Nonparametric Quantile Regression for Homogeneity Pursuit in Panel Data Models

Abstract

Many panel data have the latent subgroup effect on individuals, and it is important to correctly identify these groups since the efficiency of resulting estimators can be improved significantly by pooling the information of individuals within each group. However, the currently assumed parametric and semiparametric relationship between the response and predictors may be misspecified, which leads to a wrong grouping result, and the nonparametric approach hence can be considered to avoid such mistakes. Moreover, the response may depend on predictors in different ways at various quantile levels, and the corresponding grouping structure may also vary. To tackle these problems, this article proposes a nonparametric quantile regression method for homogeneity pursuit in panel data models with individual effects, and a pairwise fused penalty is used to automatically select the number of groups. The asymptotic properties are established, and an ADMM algorithm is also developed. The finite sample performance is evaluated by simulation experiments, and the usefulness of the proposed methodology is further illustrated by an empirical example.

KEYWORDS:

• Homogeneity pursuit
• Nonparametric approach
• Oracle property
• Panel data model
• Quantile regression

Supplementary Materials

The supplementary materials contain all technical proofs and additional simulation results.

Acknowledgments

We are grateful to the coeditor, the associate editor and two anonymous referees for their valuable comments which led to substantial improvement of this article. Lian and Li are the co-corresponding authors.

Disclosure Statement

The authors report there are no competing interests to declare.

Additional information

Funding

Lian’s research is partially supported by the Hong Kong Research Grant Council (GRF grants 11300721 and 11311822). Li’s research is partially supported by the Hong Kong Research Grant Council (GRF grants 17306519, 17305319 and 17306121) and the National Social Science Fund of China (grant No. 72033002).