One approach to the age-period-cohort problem: Just don’t.

Just to cause yourself more problems, you seek for something. But there is no need for you to seek anything. You have plenty, and you have just enough problems.

Shunryū Suzuki in a 1971 talk

A P C, it’s easy as 1 2 3

There is no way around the age-period-cohort problem. It arises whenever we are interested in how age affects an outcome, or how the point of time in history (period) affects an outcome, or how the year one was born in (cohort) affects an outcome. The fundamental issue is that cohort (e.g., your birth year) + age (e.g., your current age) = period (e.g., the current year in which you are reading this post).  While this dependency comes in handy in case you ever forget your own age, it causes considerable headaches for any attempt to separate these three variables.

But let’s make this as specific as possible. Let’s say you are interested in whether recent modern times make people miserable. That is, is there a period effect on well-being? To investigate that, you may, for example, compare the well-being of people nowadays (2026) to the well-being of people ten years ago (2016, pre-pandemic exhaustion, in the year of Harambe^[1]according to a quick online search, that was the main world event that year, and everybody was happy otherwise.). 

Even under the best circumstances, your 2026 and your 2016 samples won’t be quite comparable. For example, your 2026 sample will include cohorts that were too young to fill out surveys in 2016, and it will lack representation of the cohorts who have died away in the meantime. And surely cohorts may differ in their general well-being level! People born in different years may turn out quite differently due to differences in socialization and the like.^[2]Your parents were released into the wilderness at age two with a stick and a vague sense of north. Your middle schooler loses outdoor privileges the moment their AirTag registers that they are approaching the garden gate. So, we are comparing apples to oranges here, which is not a great way to isolate the effects of the historical period.

We can fix that by controlling for cohort. Conceptually, that’s like only comparing people belonging to the same cohort over the 10 years – so we keep cohort fixed but vary period. If you have longitudinal data available, you could even compare people to themselves over time! That should do a great job isolating changes over time. Except when you think about it, people belonging to a given cohort will, 10 years later, have aged by 10 years. So, for example, if we compare people born into the 1990 cohort in 2016 to people of that very cohort in 2026, we are comparing 26-year-olds to 36-year-olds. That’s like comparing grapes to raisins! So again, not a great comparison if we want to isolate the effects of period. 

Clearly, the solution here is to hold both cohort and age fixed and only vary the historic period. In principle, that’s the way to go, except it is chronologically impossible. We cannot compare 26-year-old members of the 1990 cohort in 2016 to 26-year-old members of the 1990 cohort in 2026 because the latter group doesn’t exist. Now we may think “well duh, in that case let’s compare them to 26-year-old members of the 2000 cohort in 2026,” which may seem like the next best thing, except now we are back in a situation where we are comparing people from different cohorts, which was the issue we initially set out to fix.

No matter how we turn things, something about the comparison is going to be flawed. The same applies if your central interest is age effects: Comparing the same cohort with itself as it ages will give you a combination of age effects and period effects. Comparing people of different ages at a single point in time, that is, holding period constant, gives you a combination of age effects and cohort effects—that’s the central reason why people are prone to dismiss cross-sectional designs if aging is of interest.

Likewise, if you are interested in cohort effects: Comparing different cohorts at the same point in time (precisely the same cross-sectional design as just before) gives you a combination of cohort effects and age effects. Comparing different cohorts at the same age—say, the 1990 cohort at age 20 and the 2000 cohort at age 20—gives you a combination of cohort and period effect (because you’re comparing the 1990 cohort in 2010 with the 2000 cohort in 2020, so this is a pre-post-Harambe design). Lastly, comparing different cohorts of different ages at different points in time gives you a combination of age effects, cohort effects, period effects.^[3]And a book deal for the next moral panic.

That is the essence of the age-period-cohort identification problem, and it just is what it is because that’s how time and age work. It’s not really a problem of statistics; it’s a problem of a woefully inadequate reality in which time machines have not been invented. Since it’s not a problem of statistics, that also means that there can be no statistical solutions. But there are “solutions” that work by imposing assumptions about reality. For example, one can assume that one temporal variable (e.g., period) does not affect the variable of interest; or one can make assumptions about the shapes of the effects of temporal variables; or one can go even wilder and make the assumption that the effects of one temporal variable are fully mediated through known (and appropriately modeled) mechanisms. If you are interested in those solutions, I provide an overview in Thinking clearly about age, period, and cohort effects.

But here, I want to suggest another approach, for which we will take a step back and proceed with:

Thinking not at all about age, period, and cohort effects

If you think about it, the counterfactuals involved in age, period, and cohort effects are a bit funky. What if…you were a member of the same cohort in the same historic time but suddenly aged by ten years in an instant? What if…we took a member of a given cohort at a given age but suddenly transported them ten years into the future? What if you, at your current age and right now in time, but born ten years earlier?

Some of that weirdness can be dissolved by thinking of age, period, and cohort as stand-ins for their respective mechanisms, and so “you suddenly aged by ten years” is “you, but your brain undergoes all the changes it undergoes in ten years, and you speed-run all the social role changes and the like that happen in ten years”.^[4]See Bijlsma et al. (2017) for the corresponding potential outcomes notation Developmental psychologists sometimes like to say that age is an empty variable, and I guess that’s one way of saying that age is really just the stuff that happens as you age. 

So, let’s say you did somehow solve the problem and knew the true age, period, and/or cohort effects. That’s like knowing the effect of some treatment package, without precisely knowing what is driving the effect. For example, if you know the true trajectory of period effects, you still can’t just draw a line and say “it’s because the iPhone was released in 2007” – after all, there are all sorts of other things that may mediate those period effects.^[5]Rumor has it some other important global stuff happened briefly after the release of the iPhone. Even if you know the true trajectory of the age effects, that doesn’t mean it’s some biological aging mechanism; it may as well be people entering or exiting the labor force, or doing all the other things one is expected to do as one ages, like finding yourself a girl and settling down to live a simple life in a quiet town. And finally, let’s assume you know the true cohort effect. That doesn’t mean you get to do the “cohort-as-character-arc” thing, where you narrate a generation like it’s a protagonist in a coming-of-age/period film. “They grew up being coddled, so of course they’ve never learned resilience.” Maybe. Or maybe you’re just reading a retrospective bedtime story for boomers into a regression coefficient. 

Now, usually it’s quite nice to know the effect of some treatment package, even if you don’t know the precise mediators. Actually, I’m usually the last person to ask, “Yes, but what’s the mechanism?” because the answer is “how would anybody know, mediation analysis is a mess.” However, here, we are talking about a treatment package that you cannot actually administer to anybody, so it’s not like there were any obvious implications. That being said, I’d enjoy reading a study that suggests reducing age for the benefit of public health. It’s a particular style of humor.^[6]A style of humor shared by this Nature Aging study that suggested randomized controlled trials could explicitly manipulate multilingualism and directly assess its effects on aging clocks. 

Leaving aside the question of whether age, period, and cohort effects can ever be a satisfying explanation for anything, researchers often purport to be interested in prediction. Unfortunately, the effects fail on that front, too; knowing the temporal effects is not even necessarily helpful to predict anything. Let’s say you manage to isolate the age effects, which are probably the ones that are most easily taken as some sort of generalizable law. Future cohort effects may look different; nobody can say which period effects the future will bring, but it’s a given that everybody passes the same ages. Now, even if we assume that the age effects remain the same over time (big assumption),^[7]Which, by the way, underlies many approaches to the age-period-cohort problem because allowing for interactions makes everything even less identified that still does not mean we can predict what will happen as a future individual ages. Because unfortunately, people age in time, and so beyond the age effects, we would also need to know future (unknowable) period effects, otherwise our predictions will be biased. One “easy way out” is assuming that there are no large or systematic period effects. That’s a strong assumption that can be plausible for some constructs. I’d be happy to predict no relevant future period effects on the physical height of my kids, given their current life circumstances (fingers crossed). But for something as elusive as subjective well-being or loneliness or attitudes, I’m a lot less certain.

So, that’s what you get for solving an empirically unsolvable identification issue. Some effects, but you don’t know why they happen, you cannot use them to intervene on anything, and you often can’t even use them to predict what will happen to people. Not exactly a great return on investment, is it?

Alternative things you can do
Just describe stuff

Here’s an alternative suggestion: Don’t even try solving the unsolvable. Be content with more attainable achievements. Just observe, don’t infer.^[8]#TangPing. If reading this just gave you whiplash because I’m the person going around telling everybody “no, you actually do want to do causal inference and not just look at associations,” rest assured, I’m still all about causal inference. We will return to that at the very end of this post.

After all, there is no way to age but in time. There is no way to be a member of a particular cohort without also aging. And there is no way to experience a particular historic moment but as a member of a particular cohort, at a particular age. For some constructs, and in some particular populations, a disembodied age, period, or cohort effect may be easier to imagine – for example, one may meaningfully speculate about the age trajectory of cortical thickness in genetically uniform rats held in some standardized “neutral” environment. So I’m not saying it never makes sense to try to get at the isolated effects. But it’s so much harder to figure out what an isolated age trajectory in human well-being would mean, partialling out all differences between cohorts and removing all effects of historic time.^[9]And it only gets worse if we additionally consider that we cannot directly observe people’s well-being, so changes in how the measurement process works — which could be driven by age (e.g., the wisdom of age putting things into a new perspective), cohort (e.g., millennials grew up being coddled, so of course they feel overly entitled to a perfect life), or period (e.g., everybody getting richer, which may increase the standard against which one evaluates their own life) — are layered on top, making the inferential mess even worse. So, maybe instead we should ask questions about more tangible things.^[10]How’s your lower back? Your bank account? Did you sleep last night, or did you just lie down next to your phone until morning happened?

That does not mean lying flat giving up on either age, period, or cohort; it just means giving up on trying to cleanly separate them. One approach that does not even try to separate them is cohort analysis (see Fosse & Winship, 2023) in which you essentially just look at how different cohorts change and end up with an overall intracohort trend and intercohort trends. Now, the important thing is that your interpretation here should not lapse back into age/cohort/period effects. You still need to understand the age-period-cohort problem to understand which interpretations are justified and which aren’t; so there’s not only no way around the age-period-cohort problem, but also no way around understanding it, if you want to handle the involved variables.

Just plot stuff

Going even more “low-tech”, you can also…just look at your data. If you have data for multiple cohorts at various ages, you can just plot them. As Andrew Bell points out, there are different ways to do that, and those will make it tempting to interpret the results in various ways as evidence for particular age, period, or cohort effects, so again one needs to proceed with some degree of caution. But that doesn’t mean that one can’t proceed. And also, you can plot your data all sorts of different ways to make things less suggestive and confuse yourself thoroughly.

For example, in my age-period-cohort primer, I looked at German respondents’ attitudes towards working mothers.^[11]Research being me-search etc.; approval was assessed with three items: A working mother can have a relationship with her children that is just as loving and trusting as a non-working mother; It is even good for a child if the mother works and is not only focused on the household; reverse coded: A small child will surely suffer when their mother works. Now, we can plot average approval over age and connect by either birth cohort or survey year, but we can also plot average approval over survey year and connect by either birth cohort or age. Actually, we could also plot data over birth cohort (and then connect by either age or survey year), but somehow that doesn’t feel very natural to me as a psychologist, which I guess tells you something about what we are usually interested in.

In any case, we end up with the following picture:

What can we learn from that? Graphs go up^[12]Yay! except for the cross-sectional age trajectories.^[13]Boo! Over time, all age groups and all cohorts become more likely to approve of working mothers. Going one step further, we could take the mean changes to (for example) even derive something like an average “aging in time” trajectory across the observed cohorts. This wouldn’t be an average of the age effects across cohorts, but rather the average of the age effects plus the period effects that the people in our data experienced. That is, the average of things that happened to these specific cohorts as they aged in time, for the ages that we observed them. This would go up as well, but unlike an upwards trajectory of age effects, we would have no inherent expectations that what happens here necessarily extends into the future – maybe the increases here ought to be attributed to the times through which these cohorts aged, and maybe those times are a-changin.^[14]In my age-period-cohort analysis of the matter, I do actually conclude no relevant period increase between the last two survey waves. Double boo!

So, what we can learn from this plot in isolation is what happened in the past. What we cannot learn from it (unless we add assumptions) is to what extent that was driven by age mechanisms (e.g., age → having kids → letting go of romanticized ideas of motherhood), by cohort mechanisms (e.g., cohort → being socialized with less traditional values → openness to working mothers), or by period mechanisms (e.g., period → share of women in the labor market → normalization of the idea that mothers work). We may make some educated guesses based on additional knowledge about the world; that knowledge can, in principle, be translated into assumptions, and then those assumptions may help us to disentangle the effects (check out my 2025 paper to see how to proceed with one set of such assumptions). 

But keep in mind that even if we succeeded at correctly disentangling the effects, we still wouldn’t know which specific mechanisms are at work. Maybe the age effect is not driven by having kids but rather by cognitive decline? Maybe the cohort effect is not driven by values but by improved schooling? Maybe the period effect is not driven by women in the labor market but by contemporary feminist discourse?

Just study stuff

Which leads to another thing one can do without solving the age-period-cohort problem: Actually investigating the hypothesized mechanisms and whether they affect the outcome of interest. For example, you could investigate how parenthood or schooling or exposure to the feminist discourse shape attitudes.

Now, if you think about these research questions more closely, you may realize that each of them poses its own major causal inference issues (correlation does not equal causation; causes that are not easily randomized; etc….) and we need some credible identification strategy, yadda yadda. But! If you do manage to find some answer, you’ve actually found something that at least hypothetically could be used to intervene in the world. And at least for these questions, it isn’t guaranteed that you are going to run into a fundamentally unsolvable identification issue. You just have the usual causal inference problems. And those are just enough.