Dynamic Factor Models with Clustered Loadings: Forecasting Education Flows using Unemployment Data

Abstract

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. Since unemployment data is available for a longer time period than our detailed education data panel, we propose a twostep estimation procedure. First, we consider a score-driven model which filters the conditional expectation of the unemployment rate. Second, we consider a multivariate regression model for the number of students featuring the dynamic macroeconomic factor as a regressor, 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.