Comment of Liying Luo’s Article, “Assessing Validity and Application Scope of the Intrinsic Estimator Approach to the Age-Period-Cohort Problem”

Liying Luo’s article (this issue) addresses three important properties of the intrinsic estimator (IE). First, the constraint used to produce the IE (b_ie ⋅ b₀ = 0) constrains the linear trends of the age coefficients, period coefficients, and cohort coefficients. Second, the IE is a biased estimate of the age, period, and cohort coefficients that generated the outcome data, unless the constraint on the linear trends imposed by the IE is the same as the linear trends for the parameter values that generated the outcome data. Third, the IE is not a consistent estimator of the parameters that generated the outcome data unless its constraint corresponds to those generating parameters. She is successful in showing the form of the linear constraint (for some models) and that the IE is a biased and inconsistent estimate unless its constraint is consistent with the parameters that generated the outcome data....