Constructing And Analyzing Spatial Weight Matrix Of Spatial Econometric Model

The issue of selecting the spatial weight matrix constitutes an essentialresearch area in the field of spatial econometrics. It really counts that areasonable spatial weight matrix should be specified according to the itscorresponding local conditions, since the choice of weight matrix willsignificantly impact the parameter estimate, test results, as well as theoverall well-being of the spatial model fitting.This paper will review the process of constructing spatial weightmatrix, together with their state-of-the-art theoretical development andapplications in the aspects of econometrics. Then those classicalapproaches will be summarized and categorized, while a multidirectionaloptimum ecotope-based algorithm generated from local statistics will beintroduced. Additionally, an improved algorithm based on all theseapproaches will be put forward to enhance the computational efficiencyand fitting performance. Next a spatial econometric model with spatial lagwill be introduced and solved by means of maximum likelihood estimationand generalized moment method. Finally a comparison will be made toexplain the influence from the combinations of different spatial weightmatrix in terms of parameter solving and overall fitting.According to the outcomes from different estimating methods,combinations of spatial weight matrix and the specification of spatialeconometric models, the following conclusions can be reached:(1) From the aspect of spatial lag coefficient, the choice of differentspatial weight matrix impacts significantly. Both the results frommaximum likelihood estimation approach and generalized moment methoddemonstrates that adopting the spatial weight matrix from optimumecotope-based algorithm yields meaningful results. (2) Concerning AIC information criteria and BIC information criteria,the selection of different spatial weight matrix impacts the fittingperformance. According to the outcomes, the matrix of optimumecotope-based double power distance outperforms other weight matrix.Meanwhile fitting the data via high order spatial autoregressive model withautoregressive error achieves a relatively better fitting result among allthese model specifications.(3) When it comes to the implementation of parameter-solving andresiduals of model-fitting, it turns out that MLE is not a sound choice andGMM is an ideal alternative since it can address the problems encounteredin MLE with sound performances in these perspectives.(4) Concerning the issue of selecting spatial weight matrix for highorder spatial model, this paper adopts the component-wise boostingalgorithm to enhance its iterative efficiency, additionally defining iterativenumber via AIC criteria helps to accelerate the computation process.