Arriaga Decomposition
Also known as: Arriaga's method, Life-expectancy decomposition, Age decomposition of life expectancy, Arriaga Ayrıştırması
Arriaga decomposition is a demographic technique that breaks down the difference in life expectancy between two life tables — two countries, two time points, or two groups — into the contributions of mortality change at each age. Introduced by Eduardo Arriaga in 1984, it tells the analyst not just that life expectancy rose or fell, but exactly which ages drove the change, separating the direct effect of mortality change within an age interval from the indirect effect of the extra survivors that change passes on to older ages.
Key highlights
- Provides an exact, age-specific decomposition whose contributions sum precisely to the total life-expectancy difference with no residual.
- Distinguishes the direct effect of mortality change within an age from its indirect downstream effect on later survival, a uniquely demographic insight.
- Requires only standard life-table outputs, which are routinely produced for most national populations.
- Extends naturally to age-by-cause decomposition, allowing attribution of life-expectancy change to specific causes at specific ages.
Intuition
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How it works
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When to use it
Use Arriaga decomposition when you want to explain a change or difference in life expectancy by identifying which ages contributed, for two life tables — across time, between countries, or between subgroups such as sexes or social classes. It is the standard tool for the age decomposition of life-expectancy gaps and is frequently combined with cause-of-death partitioning to attribute change to age-by-cause cells. Assumptions: two comparable, complete life tables exist with consistent age intervals, and the life-table relationships (the linear-in-the-interval survivorship convention) hold. Do NOT use it as a substitute for a causal model — the contributions are an exact arithmetic attribution, not an estimate of what intervention would change. For more than two populations or several interacting non-age factors, use the Das Gupta generalization instead.
Strengths & limitations
- Provides an exact, age-specific decomposition whose contributions sum precisely to the total life-expectancy difference with no residual.
- Distinguishes the direct effect of mortality change within an age from its indirect downstream effect on later survival, a uniquely demographic insight.
- Requires only standard life-table outputs, which are routinely produced for most national populations.
- Extends naturally to age-by-cause decomposition, allowing attribution of life-expectancy change to specific causes at specific ages.
- Defined for comparing two life tables at a time; multi-population or multi-factor problems require the Das Gupta generalization.
- Sensitive to the life-table assumptions used to build Lₓ, especially the linearity convention within wide age intervals at very young or very old ages.
- Folding the interaction into the indirect term makes the split slightly asymmetric, so swapping the order of populations changes the within-component allocation.
- Like all decompositions it is descriptive accounting, not a causal estimate of the effect of changing mortality at a given age.
Common pitfalls
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Applications
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Frequently asked
What is the difference between the direct and indirect effects?
The direct effect is the change in years lived within an age interval caused by the mortality change inside that interval itself. The indirect effect is the downstream consequence: changing mortality at one age alters how many people survive to all later ages, and those survivors contribute the years lived beyond the interval. Saving a young life has a large indirect effect (many later years), while saving an old life has almost none.
How does Arriaga decomposition relate to Kitagawa decomposition?
Both belong to the demographic decomposition family that began with Kitagawa (1955). Kitagawa splits a difference between two crude rates into rate and composition components. Arriaga adapts the same exact-additivity philosophy to a more complex, nonlinear summary — life expectancy — by exploiting life-table structure to allocate the change across ages, which a simple two-component rate decomposition cannot do.
Can it decompose life-expectancy change by cause of death as well as by age?
Yes. A standard extension distributes each age interval's contribution across causes of death in proportion to the change in age- and cause-specific mortality rates. This produces an age-by-cause matrix of contributions that still sums exactly to the total life-expectancy change, and it is one of the most common applied uses of the method in epidemiology.
Sources
- 1.Arriaga, E. E. (1984). Measuring and explaining the change in life expectancies. Demography, 21(1), 83–96.
- 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). Arriaga Decomposition. ScholarGate. https://scholargate.app/demography/arriaga-decomposition