Subspace clustering for panel data with interactive effects

Abstract

We study a statistical model for panel data with unobservable grouped factor structures which are correlated with the regressors and whose group membership can be unknown. We assume the factor loadings belong to different subspaces and consider the subspace clustering for factor loadings. We propose a method called least‐squares subspace clustering (LSSC) to estimate the model parameters by minimizing the least‐squares distance while simultaneously performing the subspace clustering. We establish the consistency of our proposed subspace clustering method and study the asymptotic properties of our proposed estimators under certain conditions. Monte Carlo simulation studies illustrate the advantages of our proposed methodologies. To choose the subspace dimensions consistently, we use a model selection criterion. We also outline further considerations for situations when the number of subspaces and the dimensions of factors are unknown. For illustrative purposes, our proposed methods are applied to study the linkage between income and democracy across countries.