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.Specifications and estimation methods of models with an endogenous spatial weight matrix are widely presented in [15,17]. However, these issues are not within the scope of this research paper.In this paper, an attempt was made to verify the research hypothesis that the selected methods and tools of geostatistics (the standard deviation ellipsis, semivariograms, and surface trend models) can be used to specify and develop values in a spatial weight matrix endogenously. This study also evaluates the effect of using different variants of spatial weight matrices on the results of exploratory spatial data analysis (ESDA) as well as econometric modelling, and identifies the differences that significantly occurred (over the space and in the time span). The analysis was conducted on a sample of 279 Polish cities from 2005 to 2015. Variables were related to the quantity of collected municipal mixed waste (it covers waste from households, including bulky waste, and similar waste from commerce and trade, office buildings, institutions, small businesses, yard and gardens, street sweepings, contents of litter containers, and market cleansing. Waste from municipal sewage networks and treatment and municipal construction and demolition is excluded [18]) and the economic development of cities (the value of the revenue of the city budget is in PLN per capita, Revenues). The ESDA, estimations of the spatial panel, and seemingly unrelated regression (SUR) models (with spatial error) were performed by including particular row-standardised spatial weight matrices in the study (exogenous as a random one and distance and directional matrices constructed endogenously based on the data). The research was conducted in ArcMap (by Environmental Systems Research Ins...

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