Oxford Research Encyclopedia of Economics and Finance is now available via subscription and perpetual access. Visit About to learn more, meet the editorial board, or learn how to subscribe.

Dismiss
Show Summary Details

Page of

PRINTED FROM the OXFORD RESEARCH ENCYCLOPEDIA, ECONOMICS AND FINANCE (oxfordre.com/economics). (c) Oxford University Press USA, 2020. All Rights Reserved. Personal use only; commercial use is strictly prohibited (for details see Privacy Policy and Legal Notice).

date: 26 September 2020

Summary and Keywords

Outcomes of interest often depend on the age, period, or cohort of the individual observed, where cohort and age add up to period. An example is consumption: consumption patterns change over the lifecycle (age) but are also affected by the availability of products at different times (period) and by birth-cohort-specific habits and preferences (cohort). Age-period-cohort (APC) models are additive models where the predictor is a sum of three time effects, which are functions of age, period, and cohort, respectively. Variations of these models are available for data aggregated over age, period, and cohort, and for data drawn from repeated cross-sections, where the time effects can be combined with individual covariates.

The age, period, and cohort time effects are intertwined. Inclusion of an indicator variable for each level of age, period, and cohort results in perfect collinearity, which is referred to as “the age-period-cohort identification problem.” Estimation can be done by dropping some indicator variables. However, dropping indicators has adverse consequences such as the time effects are not individually interpretable and inference becomes complicated. These consequences are avoided by instead decomposing the time effects into linear and non-linear components and noting that the identification problem relates to the linear components, whereas the non-linear components are identifiable. Thus, confusion is avoided by keeping the identifiable non-linear components of the time effects and the unidentifiable linear components apart. A variety of hypotheses of practical interest can be expressed in terms of the non-linear components.

Keywords: age, period, cohort, time, identification, fixed effects, controls, invariance, over-parametrization

Access to the complete content on Oxford Research Encyclopedia of Economics and Finance requires a subscription or purchase. Public users are able to search the site and view the abstracts and keywords for each book and chapter without a subscription.

Please subscribe or login to access full text content.

If you have purchased a print title that contains an access token, please see the token for information about how to register your code.

For questions on access or troubleshooting, please check our FAQs, and if you can''t find the answer there, please contact us.