The impossibility of separating age, period and cohort effects

doi:10.1016/j.socscimed.2013.04.029

Social Science & Medicine

Volume 93, September 2013, Pages 163-165

https://doi.org/10.1016/j.socscimed.2013.04.029 Get rights and content

Highlights

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Age, period and cohort (APC) trends cannot be disentangled mechanically.
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Explicit assumptions must be made for APC models to be identified.
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Imposing arbitrary assumptions leads to arbitrary model results.
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Assumptions should be based on strong theory and be stated explicitly.

Abstract

This commentary discusses the age–period–cohort identification problem. It shows that, despite a plethora of proposed solutions in the literature, no model is able to solve the identification problem because the identification problem is inherent to the real-world processes being modelled. As such, we cast doubt on the conclusions of a number of papers, including one presented here (Page, Milner, Morrell, & Taylor, 2013). We conclude with some recommendations for those wanting to model age, period and cohort in a compelling way.

Introduction

This commentary addresses this issue of statistically modelling separate age, period and cohort (APC) effects. The issue has been hotly debated for decades (Ryder, 1965), in sociology (Glenn, 1976; Mason, Mason, Winsborough, & Poole, 1973), medical science (Osmond & Gardner, 1989; Robertson & Boyle, 1986) and elsewhere. However, the publication of an article in this issue (Page et al., 2013) alongside more recent methodological developments in APC modelling (Tu, Smith, & Gilthorpe, 2011; Yang & Land, 2006; Yang, Schulhofer-Wohl, Fu, & Land, 2008), shows that there is still profound interest in modelling and discerning APC effects.

This commentary does not directly critique Page et al.'s paper in terms of its substantive conclusions; rather, we address the key methodological issues in modelling APC effects. However the implications of our argument call into question the results found by Page et al., and should act as a warning for others researchers wishing to disentangle APC effects in a meaningful way.

We first outline what APC effects are substantively, and describe the identification problem which makes them so difficult to model. We then outline some proposed solutions to the identification problem, including that used by Page et al., and explain why they will only work in very specific and arguably usually unrealistic circumstances. The commentary finishes with some recommendations for researchers wishing to model APC effects.

Section snippets

Age, period and cohort effects

The difference between age effects, period effects and cohort effects is well explicated by this fictional dialogue by Suzuki (2012, p. 452):

A: I can't seem to shake off this tired feeling. Guess I'm just getting old. [Age effect]
B: Do you think it's stress? Business is down this year, and you've let your fatigue build up. [Period effect]
A: Maybe. What about you?
B: Actually, I'm exhausted too! My body feels really heavy.
A: You're kidding. You're still young. I could work all day long when I was

Solutions to the identification problem, and why they do not work

Despite this scepticism, there have been numerous attempts to find a way around the identification problem. The most common, and that suggested by Mason et al. (1973), is to constrain certain parameters in a model to be equal. So, each age group, period group and cohort group is included in a regression model as a dummy variable, but 2 age groups (or period groups, or cohort groups) are combined together as if they were a single group. This breaks the exact collinearity and allows the model to

Recommendations

So far, there is little good news for the researcher hoping to find separate APC effects. However, we believe that theorising and finding age, period and cohort is often very important in social science, and that they can be modelled, so long as the assumptions that are being made by the model are justified by theory and stated explicitly.

It is often the case that we can assume that continuous period effects are non-existent. It seems to us that theory often indicates that progress over time is

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Citation Excerpt :
The literature makes several attempts to find a solution to this problem, one of the most common of which is to constrain certain parameters in a model so they are equal. ( See Bell and Jones [41] for details.) Each age and birth cohort group is included in a regression model as a dummy variable, but two age groups and cohort groups are combined into a single group (e.g., [42]).
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View full text

CommentaryThe impossibility of separating age, period and cohort effects

Highlights

Abstract

Introduction

Section snippets

Age, period and cohort effects

Solutions to the identification problem, and why they do not work

Recommendations

Social Science & Medicine

Another ‘futile quest’? A simulation study of Yang and Land's Hierarchical Age–Period–Cohort model

Current practice in the modelling of Age, Period and Cohort effects with panel data: A commentary on Tawfik et al (2012), Clarke et al (2009), and McCulloch (2012)

Cohort analysts futile quest – statistical attempts to separate age, period and cohort effects

American Sociological Review

Cohort analysis

Age, period and cohort effects – a confounded confusion

Journal of Applied Statistics

The cross-classified age–period–cohort model as a constrained estimator

Cohort variation in the membership of voluntary organisations in Great Britain, 1991–2007

Commentary
The impossibility of separating age, period and cohort effects