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Age period cohort brouhaha

Hi everybody!

In August, I announced a break from blogging. And this is my first new post since then. (not counting various interpolated topical items on polling, elections, laughable surveys comparing North Carolina to North Korea, junk science on pizza prices, etc)

I’m still trying to figure out how to do this; I have a file chock full of blogging material and I have this idea of just sitting down and writing 365 posts to get the whole year out of the way. But I guess I’ll start with one a day for awhile.

This is the first.

So. Several years ago the American Journal of Sociology asked me to write a comment for a paper they were running on age period cohort analysis. What happened was that Yang et al. had written a paper on disentangling these additive terms, and Steve Fienberg and someone else, I think, were saying that Yang et al. were wrong, and I was brought in for an outside opinion.

I wrote my comment—here it is—pretty much agreeing with Fienberg but expressing some sympathy for Yang et al. because age-period-cohort decomposition is something that in theory seems completely impossible but can actually be done in the context of real applications where there is prior information that can be used to parameterize and structure the answer. So I didn’t want to be completely negative, even though the solution of Yang et al., which attempts to be completely automatic, can’t possibly work.

For some reason the AJS decided they weren’t running my discussion. Soooo annoying. I hate when that happens. I write a paper to do someone a favor and then they decide they don’t want it. In the meantime, I did some more age-period-cohort analysis with Yair, though, so I guess that this earlier work wasn’t entirely wasted.

Anyway, I’d pretty much forgotten that episode until the other day when Chris Winship sent me this paper by Liying Luo, James Hodges, Daniel Powers, and himself, which appeared in AJS recently. Here’s the punchline:

“The Intrinsic Estimator for Age-Period-Cohort Analysis” (Yang et al. 2008) has been cited 189 times as of October 2016 and has been used by researchers in different disciplines to address important substantive questions. Many researchers appear convinced that the assumptions implicit in the IE do not affect the IE’s ability to estimate, even if only approximately, the “true” age, period, and cohort effects . . . The empirical and mathematical results presented in this comment contradict that optimistic view. . . .

Social scientists have long looked for statistical methods that will provide assumption-free results revealing the underlying structure of empirical data. As with causal analysis of observational data . . . we believe this is an impossible goal. Heckman and Robb (1985) stated the situation correctly nearly three decades ago: “The age-period-cohort effect identification problem arises because analysts want something for nothing: a general statistical decomposition of data without specific sub- ject matter motivation underlying the decomposition. . . .”

I agree. Again, I did not feel comfortable completely shooting down Yang et al. because I could imagine that their structure could be useful for researchers who want to include subject-matter knowledge in their inferences, but, sure, if it’s a take it or leave it on Yang et al., I’d have to say, leave it.

But then there’s more to the story. A different set of authors, Kenneth Land, Qiang Fu, Xin Guo, Sun Jeon, Eric Reither, and Emma Zhang (a group that includes one of the authors of the earlier Yang et al. paper) responded with an article in AJS. Their response had the aggressive title, “Playing with the rules and making misleading statements,” and they continued to fire with both barrels in the text:

Luo et al. then claim to raise “concerns about the robustness” and thus usefulness of the IE by showing that IE estimates can be “highly sensitive” to a researcher’s choice of coding scheme or model parameterization. In this response, we find these “concerns” to be based on misinterpretations, misunderstandings, and misrepresentations of the IE and, accordingly, misleading.

What’s with all the scare quotes, huh? Kinda iffy to be going against high-powered methodologists like Chris Winship and Steve Fienberg!

But let’s get to the conclusion of Land et al.:

The APC [age-period-cohort] accounting/multiple classification model is not identified unless we impose one additional constraint whose validity cannot be tested with any data. Just as there are infinitely many generalized inverse matrices to calculate the coefficient vector of this model, there are infinitely many corresponding possible constraints. . . . Given this, researchers should not use the IE [that estimate from Yang et al., 2008], or any other constraint such as equality-of-coefficients or a cohort characteristic proxy constraint, without careful thought about whether it is reasonable in their particular context.

I think we’re all in agreement on that point. The key point of disagreement is on whether the Yang et al. method is useful in a wide range of applications.

If you go to the conclusion of the original Yang et al. (2008) paper, you’ll see some mixed messages. First a full-steam-ahead:

Glenn (2005, p. 20) has stated several strong criteria for judging the acceptability and utility of a general-purpose method of APC analysis. The IE appears to satisfy these criteria. As shown here, the IE has passed both empirical and simulation tests of validity and can be used to test theoretically motivated hypotheses and to incorporate and test side information from other studies. The IE therefore may provide a useful tool for the accumulation of scientific knowledge about the distinct effects of age, period, and cohort categories in social research. Indeed, since the APC underidentification problem is an instance of a larger family of such structural issues, the potential range of application for the IE may be even larger.

But then . . . whoa, maybe not. Yang et al. continue:

Does this mean that researchers should naively apply this method to tables of rates and expect to obtain meaningful results? Again, no. Every statistical model has its limits and will break down under some conditions. APC analysis is well known to be treacherous, for reasons articulated by Glenn (2005), and should, in all cases, be approached with great caution and an awareness of its many pitfalls.

For now, I’ll go with Luo/Hodges/Winship/Powers, who agree with Heckman/Robb and Fienberg/Mason before them.


  1. Andrew, if there were a prize for “Blogger on Blog Hiatus Who Blogs the Most and Best,” you would surely win! Welcome back, as it were.

  2. Bill Bielby says:

    Anybody remember the “automatic interaction detector”?

  3. Andy Bell says:

    I find their cautions really strange – as if a reviewer has told them ‘but you’ve got to be careful’ and so they’ve added in the sentence, but then appear to carry on using the model as if it were a universal solution (or present the limits of the model as if they are minor technicalities). FYI there is a similar ongoing debate about another of Yang and Land’s models in Social Science and Medicine (involving yours truly) that has similar themes, e.g.

    • jrc says:

      Yeah – I get the impression that, at least one of them believes that they’ve basically solved the Age-Period-Cohort problem. Like, solved it, end of story, all finished. Which is nice I guess that we don’t have to worry about that mathematically perfect co-determination that would seem like a problem.

      I get that impression because of the following conversation that took place after a seminar:

      jrc: So I see you’ve done some work on the Age-Period-Cohort problem. I love that stuff, but it gives you a real headache after a while.

      Author: We solved that problem.

      jrc: (confused) But, like, I mean, you can’t solve it solve it, right? Like, it is a problem you have to get around but nothing changes the fact that cohort plus age equals period.

      Author: No. We solve it. The optimal…

      jrc: But wait I mean it must depend on the set of outcomes and the questions you are asking….

      Author: No. We solved it. You…

      And by that point I just so completely flummoxed that this person was standing there telling me that there was a way to perfectly disentangle three completely non-separable aspects of an observation that I couldn’t even focus on their “solution.” It was just the pure hubris of the whole thing: “Oh, that logically impossible to solve problem… we solved that perfectly, with logic.”

      I think this is actually a nice example of a certain type of statistician – one who is a) incredibly good at math; and b) doesn’t really think about the world. Because you get the impression that they can’t separate out the two issues involved in solving a statistical problem: 1) set up a model of how the world is; 2) solve for some optimal solution given that world. They do 1, then promptly forget that 1 was a choice and a way to represent some aspect of the world but not the whole thing. Then they take (1) as how the world actually is and believe that, by doing (2), they’ve solved whatever problem they set up (1) to emulate. The problem is that the logic can be just fine, given the model they define in (1), but no one model of the world can ever be THE one model, and so the result of the logic is never a universal solution, just a local one. And this is how you get people saying they’ve solved the Age-Cohort-Period problem: they found a data generating process under which they can identify all three, and so it is solved.

      • Keith O'Rourke says:

        “The word butterfly is not a real butterfly. There is the word and there is the butterfly. If you confuse these two items people have the right to laugh at you.”

        • Martha (Smith) says:

          @Keith:Good quote — but things are even more complex when talking about statistics, because many of the words to not refer to physical object like butterflies, but to concepts that often are pretty fuzzy.

          Examples from statistics:

          Power: The statistical concept has morphed from the fairly well-defined concept of “ability to detect a difference of a specified amount” to things like “high power, medium power, low power” defined in terms of a standardized effect size.

          Control: The use of the term “control group” in a randomized trial, or “control for this variable” in a regression often lead people to think that something stronger is happening (perhaps like “this switch controls this light”) than in reality is happening. (That’s why I try to use the terms “comparison group” and “try to account for this variable” instead — they are less likely to suggest the certainty that “control” often does.)

          • Keith O'Rourke says:

            That’s an important point.

            “The word representing something is not that real something. There is the representation and there is what someone is attempting to represent. If you confuse these two items people have the right to disregard you.”

            And accuse you of not being really good at math – because in reality – you aren’t ;-)

      • Martha (Smith) says:

        I agree with everything you say in this post, except “a) incredibly good at math”. It is possible that they might in fact not be all that good at math.

    • Jona Schellekens says:

      I found your comments on HAPC models (with Kelvyn Jones) very helpful. However, I missed a reference to Chris Winship and David Harding (2008), “A Mechanism-Based Approach to the Identification of Age–Period–Cohort Models”, Sociological Methods & Research 36(3): 362-401 . I have used their approach in an individual-level APC analysis of the marriage boom in the US. My article in Population Studies, which includes a reference to one of your articles, has just become available on-line at

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