Modeling the Evolution of Age and Cohort Effects

Sam Schulhofer-Wohl, Senior Vice President and Director of Research

February 2016 | Dynamic Demographic Analysis, Vol 39, Chapter 16, p. 313-335. | With Y. Claire Yang

The conventional linear model of age, period, and cohort (APC) effects suffers from a well-known identification problem: If an outcome depends on the sum of an age effect, a period effect, and a cohort effect, one cannot distinguish these three effects because birth year = current yearage. Less well appreciated is that the linear model suffers from a conceptual problem: It assumes that the marginal effect of age is the same at all times, the marginal effect of current conditions is the same for people of all ages, and cohorts do not change over time. We propose a new way of modeling APC effects that improves substantively and methodologically on the conventional linear model. We define cohort effects as an accumulation of age-by-period interactions. Although a long-standing literature conceptualizes cohort effects in exactly this way, we are the first to provide a statistical model. Our model allows age profiles to change over time and period effects to have different marginal effects on people of different ages. Except in special cases, the parameters of our model are identified. We apply the model to analyze changes in age-specific mortality in Sweden over 150 years. Our model fits the Swedish data dramatically better than the additive model. The rate of increase of mortality with age became more steep from 1881 to 1941, but since then has been roughly constant. The impact of early-life conditions lasts for several years but is unlikely to reach to old age.