The GMM Profile Estimation of the Spatial Varying Coefficient Autoregressive Model with Error Autocorrelation

This dataset is derived from the GMM cross-sectional estimation study of spatial variable coefficient autoregressive models with error autocorrelation, mainly used to estimate the non parametric part of the variable coefficient function and spatial autoregressive parameters in the model. The data generation process follows the model settings described in the appendix, including spatial weight matrices W1 and W2, error term ϵ, variable coefficient function β (s), explanatory variable xi, and spatial position coordinates si=(ui, vi). Kronecker product, kernel smoothing method, local linear estimation, and instrumental variable GMM estimation method were used in the data processing process. The main processing steps include: constructing a local weighting matrix L, estimating the variable coefficient function β (s), estimating the spatial autoregressive parameters ρ and λ, and estimating the error variance σ 2. The tools used include matrix operations (such as Kronecker product, column straightening operation vec (Q)), kernel density estimation, Taylor expansion, central limit theorem, Cram é r-Wold theorem, and other mathematical and statistical tools.  The appendix file (in PDF format) attached to this dataset contains model settings, lemmas, and their proof processes, providing reference for understanding data processing steps and sources of errors.