Subspace Clustering for Panel Data with Interactive Effects

TL;DR

This paper introduces a novel subspace clustering method for panel data with unobservable factors, addressing correlated regressors and unknown group memberships, and demonstrates its theoretical consistency and practical advantages.

Contribution

It proposes the least squares subspace clustering estimate (LSSC) for simultaneous parameter estimation and subspace clustering in panel data models with interactive effects.

Findings

LSSC method is consistent and asymptotically valid.

Simulation studies show advantages over existing methods.

Application to income and democracy data illustrates practical utility.

Abstract

In this paper, a statistical model for panel data with unobservable grouped factor structures which are correlated with the regressors and the group membership can be unknown. The factor loadings are assumed to be in different subspaces and the subspace clustering for factor loadings are considered. A method called least squares subspace clustering estimate (LSSC) is proposed to estimate the model parameters by minimizing the least-square criterion and to perform the subspace clustering simultaneously. The consistency of the proposed subspace clustering is proved and the asymptotic properties of the estimation procedure are studied under certain conditions. A Monte Carlo simulation study is used to illustrate the advantages of the proposed method. Further considerations for the situations that the number of subspaces for factors, the dimension of factors and the dimension of subspaces are unknown are also discussed. For illustrative purposes, the proposed method is applied to study the linkage between income and democracy across countries while subspace patterns of unobserved factors and factor loadings are allowed.