Higher-order spatial autoregressive partially linear varying coefficient models

A new class of semiparametric higher-order spatial autoregressive models is proposed to make a significant contribution to spatial econometrics. In this paper, we propose a new class of semiparametric higher-order spatial autoregressive models by allowing regression function to possess partially linear spatially varying coefficient structure. The proposed model is sufficiently flexible to simultaneously capture different types of spatial correlation and more accurately characterize spatial heterogeneity of regression relationship. We develop a computationally efficient and heteroskedasticity-robust estimation method for the proposed model by utilizing generalized method of moments (GMM) and local linear smoothing method, and derive asymptotic distribution of resulting estimators. Moreover, we develop a generalized likelihood ratio testing method to check whether coefficient functions in the proposed model have interesting parametric forms, in which a bootstrap procedure is suggested to appropriate null distribution of resulting test statistic. Simulation studies show that the proposed estimation and testing methods work quite well in finite samples. The Boston housing price data are analysed to demonstrate usefulness of the proposed model and its estimation and testing methods.