Cross-Group Differences in Age, Period, and Cohort Effects: A Bounding Approach to the Gender Wage Gap

For decades, researchers have sought to understand the separate contributions of age, period, and cohort (APC) on a wide range of outcomes. However, a major challenge in these efforts is the linear dependence among the three time scales. Previous methods have been plagued by either arbitrary assumptions or extreme sensitivity to small variations in model specification. In this article, we present an alternative method that achieves partial identification by leveraging additional information about subpopulations (or strata) such as race, gender, and social class. Our first goal is to introduce the cross-strata linearized APC (CSL-APC) model, a re-parameterization of the traditional APC model that focuses on cross-group variations in effects instead of overall effects. Similar to the traditional model, the linear cross-strata APC effects are not identified. The second goal is to show how Fosse and Winship's (2019) bounding approach can be used to address the identification problem of the CSL-APC model, allowing one to partially identify cross-group differences in effects. This approach often involves weaker assumptions than previously used techniques and, in some cases, can lead to highly informative bounds. To illustrate our method, we examine differences in temporal effects on wages between men and women in the United States.