Estimation and variable selection of higher-order spatial autoregressive functional coefficient model with endogenous covariates and diverging dimension
摘要
The generalized method of moments (GMM) estimation approach has been particularly welcomed in spatial autoregressive model, but little research focused on the GMM estimation of semiparametric spatial autoregressive model with high dimensionality, especially when a number of predictors are endogenous. This paper mainly commits to providing an estimation and variable selection method for the higher-order spatial autoregressive functional coefficient model with endogenous covariates and diverging dimension. Based on the instrumental variables and basis function approximation, a series-based GMM estimation approach is firstly proposed. Then, a novel variable selection procedure is developed by utilizing the smooth-threshold estimating equations, which is convenient for implementation. Under some regularity conditions, we establish asymptotic properties of the resulting estimators. Detailed issues on computation and turning parameters selection are discussed. Extensive numerical simulations are conducted to confirm the theories and to demonstrate the finite sample performance of the proposed method.