Interquantile Shrinkage in Spatial Quantile Autoregressive Regression models

TL;DR

This paper introduces a novel penalization approach for spatial quantile autoregressive models, enabling efficient estimation of quantile-specific effects and interquantile commonality while addressing endogeneity issues.

Contribution

It develops fused adaptive LASSO and sup-norm penalty methods with oracle properties for spatial quantile regression, improving estimation efficiency and handling interquantile relationships.

Findings

Proposed methods outperform traditional quantile regression in simulations.

Fused penalties effectively identify interquantile commonality.

Methods address endogeneity with instrumental variables.

Abstract

Spatial dependent data frequently occur in many fields such as spatial econometrics and epidemiology. To deal with the dependence of variables and estimate quantile-specific effects by covariates, spatial quantile autoregressive models (SQAR models) are introduced. Conventional quantile regression only focuses on the fitting models but ignores the examination of multiple conditional quantile functions, which provides a comprehensive view of the relationship between the response and covariates. Thus, it is necessary to study the different regression slopes at different quantiles, especially in situations where the quantile coefficients share some common feature. However, traditional Wald multiple tests not only increase the burden of computation but also bring greater FDR. In this paper, we transform the estimation and examination problem into a penalization problem, which estimates the parameters at different quantiles and identifies the interquantile commonality at the same time. To avoid the endogeneity caused by the spatial lag variables in SQAR models, we also introduce instrumental variables before estimation and propose two-stage estimation methods based on fused adaptive LASSO and fused adaptive sup-norm penalty approaches. The oracle properties of the proposed estimation methods are established. Through numerical investigations, it is demonstrated that the proposed methods lead to higher estimation efficiency than the traditional quantile regression.