The shapley value of age-period-cohort effects - Maurizio Bovi (Journal of Applied Economics, 2021)
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 depen- dent 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: 330; Shapley value; estimability; age-period-cohort model