Oracally efficient estimation and specification testing of partially linear additive spatial autoregressive models

This article proposes a computationally efficient sieve-based generalized method of moments (GMM) estimator for partially linear additive spatial autoregressive models, incorporating both linear and quadratic moment conditions. The proposed GMM estimators remain valid even when all regressors are irrelevant and are shown to be consistent and asymptotically normal. To improve the convergence rate for each nonparametric additive component, we propose a more efficient two-stage estimation procedure and establish its asymptotic validity and oracle property. Additionally, we develop Lagrange multiplier (LM)-type specification tests to assess the significance and functional forms of the nonparametric additive components. These LM tests asymptotically follow a standard normal distribution after appropriate centering and scaling under the null hypotheses. Simulation studies show that the proposed GMM estimators, two-stage estimation, and LM tests perform well in finite samples. Applying our estimation and testing methods to the Boston housing data, we find strong spatial dependence in housing prices and significant interaction effects, as captured by the partially linear additive spatial autoregressive model.