Specification and Estimation of Spatial Models

University Of Maryland, College Park, College Park MD

Investigators

Abstract

This proposal relates to the specification and estimation of spatial models. These models are important tools in economics, regional science and geography in analyzing a wide range of empirical issues. In spatial models, interactions between cross sectional units are typically modeled in terms of some measure of distance between them. These interactions could be due to competition between cross sectional units, copy-cat policies, network issues, spillovers, externalities, regional issues, etc. Spatial distances could relate to geographic space, as well as other spaces such as product space or input space. Spatial models have seen many recent applications including the determinants of productivity, local public expenditures, vote seeking and tax setting behavior, population and employment growth, contagion problems such as bank failures, and the determinants of welfare expenditures. By far the most widely used spatial models are variants of the one suggested by Cliff and Ord for modeling a single spatial relationship. Even in its simplest form, maximum likelihood estimation of these types of models entails substantial, and even forbidding, computational problems if the number of cross sectional units is large. Against this background, we have suggested alternative procedures which are computationally simpler: the Gild estimator and an instrumental variable estimation procedure which is based on a generalized moments (GM) estimator of a parameter in the spatial autoregressive process. The purpose of this proposal is to generalize Cliff-Ord type models in three important directions allowing them to cover a wider range of applications and lessening the danger of model misspecification in applied work. The first extension will allow for estimation of Cliff-Ord type models with heteroskedastic innovations which are quite often encountered in empirical analysis of spatial units of different size. We also plan to relax other restrictive model assumptions, including a typically maintained assumption regarding the parameter space of the spatial autoregressive parameter. As a second generalization we propose an extension of the estimation methodology we have developed to a panel data framework in which the spatial units are observed for multiple time periods. In this framework the disturbances will be assumed to follow a spatial autoregressive process. Motivated by the error components literature, the innovations entering this process will be modeled as the sum of two error components, reflecting unit specific effects and some overall innovation. Taken together, the disturbances entering the regression model would be both spatially and time correlated. Finally, because modeling interactions between spatial units will frequently involve a system of equations, we propose an extension of Cliff-Ord type models to simultaneous equation systems. In such a framework it should be of interest to consider full information estimators. However, to the best of our knowledge, no formal results concerning the large sample distribution of such estimators exist. For each of those generalizations we will introduce estimation methodology which will involve extensions of our earlier work. In all three cases we plan to formally study the large sample properties of our proposed estimators, and to supplement those theoretical results with corresponding Monte Carlo studies.