On the Intrinsic Estimator and Constrained Estimators in Age-Period-Cohort Models

In studying temporally ordered rates of events, epidemiologists, demographers, and social scientists often find it useful to distinguish three different temporal dimensions, namely, age (age of the participants involved), time period (the calendar year or other temporal period for recording the events of interest), and cohort (birth cohort or generation). Age-period-cohort (APC) analysis aims to analyze age-year-specific archived event rates to capture temporal trends in the events under investigation. However, in the context of tables of rates, the well-known relationship among these three factors, Period − Age = Cohort, makes the parameter estimation of the APC multiple classification model difficult. The identification problem of the parameter estimation has been studied since the 1970s and still remains in debate. Recent developments in this regard include the intrinsic estimator (IE) method, the autoregressive cohort model, the age-period-cohort-characteristic (APCC) model, the regression splines model, the smoothing cohort model, and the hierarchical APC model. O’Brien (2011 ; pp. 419-452, this issue) makes a further contribution in studying constrained estimators, particularly the IE, in the APC models. The authors, however, have important disagreements with O’Brien as to what the statistical properties of the IE are and how the estimates from the IE should be interpreted. The authors point out these disagreements to conclude the article.