Dynamic nonparametric clustering of multivariate panel data

We introduce a new dynamic clustering method for multivariate panel data char- acterized by time-variation in cluster locations and shapes, cluster compositions, and, possibly, the number of clusters. To avoid overly frequent cluster switching (flickering), we extend standard cross-sectional clustering techniques with a penalty that shrinks observations towards the current center of their previous cluster as- signment. This links consecutive cross-sections in the panel together, substantially reduces flickering, and enhances the economic interpretability of the outcome. We choose the shrinkage parameter in a data-driven way and study its misclassification properties theoretically as well as in several challenging simulation settings. The method is illustrated using a multivariate panel of four accounting ratios for 28 large European insurance firms between 2010 and 2020.