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.本文提出了一种基于筛法的高效广义矩估计（Generalized Method of Moments, GMM）估计量，用于部分线性可加空间自回归模型，该估计量同时纳入了线性与二次矩条件。所提出的GMM估计量即使在所有回归元均无关的情形下依然有效，且被证明具有一致性与渐近正态性。为提升各非参数可加分量的收敛速度，本文进一步提出了一种更高效的两阶段估计流程，并论证了其渐近有效性与神谕性质（Oracle Property）。此外，本文还构建了拉格朗日乘数（Lagrange Multiplier, LM）型设定检验，用于评估非参数可加分量的显著性与函数形式。上述LM检验在原假设下经适当中心化与尺度化后，渐近服从标准正态分布。模拟研究表明，所提出的GMM估计量、两阶段估计方法以及LM检验在有限样本下均表现优异。将本文提出的估计与检验方法应用于波士顿住房数据集，我们发现住房价格存在显著的空间依赖性，且通过部分线性可加空间自回归模型捕捉到了显著的交互效应。