Age-Period-Cohort Decomposition Using Principal Components or Partial Least Squares: A Simulation Study

Age-period-cohort decomposition requires an identification assumption because there is a linear relationship among age, survey period, and birth cohort (age + cohort = period). This paper proposes new decomposition methods based on factor models such as principal components model and partial least squares model. Although factor models have been applied to overcome the problem of many observed variables with possible co-linearity, they are applied to overcome the perfect co-linearity among age, period, and cohort dummy variables. Since any unobserved factor in the factor model is represented as a linear combination of the observed variables, the parameter estimates for age, period, and cohort effects are automatically obtained after the application of these factor models. Simulation results suggest that in most cases, the performance of the proposed method is at least comparable to conventional methods but it has a model-selection problem.