The shapley value of age-period-cohort effects

Abstract

The exact linear dependency among age, period and birth cohort makes it impossible to recover the true parameters of Age-Period-Cohort (APC) models. We then propose to extract reliable information from APC models via the Shapley decomposition, a model-agnostic procedure from game theory that allows to pin down the most likely contribution of each regressor in explaining the variance of the dependent variable. The rationale is that the predicted values of APC models are estimable and the allocation of the R2 to the APC regressors – interpreted here as the APC “effects” – satisfies desirable properties and produces robust estimates, in that complementing existing methods. We apply the method to the U.S. unemployment rate.

Keywords

• shapley value
• estimability
• age-period-cohort models