A Multi-Kink quantile regression model with common structure for panel data analysis

Abstract

Stimulated by the analysis of a data set on financial portfolio returns, we propose a multi-kink quantile regression (MKQR) model with latent homogeneous structure for panel data analysis. The proposed model accounts for both homogeneity and heterogeneity among individuals and parameters in panel data analysis. From statistical modeling point of view, it well balances the risk of misspecification and the model parsimony. From practical point of view, it is able to reveal not only the impacts of covariates in the global sense, but also individual attributes. An estimation procedure is presented to estimate both the unknown parameters and the latent homogeneous structure in the proposed model. Computational issues with the implementation of the estimation procedure are also discussed. Asymptotic theory of the estimators is established. It shows the necessity of taking into account both homogeneity and heterogeneity in panel data analysis. Monte Carlo simulation studies are conducted to demonstrate the finite sample performance of the proposed estimation and the risk of ignoring the homogeneity or heterogeneity among individuals. Finally, we apply the proposed model and the estimation procedure to the data set which stimulates this work and reveal some interesting findings.