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date: 12 December 2019

Age-Period-Cohort Models

This is an advance summary of a forthcoming article in the Oxford Research Encyclopedia of Economics and Finance. Please check back later for the full article.

Outcomes from individuals often depend on their age, period, and cohort, where cohort + age = period. An example is consumption, where consumption patterns change with age, but the availability of product changes over time, the period, and this affects individuals of different birth years, the cohort, differently. Age-period-cohort models are linear models allowing different parameter values for each level of age, period, and cohort. Variations of the models are available for data aggregated over age, period, and cohort and for data stemming from repeated cross-sections, where the time effects can be combined with individual covariates. The models could potentially be extended to panel data. It is common to plot the estimated age, period, and cohort effects and analyze them as time series. Further, it is also common to conduct inference on the inclusion of the different time effects, and to use the models for forecasting, which involves extrapolation of the time effects.

The age, period, and cohort time effects are intertwined. Specifically, inclusion of an indicator variable for each level of age, period, and cohort will result in a collinarity, which is referred to as the age-period-cohort identification problem. A first approach to addressing the collinarity is to leave out a suitable number of indicator variables. This gives some difficulties in the interpretation, inference, and forecasting in relation to the time effects. A second approach is the canonical parametrization that is a freely varying parametrization, which is invariant to the identification problem and therefore more amenable to interpretation, inference, and forecasting.