The Intrinsic Estimator for Age‐Period‐Cohort Analysis: What It Is and How to Use It

Abstract

A new approach to the statistical estimation of age-period-cohort (APC) accounting models, called the intrinsic estimator (IE), recently has been developed. This article (1) further describes the IE algebraically, geometrically, and verbally, (2) reviews properties of the IE as a statistical estimator, (3) provides model validation evidence for the IE both from an empirical example and from a simulation exercise, (4) relates the coefficients of the IE to those of conventional constrained APC models using formal definitions of statistical estimability, hypothesis testing, and empirical applications that directly address a criticism that often has been lodged at generalpurpose methods of APC analysis, and (5) introduces computer software for application of the IE that interested users can readily access. The authors conclude that the IE holds the potential for applications not only to APC analysis but also to similar problems of structural underidentification in sociology.

The Non-uniqueness Property of the Intrinsic Estimator in APC Models

“…This is illustrated in Fig. 2 where we use the same dataset on U.S. female mortality as was used by Yang et al (2004Yang et al ( , 2008. These data are from the Berkeley Human Mortality…”

“…We took all possible 19 x 8 x 26=3952 triplets of omitted categories and for each triplet we calculated the corresponding set of effect coded IE estimates, using the Poisson regression model also employed by Yang et al (2004Yang et al ( , 2008. In Fig.…”

The demographic threat to Detroit's automakers

“…An early collection of technical essays on cohort analysis is Mason and Fienberg; a later, briefer explication is Mason and Wolfi nger. 13 -14 A very recent, though demanding, treatment of the technique with a proposed solution to the identifi cation problem is Yang, et al 15 A drawback of cohort analysis in marketing applications is that it is not often coupled with a set of data that extends over a substantial number of years. For this paper, however, data that ranged over 24 years were available.…”

Mapping Mortality: Using Lexis surfaces to identify complex patterns in age-year specific mortality rates within and between populations

“…For example, people born around the time of the 'Spanish Flu' of 1918 appear to have somewhat higher mortality risks at any given age than might be expected from trends observed in earlier and later cohorts, (Almond, 2006;J Minton, Vanderbloemen, & Dorling, 2013) and people born in England and Wales in the 1950s to have a somewhat lower mortality risk as they age than might be expected from broader trends. (Willets, 2003) There have been various attempts to uniquely partition away cohort effects from age effects and period effects in statistical models (for example (Yang, Fu, & Land, 2004;Yang, Schulhofer-Wohl, Fu, & Land, 2008)), but doing so is logically impossible, because each of the three effects cannot be uniquely identified (Wilmoth, 2006), leading to effects to do so being branded 'futile'. (Bell & Jones, 2014) 1.2.…”