AGES: Stata module to estimate the effects of the age structure

AGES estimates the relationship between different population cohorts shares and a dependent variable of choice, based on the polynomial transformation suggested by Fair and Dominguez (1991) and and applied later by Higgins (1998), Arnott and Chaves (2012) and Juselius and Takas (2021). Estimating the effect of changes in the population's age structure in a regression faces different methodological issues, such as weak precision if the number of population cohorts is large compared with the number of time periods, high correlation between consecutive cohorts’ shares and perfect collinearity with respect to the constant. The solution consists of restricting the age groups coefficients to lie on a Pth degree polynomial and restricting its sum to be equal to zero to remove the perfect multicolinearity. The command AGES performs all the necessary transformations and mathematical calculations to estimate and report the final effect by age-cohort, together with its standard error and confidence interval, as an output matrix and through an automated graph that displays the effect of all the age-cohorts on the dependent variable. It allows testing for different age structure effects based on different groups captured by an interaction with a dummy variable.