General spatial model meets adaptive shrinkage generalized moment estimation: Simultaneous model and moment selection

Spatial data are widely used in various scenarios of life and are highly valued, and their analysis and research have achieved remarkable results. Spatial data have spatial effects and do not satisfy the assumption of independence; thus, the traditional econometric analysis methods cannot be directly used in spatial models, and the spatial autocorrelation and spatial heterogeneity of spatial data make the research more complicated and difficult. Generalized moment estimation(GMM) is a powerful tool for statistical modeling and inference of spatial data. Considering the case where there is a set of correctly specified moment conditions and another set of possibly misspecified moment conditions for spatial data, this paper proposes a GMM shrinkage method to estimate the unknown parameters for spatial autoregressive model with spatial autoregressive disturbances. The proposed GMM estimators are shown to enjoy oracle properties; i.e., it selects the valid moment conditions consistently from the candidate set and includes them into estimation automatically. The resulting estimator is asymptotically as efficient as the GMM estimator based on all valid moment conditions. Monte Carlo studies show that the method works well in terms of valid moment selection and the finite sample properties of its estimators.