Constraints in Random Effects Age-Period-Cohort Models.

Area of Science:

• Statistics
• Demography
• Social Sciences

Background:

• Random effects (RE) models are common for contextual effects (e.g., neighborhood, school).
• Age-period-cohort (APC) models are typically unidentified due to linear dependency among predictors.
• The application of RE models to APC models aims to address this identification problem.

Purpose of the Study:

• To clarify how random effects (RE) specifications identify otherwise unidentified age-period-cohort (APC) models.
• To investigate the nature of constraints imposed by RE-APC models.
• To compare RE-APC models with traditional fixed-effects and other constrained APC estimators.

Main Methods:

• Analysis of rank deficiency in RE-APC models compared to fixed-effects APC models.
• Development of mathematical proofs and intuitive explanations for RE-APC model identification.
• Empirical examples illustrating the behavior of RE-APC models.

Main Results:

• RE-APC models exhibit greater rank deficiency than traditional fixed-effects APC models.
• For APC models with one RE, the RE specification imposes constraints equivalent to setting the linear component and random intercept to zero.
• For APC models with two REs, estimated linear components are determined by the true non-linear components of the effects.

Conclusions:

• RE-APC models impose arbitrary and obscure constraints, failing to qualitatively differ from other constrained APC estimators.
• The identification in RE-APC models is achieved through implicit, non-transparent constraints.
• Researchers should be aware of these limitations when using RE-APC models for analyzing age, period, and cohort effects.