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

TL;DR

This paper develops a novel method for estimating functional-coefficient models in panel quantile regression with latent group structures, allowing for consistent group detection and functional coefficient estimation in large, dependent panel data.

Contribution

It introduces a new clustering-based approach for identifying latent groups and estimating group-specific functional coefficients in panel quantile regression models.

Findings

Consistent estimation of group structure and number.

Effective post-grouping local linear smoothing for functional coefficients.

Application reveals heterogeneity at different quantiles in house price data.

Abstract

This paper considers estimating functional-coefficient models in panel quantile regression with individual effects, allowing the cross-sectional and temporal dependence for large panel observations. A latent group structure is imposed on the heterogenous quantile regression models so that the number of nonparametric functional coefficients to be estimated can be reduced considerably. With the preliminary local linear quantile estimates of the subject-specific functional coefficients, a classic agglomerative clustering algorithm is used to estimate the unknown group structure and an easy-to-implement ratio criterion is proposed to determine the group number. The estimated group number and structure are shown to be consistent. Furthermore, a post-grouping local linear smoothing method is introduced to estimate the group-specific functional coefficients, and the relevant asymptotic normal distribution theory is derived with a normalisation rate comparable to that in the literature. The developed methodologies and theory are verified through a simulation study and showcased with an application to house price data from UK local authority districts, which reveals different homogeneity structures at different quantile levels.