Methodological Developments in Spatial Econometrics and Statistics
LeSage, James P., Pace, R. Kelley, Tiefelsdorf, Michael, Geographical Analysis
The November 2002 North American Meetings of the Regional Science Association International in San Juan, Puerto Rico included five sessions with roughly 20 papers devoted to spatial statistics and econometrics. These paper presentations reflected recent areas of interest by those engaged in methodological as well as applied spatial statistical research. This special issue includes five papers that are representative of current methodological developments as well as innovative application and extension of existing methods.
Many traditional spatial statistical estimation methods rely on a weight matrix to model connectivity relations between the units of observation. Not surprisingly, much research centers on determining an appropriate specification of this weight matrix. Two papers in this special issue represent work in this arena, one by Arthur Getis and Jared Aldstadt entitled "Using Local Statistics in the Specification of the Spatial Weights Matrix," and another by Donald Lacombe, "Does Econometric Methodology Matter? An Analysis of Public Policy Using Spatial Econometric Techniques."
The Getis and Aldstadt paper proposes partitioning the spatial structure into two parts, one that reflects pairwise spatial relations among the observations and the other that models the individual contribution of unconnected observations. In contrast to the classical approaches in spatial statistics and econometrics, which specify global spatial relations on hypothetical grounds or by "practical convenience" as either distance-based functions or neighborhood relations, the Getis and Aldstadt approach estimates the spatial relations of each observation from the data. They apply a local statistical concept, the [G.sub.i][degrees] statistic, to determine the range beyond which no more spatial dependence for each observation can be expected. A series of simulation experiments compares the proposed weight matrix against other specifications of weight.
The second paper by Lacombe examines a methodological approach to accommodating spatial effects used in the econometrics literature, known as border matching. Economists are often concerned with the magnitude and significance of economic policies that vary across states, countries, or regions. Ordinary regression methods have been applied to selected samples that contain only observations along both sides of a border. Lacombe compares estimates and inferences from this methodological approach to an extension of conventional spatial autoregressive regression models based on two mutually exclusive weight matrices. One weight matrix captures the spatial autoregressive influence of border counties in adjacent states while a second weight matrix measures the influence of contiguous counties within the state. He argues that the regression-based border-matching method omits a large number of sample observations and fails to account for spatial autoregressive influences from bordering regions within the state. This can lead to an overestimate of the impact arising from changes in policy regime across states.
Another area of interest in the papers presented at the November 2002 conference was application of Bayesian methods to spatial statistical problems. The paper by Tony Smith and Sangyoung Song entitled "A Spatial Mixture Model of Innovation Diffusion" demonstrates an interesting case where Bayesian methods hold an advantage over conventional maximum-likelihood estimation and inference when sample sizes are small. They examine diffusion of new products or technical innovation in a spatial context, arguing that the event-based adoption process can be modeled as the outcome of two factors. One involves modeling the likelihood of a binary decision to adopt, which depends on spatial contacts or interaction between individuals and previous adopters, while the other reflects individual characteristics. Since both interaction and individual characteristics are georeferenced, the spatial diffusion process is modeled as a probabilistic spatial mixture of these two forces. …