Instrumental Variable Quantile Regression of Spatial Dynamic Durbin Panel Data Model with Fixed Effects

Danqing Chen,Jianbao Chen,Shuangshuang Li

doi:10.3390/math9243261

Danqing Chen, Jianbao Chen + Show 1 more

Open Access

https://doi.org/10.3390/math9243261

Copy DOI

Abstract

This paper studies a quantile regression spatial dynamic Durbin panel data (SDDPD) model with fixed effects. Conventional fixed effects estimators of quantile regression specification are usually biased in the presentation of lagged response variables in spatial and time as regressors. To reduce this bias, we propose the instrumental variable quantile regression (IVQR) estimator with lagged covariates in spatial and time as instruments. Under some regular conditions, the consistency and asymptotic normalityof the estimators are derived. Monte Carlo simulations show that our estimators not only perform well in finite sample cases at different quantiles but also have robustness for different spatial weights matrices and for different disturbance term distributions. The proposed method is used to analyze the influencing factors of international tourism foreign exchange earnings of 31 provinces in China from 2011 to 2017.

Highlights

A panel data set is one that follows a given sample of individuals over time and provides multiple observations on each individual in the sample (Hsiao, 2014 [1])
This paper focuses on studying estimation and inference in a quantile regression spatial dynamic Durbin panel data (SDDPD) model with fixed effects
Conventional fixed effects estimators of quantile regression specification are usually biased in their presentation of lagged response variable in spatial and time as regressors

Summary

Introduction

A panel data set is one that follows a given sample of individuals over time and provides multiple observations on each individual in the sample (Hsiao, 2014 [1]). Quantile regression for panel data models can fully describe the conditional distribution of a response variable and control individual specific heterogeneity via fixed effects. Mathematics 2021, 9, 3261 for a dynamic panel data model, the asymptotic properties of the proposed estimators were studied, and the influencing factors of commercial residential prices in large and moderate cities in China were analyzed. Dai et al [38] studied the IVQR of a spatial error panel data model with individual fixed effects. The asymptotic properties of estimators in these two papers are based on the assumption that the observations of response variable are independent and identically distributed. Our paper provides a complete set of quantile regression estimation methodologies for the SDDPD model with fixed effects, accommodating different correlations among response variable and covariates (spatial, temporally, and spatiotemporal).

Model and Estimation

Asymptotic Properties

Monte Carlo Simulations

Application

Findings

Conclusions