventually appear among the future deaths of that population. Net migration breaks that bookkeeping: in-migrants add living people who were never counted among the deaths, and out-migrants remove people who die elsewhere. Either way the reconstructed population no longer matches the deaths consistently, so the completeness estimate is biased unless the analyzed ages are effectively closed to migration.
Sources
- 1.Preston, S. H., & Coale, A. J. (1982). Age structure, growth, attrition, and accession: a new synthesis. Population Index, 48(2), 217–259.
- 2.Preston, S. H., Heuveline, P., & Guillot, M. (2001). Demography: Measuring and Modeling Population Processes. Blackwell.ISBN 9781557864512
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ScholarGate. (2026, June 22). Preston-Coale Method. ScholarGate. https://scholargate.app/demography/preston-coale-method