# Characterization and estimation of heterogeneous spatial autocorrelation in spatial autoregressive models

## TL;DR

This paper introduces a new model to better capture spatial relationships by allowing spatial correlation to vary across regions.

## Contribution

The novel SSIVCAR model allows spatial autocorrelation to vary dynamically with spatial unit characteristics.

## Key findings

- The proposed model outperforms traditional models in capturing spatial heterogeneity.
- The model shows improved estimation accuracy under finite sample conditions.
- Digital economy development has heterogeneous effects on environmental quality across regions.

## Abstract

Spatial Autoregressive (SAR) models are widely used to analyze interactions among regions. However, the traditional model assumes a constant spatial autocorrelation coefficient, which fails to effectively capture spatial heterogeneity. To address this issue, we propose proposes a novel Spatial Single-Index Varying Coefficient Autoregressive (SSIVCAR) model. By introducing a single-index varying coefficient function, this model allows the spatial correlation strength to dynamically change with the characteristics of spatial units, thereby more accurately capturing spatial dependence relationships. To estimate the model parameters, we combine spline methods with two-stage least squares, and we assess the model’s performance under finite sample conditions under Monte Carlo simulations. The simulation results show that the proposed model performs significantly better in capturing spatial heterogeneity and improving estimation accuracy. Finally, the model is applied to analyze the impact of digital economy development on environmental quality, and find that it has significant heterogeneous effects across different regions. This study provides a new framework for analyzing complex spatial dependence structures and offers valuable insights for regional governance policies.