Building W Matrices Using Selected Geostatistical Tools: Empirical Examination and Application

Abstract

This paper investigates how to determine the values (elements) of spatial weights in a spatial matrix (W) endogenously from the data. To achieve this goal, geostatistical tools (standard deviation ellipsis, semivariograms, semivariogram clouds, and surface trend models) were used. Then, in the econometric part of the analysis, the effect of applying different variants of matrices was examined. The study was conducted on a sample of 279 Polish towns from 2005–2015. Variables were related to the quantity of produced waste and economic development. Both exploratory spatial data analysis and estimations of spatial panel and seemingly unrelated regression models were performed by including particular W matrices in the study (exogenous-random as well as distance and directional matrices constructed based on data). The results indicated that (1) geostatistical tools can be effectively used to build Ws; (2) outcomes of applying different matrices did not exclude but supplemented one another, although the differences were significant; (3) the most precise picture of spatial dependence was achieved by including distance matrices; and (4) the values of the assessed parameter at the regressors did not significantly change, although there was a change in the strength of the spatial dependency.