Identifying Latent Structures in Panel Data

77 Pages Posted: 3 Dec 2014

See all articles by Liangjun Su

Liangjun Su

Singapore Management University - School of Economics

Zhentao Shi

Department of Economics, the Chinese University of Hong Kong

Peter C. B. Phillips

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

Date Written: December 2, 2014

Abstract

This paper provides a novel mechanism for identifying and estimating latent group structures in panel data using penalized regression techniques. We focus on linear models where the slope parameters are heterogeneous across groups but homogenous within a group and the group membership is unknown. Two approaches are considered -- penalized least squares (PLS) for models without endogenous regressors, and penalized GMM (PGMM) for 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. C-Lasso achieves simultaneous classification and consistent estimation in a single step and the classification exhibits the desirable property of uniform consistency. For PLS 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. An empirical application investigating the determinants of cross-country savings rates finds two latent groups among 56 countries, providing empirical confirmation that higher savings rates go in hand with higher income growth.

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 2, 2014). Cowles Foundation Discussion Paper No. 1965, Available at SSRN: https://ssrn.com/abstract=2533012 or http://dx.doi.org/10.2139/ssrn.2533012

Liangjun Su

Singapore Management University - School of Economics ( 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 (Contact Author)

University of Auckland Business School ( email )

12 Grafton Rd
Private Bag 92019
Auckland, 1010
New Zealand
+64 9 373 7599 x7596 (Phone)

Yale University - Cowles Foundation ( email )

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

Singapore Management University - School of Economics

90 Stamford Road
178903
Singapore

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