Model selection and model averaging for matrix exponential spatial models
针对空间计量模型中空间权重矩阵的选择问题，提出了矩阵指数空间规范下的模型选择与模型平均方法，证明其渐近最优性，并通过蒙特卡洛模拟和经济增长模型验证了有效性。
In this paper, we focus on a model specification problem in spatial econometric models when an empiricist needs to choose from a pool of candidates for the spatial weights matrix. We propose a model selection (MS) procedure for the matrix exponential spatial specification (MESS), when the true spatial weights matrix may not be in the set of candidate spatial weights matrices. We show that the selection estimator is asymptotically optimal in the sense that asymptotically it is as efficient as the infeasible estimator that uses the best candidate spatial weights matrix. The proposed selection procedure is also consistent in the sense that when the data generating process involves spatial effects, it chooses the true spatial weights matrix with probability approaching one in large samples. We also propose a model averaging (MA) estimator that compromises across a set of candidate models. We show that it is asymptotically optimal. We further flesh out how to extend the proposed selection and averaging schemes to higher order specifications and to the MESS with heteroscedasticity. Our Monte Carlo simulation results indicate that the MS and MA estimators perform well in finite samples. We also illustrate the usefulness of the proposed MS and MA schemes in a spatially augmented economic growth model.