No issue has been more contested in social science methodology than whether it is possible, with realistic assumptions, to estimate the separate effects of age, period, and cohort (APC) variables on social change. For example, over time the U.S. population has become increasingly alienated with the federal government. However, this could be due to a changing age distribution, period effects such as recessions, or cohort replacement with more recent birth cohorts being more alienated.
Because age, period, and cohort are linearly dependent (age = period – cohort), when we hold period and cohort fixed, there is no independent variation in age with which to estimate its linear trend. Initially, the APC literature focused on the idea of making substantive assumptions, such as a constant period effect over two or more time periods. However, the sociologist Norval Glenn (University of Texas) argued that most assumptions were hard to justify and that small changes in assumptions could radically alter results. Recently, Kenneth C. Land (Duke University) and others have argued for making statistical assumptions, but such assumptions typically lack substantive justification.
In our paper, “Age-Period-Cohort Models: Bounds, Mechanisms, and Solution Lines” to be presented at the 2016 American Statistical Association meetings, we investigate what can be learned by making weaker assumptions with inequality restrictions. Actually, often quite a lot. For example in examining trends in cigarette smoking if we assume that the effect of age among adults is negative, the cohort effect for individuals born before 1930 is positive, but negative afterwards. In general we find across multiple examples, including trends in verbal ability and changes in political affiliation, that if we assume the direction of the effect for one variable, that determines, at least qualitatively, the effects of other variables.