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.

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几十年来，研究人员一直试图了解年龄、时期和队列 (APC) 对各种结果的单独影响。然而，这些努力的一个主要挑战是三个时间尺度之间的线性依赖性。以前的方法一直受到任意假设或对模型规范的微小变化极度敏感的困扰。在本文中，我们提出了一种替代方法，通过利用有关亚群体（或阶层）的附加信息（例如种族、性别和社会阶层）来实现部分识别。我们的第一个目标是引入跨层线性化 APC (CSL-APC) 模型，这是传统 APC 模型的重新参数化，专注于效果的跨组变化而不是整体效果。与传统模型类似，未识别线性跨层 APC 效应。第二个目标是展示如何使用 Fosse 和 Winship (2019) 的边界方法来解决 CSL-APC 模型的识别问题，从而允许人们部分识别跨组效应差异。这种方法通常涉及比以前使用的技术更弱的假设，并且在某些情况下，可能会导致信息丰富的界限。为了说明我们的方法，我们研究了美国男性和女性工资的时间影响的差异。

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