A spatial panel autoregressive model specification with inverse quantile separation distances of locations

Abstract

This paper proposes an alternative spatial weight that efficiently captures a spatial dependence. In the past, researchers often used sparse or inverse distance spatial weights. A dense spatial weight is defined by partitioning the separation distances between locations based on quantile values over large spatial scales, where each partition forms conjoint neighborhood sectors and the weights of the respective inverse quantile of separation distances are assigned to each sector. Instead of joint modeling of the spatiotemporal process, a simultaneous spatial panel model is employed after the panel component is imposed on the proposed spatial weight using Kronecker product to perform maximum likelihood estimation and Bayesian inference via MCMC Gibbs method. The specification also involves space, time, and space–time simultaneous components. The performance of the models for the proposed spatial weight is compared with the existing spatial weights using parameter bias. A smaller value of the bias close to zero indicates a stronger value of the spatial error parameter for the proposed spatial weight over the existing spatial weights. It also induces spatial auto-correlations both in the spatial panel data of neighboring locations as well as in the errors. Thus, the proposed method affirms the best efficiency for the dynamic combined spatial panel autoregressive model with random effect specification over the lag and error models, and fixed effect specification.