Model Misspecification when Using Selection Criteria to Eliminate a Factor in Age-Period-Cohort Models

• In Event: 204 - Regular Session. Quantitative Methodology

Abstract

In Age-Period-Cohort (APC) models, it is not possible to estimate all of the age, period, and cohort coefficients. The problem is a linear dependency in the design matrix and this linear dependency involves the linear trends of the coefficients for ages, the linear trends for the coefficients for periods, and the linear trends for the coefficients for cohorts. One strategy to avoid this problem is to test to see if including only two of the factors in a model (for example ages and cohorts) produces a fit that is not statistically significantly different from a model that includes all three factors. If the third factor (in this example periods) does not account for a statistically significant amount of variance this strategy suggests that one should run the model with only the two factors. This is in line with model selection techniques. The two factor model is identified and produces identified estimates of the individual effects of ages and cohorts. There is, however, a fundamental flaw with this quite popular approach when used with APC models. That flaw results from the complete confounding of the linear effects of the three factors.

Author

• Robert M. O'Brien, University of Oregon