Theoretical foundations for spatial econometric research

This paper reviews the development of large sample theories for spatial econometric models. These theories form important parts on statistical foundations for spatial econometrics. Another important component is the theoretical economics foundation for spatial econometric model specifications. We discuss how spatial econometric models can be regarded as the Nash equilibrium of some complete information games. Moran's I test for spatial dependence is based on a statistic with a linear-quadratic form. Scores of the ML and moments for 2SLS and GMM are also in linear-quadratic form. A statistic with a linear-quadratic form can be characterized as a sum of martingale differences, so the central limit theorem for martingale difference arrays is crucial for asymptotic distributions of such statistics. For linear spatial models, statistics on linear-quadratic forms are the basis of spatial econometrics. For nonlinear spatial models, near-epoch dependent random fields play a crucial role. We summarize some important properties of near-epoch dependent random fields and illustrate how they are used in studying nonlinear spatial models such as spatial Tobit and spatial binary choice models.