Dynamic Clustering Methods in Panel Data
Authors:   , Custodio João Igor 
Published: October 2024

This thesis proposes new dynamic clustering methods for panel data in four chapters. The first chapter deals with a score-driven model with clustered units. The second proposes a nonparametric clustering method that can deal with excessive switching. The third chapter applies a clustered regression model in the context of state fragility, and extends it to allow for cluster switching. The fourth chapter proposes a test for clustering that maintains power even amid cluster switching.

More specifically, Chapter 2 proposes a dynamic clustering model for uncovering latent time-varying group structures in multivariate panel data. The model is dynamic in three ways. First, the cluster location and scale matrices are time-varying to track gradual changes in cluster characteristics over time. Second, all units can transition between clusters based on a Hidden Markov model (HMM). Finally, the HMM's transition matrix can depend on lagged time-varying cluster distances as well as economic covariates. Monte Carlo experiments suggest that the units can be classified reliably in a variety of challenging settings. Incorporating dynamics in the cluster composition proves empirically important in a study of 299 European banks between 2008Q1 and 2018Q2. We find that approximately 3% of banks transition per quarter on average. Transition probabilities are in part explained by differences in bank profitability, suggesting that factors contributing to low profitability for some banks can lead to long-lasting changes in financial industry structure.

Then, in Chapter 3, we introduce a new dynamic clustering method for multivariate panel data characterized 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 toward the current center of their previous cluster assignment. 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.

In Chapter 4, we explore the potential correlations between financial development and state fragility using a sample of 137 countries observed over the period from 1998 to 2019. We group countries into clusters that capture the different joint states of financial development and fragility. We introduce a new switching methodology to further allow for a qualification of the evolution of countries in terms of fragility scores with and without controlling for other variables. Irrespective of the precise methodology and state fragility measure as used in this paper, we obtain a negative correlation between financial development and state fragility after controlling for several forms of observed and unobserved heterogeneity.

Finally, in Chapter 5, I refine the test for clustering of Patton and Weller (2022) to allow for cluster switching. In a multivariate panel setting, clustering on time-averages produces consistent estimators of means and group assignments. Once switching is introduced, we lose the consistency. In fact, under switching the time-averaged k-means clustering converges to equal, indistinguishable means. This causes the test for a single cluster to lose power under the alternative of multiple clusters. Power can be regained by clustering the N times T observations independently and carefully subsampling the time dimension. When applied to the empirical setting of Bonhomme and Manresa (2015) of an autoregression of democracy in a panel of countries, we are able to detect clusters in the data under noisier conditions than the original test.