Specification Test for Spatial Autoregressive Models

This paper considers a simple test for the correct specification of linear spatial autoregressive models, assuming that the choice of the weight matrix <i>W</i>_<i>n</i> is true. We derive the limiting distributions of the test under the null hypothesis of correct specification and a sequence of local alternatives. We show that the test is free of nuisance parameters asymptotically under the null and prove the consistency of our test. To improve the finite sample performance of our test, we also propose a residual-based wild bootstrap and justify its asymptotic validity. We conduct a small set of Monte Carlo simulations to investigate the finite sample properties of our tests. Finally, we apply the test to two empirical datasets: the vote cast and the economic growth rate. We reject the linear spatial autoregressive model in the vote cast example but fail to reject it in the economic growth rate example.本文针对线性空间自回归模型的正确设定问题，构建了一种简易检验方法，前提假定所选取的权重矩阵Wₙ为真实设定。本文推导了在正确设定原假设及一系列局部备择假设下该检验的极限分布，研究表明，该检验在原假设下渐近不受多余参数（nuisance parameters）的干扰，并证明了本文所提检验的一致性。为提升该检验的有限样本表现，本文还提出了一种基于残差的野自举（wild bootstrap）方法，并论证了其渐近有效性。本文开展了一组小型蒙特卡洛（Monte Carlo）模拟实验，以考察所提检验的有限样本性质。最后，本文将该检验应用于两组实证数据集：投票数据与经济增长率数据。在投票数据案例中，本文拒绝了线性空间自回归模型的设定；而在经济增长率数据案例中，则未能拒绝该模型设定。