TY - JOUR

T1 - Estimation of Asymmetric Spatial Autoregressive Dependence on Irregular Lattices

AU - Harke, Franz H.

AU - Merk, Miryam S.

AU - Otto, Philipp

PY - 2022/7

Y1 - 2022/7

N2 - In spatial econometrics, we usually assume that the spatial dependence structure is known and that all information about it is contained in a spatial weights matrix (Formula presented.). However, in practice, the structure of (Formula presented.) is unknown a priori and difficult to obtain, especially for asymmetric dependence. In this paper, we propose a data-driven method to obtain (Formula presented.), whether it is symmetric or asymmetric. This is achieved by calculating the area overlap of the adjacent regions/districts with a given shape (a pizza-like shape, in our case). With (Formula presented.) determined in this way, we estimate the potentially asymmetric spatial autoregressive dependence on irregular lattices. We verify our method using Monte Carlo simulations for finite samples and compare it with classical approaches such as Queen’s contiguity matrices and inverse-distance weighting matrices. Finally, our method is applied to model the evolution of sales prices for building land in Brandenburg, Germany. We show that the price evolution and its spatial dependence are mainly driven by the orientation towards Berlin.

AB - In spatial econometrics, we usually assume that the spatial dependence structure is known and that all information about it is contained in a spatial weights matrix (Formula presented.). However, in practice, the structure of (Formula presented.) is unknown a priori and difficult to obtain, especially for asymmetric dependence. In this paper, we propose a data-driven method to obtain (Formula presented.), whether it is symmetric or asymmetric. This is achieved by calculating the area overlap of the adjacent regions/districts with a given shape (a pizza-like shape, in our case). With (Formula presented.) determined in this way, we estimate the potentially asymmetric spatial autoregressive dependence on irregular lattices. We verify our method using Monte Carlo simulations for finite samples and compare it with classical approaches such as Queen’s contiguity matrices and inverse-distance weighting matrices. Finally, our method is applied to model the evolution of sales prices for building land in Brandenburg, Germany. We show that the price evolution and its spatial dependence are mainly driven by the orientation towards Berlin.

KW - Akaike information criterion (AIC)

KW - maximum likelihood estimation

KW - model selection

KW - spatial autoregressive model (SAR)

KW - weights matrix

UR - http://www.scopus.com/inward/record.url?scp=85137361680&partnerID=8YFLogxK

U2 - 10.3390/sym14071474

DO - 10.3390/sym14071474

M3 - Article

AN - SCOPUS:85137361680

VL - 14

JO - Symmetry

JF - Symmetry

SN - 2073-8994

IS - 7

M1 - 1474

ER -