Identifying Latent Structures in Panel Data

75 Pages Posted: 13 Jun 2014 Last revised: 30 Jun 2016

See all articles by Liangjun Su

Liangjun Su

Singapore Management University

Zhentao Shi

Department of Economics, the Chinese University of Hong Kong

Peter C. B. Phillips

Yale University - Cowles Foundation; University of Auckland; University of Southampton; Singapore Management University - School of Economics

Date Written: December 29, 2015

Abstract

This paper provides a novel mechanism for identifying and estimating latent group structures in panel data using penalized techniques. We consider both linear and nonlinear models where the regression coefficients are heterogeneous across groups but homogeneous within a group and the group membership is unknown. Two approaches are considered — penalized profile likelihood (PPL) estimation for the general nonlinear models without endogenous regressors, and penalized GMM (PGMM) estimation for linear models with endogeneity. In both cases we develop a new variant of Lasso called classifier-Lasso (C-Lasso) that serves to shrink individual coefficients to the unknown group-specific coefficients. CLasso achieves simultaneous classification and consistent estimation in a single step and the classification exhibits the desirable property of uniform consistency. For PPL estimation C-Lasso also achieves the oracle property so that group-specific parameter estimators are asymptotically equivalent to infeasible estimators that use individual group identity information. For PGMM estimation the oracle property of C-Lasso is preserved in some special cases. Simulations demonstrate good finite-sample performance of the approach both in classification and estimation. Empirical applications to both linear and nonlinear models are presented.

Keywords: Classification; Cluster analysis; Convergence club; Dynamic panel; Group Lasso; High dimensionality; Oracle property; Panel structure model; Parameter heterogeneity; Penalized least squares; Penalized GMM

JEL Classification: C33, C36, C38, C51

Suggested Citation

Su, Liangjun and Shi, Zhentao and Phillips, Peter C. B., Identifying Latent Structures in Panel Data (December 29, 2015). Available at SSRN: https://ssrn.com/abstract=2448189 or http://dx.doi.org/10.2139/ssrn.2448189

Liangjun Su (Contact Author)

Singapore Management University ( email )

90 Stamford Road
178903
Singapore

Zhentao Shi

Department of Economics, the Chinese University of Hong Kong ( email )

Shatin, N.T.
Hong Kong

Peter C. B. Phillips

Yale University - Cowles Foundation ( email )

Box 208281
New Haven, CT 06520-8281
United States
203-432-3695 (Phone)
203-432-5429 (Fax)

University of Auckland ( email )

Private Bag 92019
Com. A room: 102
Auckland
New Zealand
+64 9 373 7599 x7596 (Phone)

University of Southampton

Southampton, SO17 1BJ
United Kingdom

Singapore Management University - School of Economics

90 Stamford Road
178903
Singapore

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