Misunderstandings, Mischaracterizations, and the Problematic Choice of a Specific Instance in Which the IE Should Never Be Applied

It is our pleasure to respond to the Editor's request for a commentary on Luo's article (this issue), which critically evaluates the utility of the intrinsic estimator (IE) that we first introduced to demography and sociology in Yang et al. (2004).We first respond to the Editor's request for "an assessment of the author's argument, evidence, and conclusions."It is truly unfortunate and fundamentally incorrect to interpret our stance on the IE method as seeing it a "holy grail" or "magic bullet" for the identification problem of the age-period-cohort (APC) accounting model/multiple classification model.Nowhere in our previous publications did we make such a claim.We were crystal clear about the circumstances in which a full-blown APC model should be used.And such circumstances equally apply to any estimator of full three-factor APC models, not just the IE.Luo completely lost sight of this starting point.Works as early as Yang (2008) and as recent as Yang and Land (2013: chapter 5) have laid out a three-step procedure that should be thoroughly applied to APC analysis using the accounting model.It is so important that we believe it is worth repeating here.Step 1 is to conduct descriptive data analyses using graphics, with the objective being to provide qualitative understanding of patterns of temporal variations.Step 2 is model fitting and calculation of model fit statistics, such as the Bayesian information criterion (BIC).The objective is to ascertain whether the data are sufficiently well described by any single-factor or two-factor model of age (A), time period (P), and cohort (C) effects for which there is no identification problem.Only when these analyses suggest that all three dimensions are operative should one proceed with Step 3: a three-factor APC model to which a constrained estimator can be applied to identify the A, P, and C effects.