Inference on varying coefficients in spatial autoregressions

Abstract: We present simple to implement Wald-type statistics that deliver a general nonparametric inference theory for linear restrictions on varying coefficients in a range of spatial autoregressive models. Our theory covers error dependence of a general form, allows for a degree of misspecification robustness via nonparametric spatial weights and permits inference on both varying regression and spatial coefficients. One application of our method finds evidence for constant returns to scale in the production function of the Chinese nonmetal mineral industry, while another finds a nonlinear impact of the distance to the employment center on housing prices in Boston. A simulation study confirms that our tests perform well in finite-samples.