Chris Winship and Ethan Fosse write:
Since its beginnings nearly a century ago, Age-Period-Cohort analysis has been stymied by the lack of identification of parameter estimates resulting from the linear dependence between age, period, and cohort (age= period – cohort). In a series of articles, we [Winship and Fosse] have developed a set of methods that allow APC analysis to move forward despite the identification problem. We believe that our work provides a solid methodological foundation for APC analysis, one that has not existed previously. By a solid methodological foundation, we mean a set of methods that can produce substantively important results where the assumptions involved are both explicit and likely to be plausible.
After nearly a century of effort this is a big claim. How might we test it? In mathematics, if someone claims to have proved a theorem, the proof is not considered valid until others have rigorously analyzed it. Our request and hope that researchers will interrogate our claim with similar rigor. Have we in fact succeed after so many years of efforts by others?
My own articles on age-period-cohort analysis are here, here, and here. The first of these was an invited discussion for the American Journal of Sociology that they decided not to publish; the second (with Jonathan Auerbach) is our summary of what went wrong with that notorious claim a few years ago about the increasing death rate of middle-aged white Americans, and the third (with Yair Ghitza and Jonathan Auerbach) is our very own age-period-cohort analysis of presidential voting.
I have not looked at Winship and Fosse’s work in detail, but I agree with their general point that the the right way forward with this problem is to think about nonlinear models.