Semiparametric Estimation and Testing of Smooth Coefficient Spatial Autoregressive Models

Abstract

This paper considers a flexible semiparametric spatial autoregressive (mixed-regressive) model in which unknown coefficients are permitted to be nonparametric functions of some contextual variables to allow for potential nonlinearities and parameter heterogeneity in the spatial relationship. Unlike other semiparametric spatial dependence models, ours permits the spatial autoregressive parameter to meaningfully vary across units and thus allows the identification of a neighborhood-specific spatial dependence measure conditional on the vector of contextual variables. We propose several (locally) nonparametric GMM estimators for our model. The developed two-stage estimators incorporate both the linear and quadratic orthogonality conditions and are capable of accommodating a variety of data generating processes, including the instance of a pure spatially autoregressive semiparametric model with no relevant regressors as well as multiple partially linear specifications. All proposed estimators are shown to be consistent and asymptotically normal. We also contribute to the literature by putting forward two test statistics to test for parameter constancy in our model. Both tests are consistent.

Keywords: Consistent Test, Constrained Estimation, Local Linear Fitting, Nonparametric GMM, Partially Linear, Quadratic Moments, SAR, Spatial Lag

JEL Classification: C12, C13, C14, C21