GMM estimation of fixed effects partially linear additive SAR model with space-time correlated disturbances

In order to study the ubiquitous space-time panel data in real world, a fixed effects partially linear additive spatial autoregressive (SAR) model with space-time correlated disturbances is proposed. Compared to the linear panel model with space-time correlated disturbances, it can simultaneously capture substantial spatial dependence of response, linearity and nonlinearity between response and regressors, spatial and serial correlations of disturbances, and avoid “curse of dimensionality” of nonparametric regression. By using B-splines to fit additive components and constructing linear and quadratic moment conditions which incorporate information in disturbances, the generalized method of moments (GMM) estimators of unknown parameters and additive components are obtained. Under certain regularity assumptions, it is proved that the GMM estimators are consistent and asymptotically normal. Furthermore, the asymptotically efficient best GMM estimators under normality are derived. Monte Carlo simulation and empirical analysis illustrate that the developed estimation method has good finite sample performance and application prospects.