2. A Methodological Comparison of Age-Period-Cohort Models: The Intrinsic Estimator and Conventional Generalized Linear Models

Age-period-cohort (APC) accounting models have long been objects of attention in statistical studies of human populations. It is well known that the identification problem created by the linear dependency of age, period, and cohort (Period = Age + Cohort or P = A + C) presents a major methodological challenge to APC analysis, a problem that has been widely addressed in demography, epidemiology, and statistics. This paper compares parameter estimates and model fit statistics produced by two solutions to the identification problem in age-period-cohort models—namely, the conventional demographic approach of constrained generalized linear models (Fienberg and Mason 1978, 1985; Mason and Smith 1985) and the intrinsic estimator method recently developed by Fu (2000; Knight and Fu 2000; Fu, Hall, and Rohan 2004). We report empirical analyses of applications of these two methods to population data on U.S. female mortality rates. Comparisons of parameter estimates suggest that both constrained generalized linear models and the intrinsic estimator method can yield similar estimates of age, period, and cohort effects, but estimates obtained by the intrinsic estimator are more direct and do not require prior information to select appropriate model identifying constraints. We also describe three statistical properties of the estimators: (1) finite-time-period bias, (2) relative statistical efficiency, and (3) consistency as the number of periods of observed data increases. These empirical analyses and theoretical results suggest that the intrinsic estimator may well provide a useful alternative to conventional methods for the APC analysis of demographic rates.