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06th Feb 2019

There has been interest in finding separate effects of age, year and birth cohort for decades, in both the biological and social sciences. However, the exact collinearity between these three (Age = Year – Birth Year) lead to difficulty in estimating these effects. Because of this, it is impossible to estimate near-linear effects (or linear components of these effects) without making strong assumptions about at least one of these. This is a problem for anyone interested in any of age, period and/or cohort patterns in a particular outcome.

There have been many attempts to ‘solve’ this identification problem without having to make strong assumptions – however in each case, it turns out such models are, in fact, making hidden assumptions that were not intended by the user, as I show with simulations. I then consider what researchers should do, drawing on literature from across the social, biological and health sciences. This includes consideration of non-linearities around linear APC effects (with both statistical and graphical techniques), strong and explicit assumptions based on theory (for example assuming there are no linear period effects), including constraints on certain parameters to estimate ranges within which other parameters must fall. I provide an example focusing on mortality in the twentieth century. In each case, these methods acknowledge that there is a ‘line of solutions’ of possible combinations of APC effects, and not a single answer that can be estimated empirically. None of these methods represent a solution to the identification problem – rather they are an honest acknowledgement of the problem, with an awareness that the methods are limited by their assumptions.

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