Publication Type

Journal Article

Version

Preprint

Publication Date

11-2016

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 consideredpenalized 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. C-Lasso 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 in both classification and estimation. Empirical applications to both linear and nonlinear models are presented.

Keywords

Classification, cluster analysis, dynamic panel, group Lasso, high dimensionality, nonlinear panel, oracle property, panel structure model, parameter heterogeneity, penalized least squares, penalized GMM, penalized profile likelihood

Discipline

Econometrics

Research Areas

Econometrics

Publication

Econometrica

Volume

84

Issue

6

First Page

2215

Last Page

2264

ISSN

0012-9682

Identifier

10.3982/ECTA12560

Publisher

Econometric Society: Econometrica

Copyright Owner and License

Authors

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

Additional URL

http://doi.org/10.3982/ECTA12560

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Econometrics Commons

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