Keyfitz Entropy
Also known as: Life-Table Entropy, Keyfitz-Leser Entropy, Entropy of the Survival Curve
Keyfitz's entropy, usually written H, is a dimensionless summary of a life table that measures how sensitive life expectancy is to a proportional change in mortality, and equivalently how unequal the distribution of ages at death is. Introduced by Nathan Keyfitz, it is the elasticity of life expectancy at birth with respect to the force of mortality: an H near one means deaths are spread across all ages so that reducing mortality everywhere lengthens life proportionally, while an H near zero means deaths are concentrated near the maximum lifespan so further mortality reductions yield little gain. It bridges the demography of survival and the broader study of lifespan inequality.
Key highlights
- Dimensionless and bounded, so it places populations on a common normalized scale of lifespan dispersion.
- Carries a precise interpretation as the elasticity of life expectancy to proportional mortality change.
- Computable directly from standard life-table columns, requiring no extra data.
- Links survival demography to the wider literature on lifespan inequality and the rectangularization of survival curves.
Intuition
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How it works
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When to use it
Use Keyfitz entropy when you want a scale-free measure of how concentrated or dispersed ages at death are, or how responsive life expectancy is to proportional mortality change — for example to characterize where a population sits on the path from high-mortality (high H) to low-mortality rectangularized (low H) regimes. It is useful for comparing lifespan inequality across populations on a common normalized scale. Assumptions: a complete and accurate life table, and that proportional mortality change is the relevant counterfactual for the elasticity interpretation. Do NOT treat H as a measure of the absolute spread of ages at death (use life disparity e† or the standard deviation for that), and do NOT compare H across populations without recognizing that it is a ratio, so equal H can arise from very different absolute lifespan distributions.
Strengths & limitations
- Dimensionless and bounded, so it places populations on a common normalized scale of lifespan dispersion.
- Carries a precise interpretation as the elasticity of life expectancy to proportional mortality change.
- Computable directly from standard life-table columns, requiring no extra data.
- Links survival demography to the wider literature on lifespan inequality and the rectangularization of survival curves.
- Being a ratio (life disparity over life expectancy), it can mask large differences in the absolute spread of ages at death.
- The elasticity interpretation assumes a uniform proportional change in mortality, which rarely matches real interventions.
- It is sensitive to mortality at young ages, so populations differing mainly in old-age mortality may show similar H.
- Estimates depend on accurate life-table construction, especially the open-ended oldest age interval.
Common pitfalls
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Applications
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Frequently asked
What does it mean when Keyfitz entropy equals one?
An entropy of one corresponds to an exponential survival curve with a constant force of mortality at all ages, where a proportional reduction in mortality produces an exactly proportional gain in life expectancy. Values below one indicate that deaths are increasingly concentrated near older ages, so uniform mortality reduction yields proportionally smaller longevity gains.
How is Keyfitz entropy related to life disparity e†?
Keyfitz entropy is closely approximated by the ratio e†/e₀, where e† is life disparity — the average remaining life expectancy lost at the ages where people die. Thus entropy is essentially life disparity normalized by life expectancy, which is why it serves both as a sensitivity elasticity and as a relative measure of lifespan inequality.
Does a falling entropy mean people are living longer?
Not directly; entropy measures the shape of the survival curve, not its level. Falling entropy means ages at death are becoming more concentrated (rectangularization), which historically accompanied rising life expectancy as early deaths were eliminated. But life expectancy and entropy are distinct: two populations can share a life expectancy yet differ in entropy.
Sources
- 1.Keyfitz, N. (1977). Applied Mathematical Demography. John Wiley & Sons, New York.ISBN 9780471473503
- 2.Demetrius, L. (1979). Relations between demographic parameters. Demography, 16(2), 329–338.
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ScholarGate. (2026, June 22). Keyfitz Entropy. ScholarGate. https://scholargate.app/demography/keyfitz-entropy