Estimable Functions of Age, Period, and Cohort Effects

Abstract

The main and interactive effects of age, period, and cohort are not estimable, although certain combinations of those effects are. A method used to obtain estimates of the effects of these variables involves the assumption of additivity and the imposition of one or more constraints on the relative effects of particular age levels, periods, or cohorts. This method can rarely if ever be justified for three reasons: first, the possibility of interactive effects cannot be ruled out a priori; second, although a constraint on the relationship of two groups may appear appropriate on a priori grounds, even small errors in the specification can have large effects on the estimates; and third, measurement error can lead to highly inaccurate estimates even if the constraint is precisely correct. A solution to the dilemma lies in the specification and measurement of the theoretical variables for which age, period, and cohort are indirect indicators.