ages: A new community-contributed command to estimate the impact of the population's age structure

ages is a new community-contributed module that estimates the relationship between different population-age groups (cohorts) and a dependent variable of choice, based on the polynomial transformation suggested by Fair and Dominguez (1991) and applied later by Higgins (1998), Arnott and Chaves (2012), and Juselius and Takas (2021). Capturing the effect of the age structure in a regression involves different methodological issues, such as weak precision if the number of population cohorts is large compared with the number of time periods, large 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 ages command 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 impact of age cohort on the dependent variable. It allows testing for different age structure effects based on different groups captured by an interaction with a dummy variable. It also allows estimating a fully dynamic model, allowing the user to define the desired number of lags of the age structure groups, reporting the age structure by each lag and as sum of all them. ages also allows the user to choose the preferred time-series or panel-data method. The user can easily choose different options for the graph with the impact by age group, as well as several other options to save and use the results.