LAUSR

Estimable functions play an important role in learning about certain aspects of the impact of ages, periods, and cohorts in age-period-cohort multiple classification (APCMC) models. The advantage of these estimates is that they are unbiased estimates of, for example, the deviations of age, period, and cohort effects from their linear trends, or changes in the linear trends of cohort effects within cohorts, or the residuals of fixed effect APCMC models. If the fixed effect APCMC model contains the relevant variables (is well specified), these estimable functions are unbiased estimates of functions of the parameters that generated the dependent variable data, even though the parameters that generated that data are not identified. I provide a simplified approach to establishing which functions are estimable in fixed effect APCMC models that provides an intuitive understanding of estimable functions by showing clearly and simply why they are estimable. This approach involves the partitioning of the age, period, and cohort effects into linear components and deviations from the linear components; the use of the "line of solutions"; and of the "extended null vector."