Moore-Penrose Estimators of Age-period-cohort Effects: Their Interrelationship and Properties

• In Event: 4252 - New Statistical Methods in Social Science Research

Abstract

Estimators based on the Moore-Penrose pseudo-inverse (MP-estimators), particularly Yang and Land's Intrinsic Estimator (IE), have become popular tools for the analysis of Age-Period-Cohort data. Recent papers (Pelzer et al. 2015, Luo et al. 2016, Grotenuis et al. 2016) have shown that different MP-estimators can lead to radically different estimates of age, period, cohort effects. We explore in what ways these estimates differ and in what way they are similar. Basic to our approach is separating the linear from the nonlinear effect estimates. This makes it transparent that it is the nonlinear, but not the linear effect estimates that are identified. This analysis then provides new insights into: (1) when an MP-Estimator will do well at recovering the underlying data generating parameters; (2) why some, but not other MP-estimators are affected by the number of periods used; (3) the convergence properties of MP-estimators.

Authors

• Ethan Fosse, Princeton University

• Christopher Winship, Harvard University