  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.
