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Functional-Coefficient Quantile Regression for Panel Data with Latent Group Structure.

Xiaorong Yang1, Jia Chen2, Degui Li3

  • 1School of Statistics and Mathematics,Zhejiang Gongshang University.

Journal of Business & Economic Statistics : a Publication of the American Statistical Association
|July 18, 2024
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Summary
This summary is machine-generated.

This study introduces a new method for estimating complex panel quantile regression models by identifying latent group structures. This approach simplifies estimation and accurately reveals underlying data homogeneity at various quantile levels.

Keywords:
Cluster analysisfunctional-coefficient modelsincidental parameterlatent groupslocal linear estimationpanel dataquantile regression

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Area of Science:

  • Econometrics
  • Statistical Modeling
  • Quantitative Analysis

Background:

  • Panel quantile regression models are essential for analyzing heterogeneous data with individual effects.
  • Estimating functional-coefficient models in this context presents challenges due to cross-sectional and temporal dependence in large datasets.
  • Existing methods often struggle to efficiently handle the complexity of nonparametric functional coefficients.

Purpose of the Study:

  • To develop a robust method for estimating functional-coefficient models in panel quantile regression with individual effects.
  • To impose a latent group structure to reduce the number of nonparametric functional coefficients.
  • To accurately estimate group-specific coefficients and determine the optimal number of groups.

Main Methods:

  • Utilizing preliminary local linear quantile estimates of subject-specific functional coefficients.
  • Employing a classic agglomerative clustering algorithm to estimate the unknown group structure.
  • Proposing an easy-to-implement ratio criterion for determining the group number.
  • Introducing a post-grouping local linear smoothing method for estimating group-specific coefficients.

Main Results:

  • Consistent estimation of the group number and structure.
  • Derivation of asymptotic normal distribution theory for the estimators with a competitive normalization rate.
  • Demonstration of the method's efficacy through a simulation study.
  • Identification of varying homogeneity structures across different quantile levels in real-world data.

Conclusions:

  • The proposed method effectively estimates functional-coefficient models in panel quantile regression by leveraging latent group structures.
  • The approach simplifies complex models and provides consistent estimates for group structures and coefficients.
  • The findings are validated by simulations and practical application, highlighting its utility in diverse datasets like housing prices.