Spatial weights matrix selection and model averaging for multivariate spatial autoregressive models

In this article, we focus on the model specification problem in multivariate spatial econometric models when a candidate set for the spatial weights matrix is available. We propose a model selection method for the multivariate spatial autoregressive model when the true spatial weights matrix may not be in the candidates. We show that the selected estimator is asymptotically optimal in the sense of minimizing the squared loss. If the candidate set contains the true spatial weights matrix, the method has selection consistency. We further propose a model averaging estimator that combines a set of candidate models and show its asymptotic optimality. Monte Carlo simulation results indicate that the proposed model selection and model averaging estimators perform quite well in finite samples. The proposed methods are applied to a Sina Weibo data to reveal how the user’s posting behavior is influenced by the users that he follows. The analysis results indicate that the influence tends to be uniformly distributed among the user’s followee, or linearly correlated with the number of followers of the followee.

本文聚焦于存在空间权重矩阵候选集时的多元空间计量模型设定问题。针对真实空间权重矩阵可能不在候选集中的多元空间自回归模型，我们提出了一种模型选择方法。本文证明，所提出的选择估计量在平方损失最小化意义下具有渐近最优性。若候选集包含真实空间权重矩阵，则该方法具备选择一致性。此外，我们还提出了一种结合一组候选模型的模型平均估计量，并证明其同样具有渐近最优性。蒙特卡洛（Monte Carlo）模拟结果表明，所提出的模型选择与模型平均估计量在有限样本下表现优异。我们将所提方法应用于新浪微博（Sina Weibo）数据集，以探究用户的发帖行为如何受其关注用户的影响。分析结果显示，该影响要么在该用户的所有关注对象间呈均匀分布，要么与各关注对象的粉丝数呈线性相关。