Construct · 3 fields · 3 citations

age–period–cohort problem: one construct, many systems

One name. One construct. Different systems. One map.

● invariant · one identification problem, three disciplines Nearest construct by meaning·not indexed
same identity, in rate modelssame identity, in pseudo-panelsage–period–cohortproblem3 SYSTEMSCohort analysisMASON ET AL · 1973APC for vital ratesHOLFORD · 1983Cohort effects in econDEATON & PAXSON · 1994

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1973Cohort analysis1983APC for vital rates1994Cohort effects in econ
2026

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Sociology and demography

the impossibility of uniquely separating age, period, and birth cohort effects, because cohort equals period minus age.

The age–period–cohort problem is the impossibility of uniquely separating the effects of age, calendar period, and birth cohort on an outcome, because cohort equals period minus age: the three are exactly linearly dependent, so a model containing all three is unidentified without an outside constraint. Mason, Mason, Winsborough, and Poole's 1973 Some methodological issues in cohort analysis of archival data stated the problem sharply for social data and examined the constraints that can break the tie. The referent is a structural identification failure in data arrayed by age and time, the same obstacle that reappears, unchanged, in epidemiology and economics.[1]

Unit
A parameter-identification condition (no measured unit)
Recovery means
Not applicable
Measured by
Diagnosed by the exact collinearity of age, period, and cohort; handled by constraints, nonlinear specifications, or outside information

Epidemiology and biostatistics

the inability to apportion linear trends in disease or death rates among age, period, and birth cohort.

Epidemiology meets the identical obstacle when it models how disease or death rates depend on age, period, and cohort of birth: only the curvatures of each effect are estimable, while the linear trends cannot be apportioned among the three because of the age = period − cohort identity. Holford's 1983 The estimation of age, period and cohort effects for vital rates showed precisely which functions of the parameters are identifiable and which are not. It is the same construct as in sociology, realised in rate models for vital statistics.[2]

Unit
Identifiable effects limited to nonlinear curvatures (no measured unit)
Recovery means
Not applicable
Measured by
Resolved by estimating identifiable curvature components or imposing constraints in log-linear rate models

Economics

the difficulty of disentangling life-cycle, macroeconomic, and generational effects when following cohorts through repeated cross-sections.

Economists face the same identification problem when they use repeated cross-sections to follow cohorts over the life cycle and must disentangle age (life-cycle) effects, time (macroeconomic) effects, and cohort (generational) effects on outcomes like consumption, saving, and inequality. Deaton and Paxson's 1994 Intertemporal choice and inequality builds synthetic cohorts and confronts the age–period–cohort constraint directly, typically by normalising the time effects so that age and cohort profiles can be read off. It is the same linear-dependency construct as in sociology and epidemiology, met in economic panel and pseudo-panel data.[3]

Unit
A parameter-identification condition (no measured unit)
Recovery means
Not applicable
Measured by
Handled by synthetic-cohort construction with identifying restrictions (e.g. time effects summing to zero and orthogonal to a trend)

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Nearby constructs

Lexis diagram1 fields · 2 citationsanchor · the time-age coordinate grid of demographycohort-component method1 fields · 1 citationsanchor · the standard engine of population projectionbirth3 fields · 5 citationsjingle · one word, three constructs

References

  1. Mason, K. O., Mason, W. M., Winsborough, H. H., & Poole, W. K. (1973). Some methodological issues in cohort analysis of archival data. American Sociological Review, 38(2), 242–258. https://doi.org/10.2307/2094398
  2. Holford, T. R. (1983). The estimation of age, period and cohort effects for vital rates. Biometrics, 39(2), 311–324. https://doi.org/10.2307/2531004
  3. Deaton, A., & Paxson, C. (1994). Intertemporal choice and inequality. Journal of Political Economy, 102(3), 437–467. https://doi.org/10.1086/261941

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