New Methods and Software for Spatial-Regression Analysis

DESCRIPTION (provided by applicant): Researchers in health, social sciences, and many other fields are confronting an increasing number of ever-larger spatial datasets that permit the exploration of spatial (cross-sectional) dependencies and interactions. The objective of this project is to create new statistical methods and software that expand the scope of spatial-regression methods and analyzable datasets. The new methods and software will provide the research community with important tools to better understand spatial aspects of human behavior and their effect on health. The project will derive and statistically analyze generalized method of moments (GMM) and instrumental variable (IV) estimation methods for important classes of cross-sectional and panel-data spatial- regression models for which maximum likelihood (ML) estimators cannot be formulated, or where their statistical properties have not yet been formally established. The project will also implement those methods in the widely used statistical software program Stata, paying particular attention to user friendliness, numerical efficiency, and the ability to handle large datasets. Cross-sectional units are often heterogeneous. Phase I of the project considered an important cross- sectional spatial model allowing for heteroskedasticity of unknown form in the innovations. The Phase I project derived the statistical properties of a new GMM/IV estimation method for this model. Analytic and simulation results showed that the GMM/IV estimation method can be successfully applied in this situation, whereas the standard ML methods cannot. The results also demonstrated that the GMM/IV estimators can be computed in signficantly less time than comparable ML estimators. The model considered by the Phase I project belongs to a class of spatial models often referred to as Cliff-Ord models. Previous estimation methods for Cliff-Ord models have focused mostly on models for cross-sectional data. Extensions of Cliff-Ord models to panel-data are sparse. Also, these extensions only consider random-effects specifications, and do not allow for spillovers in the endogenous variables, or for time dynamics, and hence these models may not be appropriate in many applications. The Phase II project has two general aims. First, it will develop new GMM/IV estimators, complete with asymptotic distribution theory, for more general panel-data spatial-regression models which allow for fixed effects; spillovers in the endogenous variables, exogenous variables, and disturbances; time dynamics; and systems formulations. The new GMM/IV estimators will handle cases in which either ML estimators cannot be properly formulated or the estimation theory for ML estimators is currently known. Second, it will implement the estimation methods in Stata to make them readily available to the research community, and develop tools that reduce the computational cost of estimation to accommodate large datasets. This project will have substantial broad impacts by facilitating sound empirical analysis of topics in health and other fields by developing and implementing in Stata estimation methods that incorporate spatial (cross-sectional) dependencies and interactions. The tools will help us better understand the spatial aspects of human behavior and their effects on health, including the spread of disease, which will benefit society through better public health policy and planning.