On the Linear Algebra and Statistical Properties of Intrinsic and Related Estimators

• In Event: 4150 - Topics in Sociological Methodology, Session 1

Abstract

As a sophisticated and popular age-period-cohort method, the Intrinsic Estimator (IE) and related estimators have evoked intense debate in demography, sociology, epidemiology and statistics. Given that the debate is often driven by results from data simulation and shows less attention to the mathematical foundations, this study aims to provide a more holistic and critical assessment of the overall methodological significance of the IE and related estimators in age-period-cohort analysis. In particular, it derives the statistical properties of the IE from a linear algebraic perspective, provides more precise mathematical proofs relevant to the current debate, and demonstrates the essential, yet overlooked, link between the IE and classical statistical tools that have been employed by scholars for decades. By integrating the fundamental principles of age-period-cohort analysis established since the 1970s, this study also offers guidelines for the use of the IE and related estimators in empirical research, which are illustrated with an empirical example. The exposition of the IE and related estimators may help redirect, if not settle, the logic of the debate.

Authors

• Qiang Fu, The University of British Columbia

• Kenneth C. Land, Duke University

• Emma Zang, Yale University

• Eric N. Reither, Utah State University

• Sun Young Jeon, Utah State University