We propose a dynamic factor model which we use to analyze the relationship between education participation and national unemployment, as well as to forecast the number of students across the many different types of education. By clustering the factor loadings associated with the dynamic macroeconomic factor, we can measure to what extent the different types of education exhibit similarities in their relationship with macroeconomic cycles. To utilize the feature that unemployment data is available for a longer time period than our detailed education panel data, we propose a two-step procedure. First, we consider a score-driven model which filters the conditional expectation of the unemployment rate. Second, we consider a multivariate model in which we regress the number of students on the dynamic macroeconomic factor, and we further apply the $k$-means method to estimate the clustered loading matrix. In a Monte Carlo study, we analyze the performance of the proposed procedure in its ability to accurately capture clusters and preserve or enhance forecasting accuracy. For a high-dimensional, nation-wide data set from the Netherlands, we empirically investigate the impact of the rate of unemployment on choices in education over time. Our analysis confirms that the number of students in part-time education covaries more strongly with unemployment than those in full-time education.

我们提出了一个动态因素模型，我们用它来分析教育参与与全国失业率之间的关系，以及预测许多不同类型教育的学生人数。通过对与动态宏观经济因素相关的因素负荷进行聚类，我们可以衡量不同类型的教育在多大程度上与宏观经济周期的关系表现出相似性。为了利用失业数据的可用时间比我们详细的教育面板数据更长的特征，我们提出了一个两步程序。首先，我们考虑一个分数驱动模型，它过滤了失业率的条件期望。其次，我们考虑一个多元模型，在该模型中我们根据动态宏观经济因素对学生人数进行回归，并进一步应用$克$-means 估计聚类加载矩阵的方法。在蒙特卡罗研究中，我们分析了所提出的程序在准确捕获集群和保持或提高预测准确性的能力方面的性能。对于来自荷兰的高维、全国性数据集，我们实证调查了失业率随时间推移对教育选择的影响。我们的分析证实，与全日制教育相比，非全日制教育的学生人数与失业率的相关性更强。