Wild Bootstrap-Based Bias Correction for Spatial Quantile Panel Data Models with Varying Coefficients

This paper studies quantile regression for spatial panel data models with varying coefficients, taking the time and location effects of the impacts of the covariates into account, i.e., the implications of covariates may change over time and location. Smoothing methods are employed for approximating varying coefficients, including B-spline and local polynomial approximation. A fixed-effects quantile regression (FEQR) estimator is typically biased in the presence of the spatial lag variable. The wild bootstrap method is employed to attenuate the estimation bias. Simulations are conducted to study the performance of the proposed method and show that the proposed methods are stable and efficient. Further, the estimators based on the B-spline method perform much better than those of the local polynomial approximation method, especially for location-varying coefficients. Real data about economic development in China are also analyzed to illustrate application of the proposed procedure.

Automated summary

This paper investigates the quantile regression for spatial panel data models with varying coefficients, which considers the changing impacts of covariates over time and location. Smoothing methods like B-spline and local polynomial approximation are used for approximating the varying coefficients. The fixed-effects quantile regression (FEQR) estimator is biased when there is a spatial lag variable, and the wild bootstrap method is employed to mitigate the bias. Simulations show that the proposed methods are stable and efficient, with the B-spline method outperforming the local polynomial approximation method, especially for location-varying coefficients. Real data on China's economic development are analyzed to demonstrate the application of the proposed procedure.