Identifying latent group structures in spatial dynamic panels

Abstract

This paper considers the identification of latent group structures in spatial dynamic panels. We follow Lee and Yu (2010) and consider a rich spatial dynamic panel data (SDPD) model with two-way fixed effects. In addition, we also allow for latent panel structures where individuals can be classified into a few groups such that individuals within the same group share the common slope parameters and do not otherwise. Both the number of groups and the individuals’ group membership are unknown. To identify the latent group structures, we first adopt the GMM to obtain the preliminary unconstrained estimates of the slope coefficients. Then we apply the sequential binary segmentation algorithm (SBSA) of Wang and Su (2021) to these estimates and obtain the clusters. A BIC-type information criterion is proposed to choose the number of latent groups consistently. The asymptotic analysis shows that this method can identify the true group structure consistently, and the post-classification estimators enjoy the oracle property. Monte Carlo simulations demonstrate that our method has good finite sample performance. Finally, we apply our approach to the US housing market and identify two latent Metropolitan Statistical Areas groups.