We propose a new test for the specification of linear spatial autoregressive models where the spatial weights matrix is prespecified. Our test is built on the difference of two estimates of the spatial parameter where the two estimates are obtained by the parametric and nonparametric GMM estimation methods, respectively. Under mild assumptions, we derive the limiting null distribution and show consistency for our test. Unlike the general nonparametric test, our test can detect the local alternatives that approach the null at a rate $n^{-1/2}$, where $n$ is the sample size. Monte Carlo simulations are conducted to study the finite sample performance of our test. Finally, we apply our test to check the model specification for the economic growth rate example.

我们提出了一种新的线性空间自回归模型规范测试，其中空间权重矩阵是预先指定的。我们的测试建立在空间参数的两个估计值的差异之上，其中两个估计值分别通过参数和非参数 GMM 估计方法获得。在温和的假设下，我们得出限制零分布并显示我们的测试的一致性。与一般的非参数测试不同，我们的测试可以检测以一定速率接近零值的局部替代方案$n^{-1/2}$， 在哪里$n$是样本大小。进行蒙特卡罗模拟是为了研究我们测试的有限样本性能。最后，我们应用测试来检查经济增长率示例的模型规范。