A Partially Heterogeneous Framework for Analyzing Panel Data

Abstract

This article proposes a partially heterogeneous framework for the analysis of panel data with fixed T. In particular, the population of cross‐sectional units is grouped into clusters, such that slope parameter homogeneity is maintained only within clusters. Our method assumes no a priori information about the number of clusters and cluster membership and relies on the data instead. The unknown number of clusters and the corresponding partition are determined based on the concept of ‘partitional clustering’, using an information‐based criterion. It is shown that this is strongly consistent, that is, it selects the true number of clusters with probability one as N→∞. Simulation experiments show that the proposed criterion performs well even with moderate N and the resulting parameter estimates are close to the true values. We apply the method in a panel data set of commercial banks in the US and we find five clusters, with significant differences in the slope parameters across clusters.

Identifying Latent Structures in Panel Data

“…The second approach is based on the K-means algorithm in statistical cluster analysis. Lin and Ng (2012) and Sarafidis and Weber (2015) considered linear panel data models where the slope coefficients have latent group structure. They modified the K-means algorithm to estimate the models but did not provide any inference theory.…”

Determining the number of groups in latent panel structures with an application to income and democracy

“…Alternatively, one can apply the K-means algorithm as advocated by Lin and Ng (2012), BM, Sarafidis and Weber (2015), and Ando and Bai (2016). Let g = {g 1 g N } denote the group membership such that g i ∈ {1…”

“…Recently, latent group structures have received much attention in the panel data literature; see, for example, Sun (2005), Lin and Ng (2012), Deb and Trivedi (2013), Bonhomme and Manresa (2015;BM hereafter), Sarafidis and Weber (2015), Ando and Bai (2016), Bester and Hansen (2016), Su, Shi, and Phillips (2016;SSP hereafter), and Su and Ju (forthcoming). In comparison with some other popular approaches to model unobserved heterogeneity in panel data models such as random coefficient models (see, e.g., Hsiao (2014, Chapter 6)), one important advantage of the latent group structure is that it allows flexible forms of unobservable heterogeneity while remaining parsimonious.…”

“…Sun (2005) uses a parametric multinomial logit regression to model membership. Lin and Ng (2012), BM, Sarafidis and Weber (2015), and Ando and Bai (2016) extend K-means classification algorithms to the panel regression framework. Deb and Trivedi (2013) propose expectation-maximization (EM) algorithms to estimate finite mixture panel data models with fixed effects.…”

Classification of nonparametric regression functions in heterogeneous panels

“…. , G K 0 in this parametric framework has been considered, for example, in Sarafidis and Weber (2014) and Su et al (2014) who work with penalization techniques, and in Lin and Ng (2012) who employ thresholding and k-means clustering methods.…”