James P. LeSage

An Introduction to Spatial Econometrics

An introduction to spatial econometric models and methods is provided that discusses spatial autoregressive processes that can be used to extend conventional regression models. Estimation and interpretation of these models are illustrated with an applied example that examines the relationship between commuting to work times and transportation mode choice for a sample of 3,110 US counties in the year 2000. These extensions to conventional regression models are useful when modeling cross-sectional regional observations or and panel data samples collected from regions over both space and time can be easily implemented using publicly available software. Use of these models for the case of non-spatial structured dependence is also discussed.

Bayesian Estimation of Spatial Autoregressive Models

Spatial econometrics has relied extensively on spatial autoregressive models. Anselin (1988) developed a taxonomy of these models using a regression model framework and maximum likelihood estimation methods. A Bayesian approach to estimating these models based on Gibbs sampling is introduced here. It allows for non-constant variance over space taking an unspecified form and outliers in the sample data. In addition, estimates of the non-constant variance at each point in space allow inferences regarding the spatial nature of heteroskedasticity and the position of outliers.

Spatial Econometric Modeling of Origin-Destination Flows

ABSTRACT Standard spatial autoregressive models rely on spatial weight structures constructed to model dependence among n regions. Ways of parsimoniously modeling the connectivity among the sample of N=n2 origin‐destination (OD) pairs that arise in a closed system of interregional flows has remained a stumbling block. We overcome this problem by proposing spatial weight structures that model dependence among the N OD pairs in a fashion consistent with standard spatial autoregressive models. This results in a family of spatial OD models introduced here that represent an extension of the spatial regression models described in Anselin (1988).

Spatial Growth Regressions: Model Specification, Estimation and Interpretation

Abstract We attempt to clarify a number of points regarding use of spatial regression models for regional growth analysis. We show that as in the case of non-spatial growth regressions, the effect of initial regional income levels wears off over time. Unlike the non-spatial case, long-run regional income levels depend on: own region as well as neighbouring region characteristics, the spatial connectivity structure of the regions, and the strength of spatial dependence. Given this, the search for regional characteristics that exert important influences on income levels or growth rates should take place using spatial econometric methods that account for spatial dependence as well as own and neighbouring region characteristics, the type of spatial regression model specification, and weight matrix. The framework adopted here illustrates a unified approach for dealing with these issues.

Quantifying Knowledge Spillovers Using Spatial Econometric Models

This paper seeks to develop our understanding of the somewhat diffuse nature of technological externalities and space by associating a geographical dimension with the sectoral dimension. Using a panel data set containing French patents as well as private and public research expenditures by industry and region over the period from 1992 to 2000, this paper estimates a knowledge production function. The region‐ and industry-specific nature of the sample data allows us to empirically examine spatial spillovers associated with public and private research expenditures in own- and other-industry sectors for our sample of 94 French regions. We find that the largest direct and indirect effects are associated with private R&D activity that spills across industry boundaries. However, since Jacobs externalities decrease more drastically with distance than MAR externalities, our results also point to different optimal strategies for regional versus national officials.

What Regional Scientists Need to Know About Spatial Econometrics

Regional scientists frequently work with regression relationships involving sample data that is spatial in nature. For example, hedonic house-price regressions relate selling prices of houses located at points in space to characteristics of the homes as well as neighborhood characteristics. Migration, commodity, and transportation flow models relate the size of flows between origin and destination regions to the distance between origin and destination as well as characteristics of both origin and destination regions. Regional growth regressions relate growth rates of a region to past period own- and nearby-region resource inputs used in production. Spatial data typically violates the assumption that each observation is independent of other observations made by ordinary regression methods. This has econometric implications for the quality of estimates and inferences drawn from nonspatial regression models. Alternative methods for producing point estimates and drawing inferences for relationships involving spatial data samples comprise the broad topic covered by spatial econometrics. Like any subdiscipline, spatial econometrics has its quirks, many of which reflect influential past literature that has gained attention in both theoretical and applied work. This article asks the question: “What should regional scientists who wish to use regression relationships involving spatial data in an effort to shed light on questions of interest in regional science know about spatial econometric methods?”

A Comparison of the Forecasting Ability of ECM and VAR Models

The results of forecasting experiments based on an error correction mechanism (ECM) model and various types of vector autoregressive (VAR) and Bayesian vector autoregressive (BVAR) models are presented. A Bayesian error correction mechanism (BECM) model is also tested. This model represents a hybrid of the BVAR and ECM models. The results from experiments using fifty industries and monthly Ohio labor market data demonstrate that the ECM model produces forecasts with much lower errors than any of the alternative VAR or BVAR models when the variables used in the model pass the statistical tests for cointegration. The findings confirm many of the beliefs expressed by Granger (1986) and Engle and Yoo (1987) based on theoretical consideration of the ECM model versus the VAR model. A result contradictory to the contentions of Engle and Yoo is that the BECM model performs well at the longer forecast horizons for both cointegrated and non-cointegrated industries.

Chebyshev approximation of log-determinants of spatial weight matrices

Abstract To cope with the increased sample sizes stemming from geocoding and other technological innovations, this paper introduces an O( n ) approximation to the log-determinant term required for likelihood-based estimation of spatial autoregressive models. It takes as a point of departure Martins (1993) Taylor series approximation based on traces of powers of the spatial weight matrix. Using a Chebyshev approximation along with techniques to efficiently compute the initial matrix power traces results in an extremely fast approximation along with bounds on the true value of the log-determinant. Using this approach, it takes less than a second to compute the approximate log-determinant of an 890,091×890,091 matrix. This represents a tremendous increase in speed relative to exact computation that should allow researchers to explore much larger problems and facilitate spatial specification searches.

A Family of Geographically Weighted Regression Models

A Bayesian approach to locally linear regression methods introduced in McMillen (1996) and labeled geographically weighted regressions (GWR) in Brunsdon et al. (1996) is set forth in this chapter. The main contribution of the GWR methodology is use of distance weighted sub-samples of the data to produce locally linear regression estimates for every point in space. Each set of parameter estimates is based on a distance-weighted sub-sample of “neighboring observations,” which has a great deal of intuitive appeal in spatial econometrics. While this approach has a definite appeal, it also presents some problems. The Bayesian method introduced here can resolve some difficulties that arise in GWR models when the sample observations contain outliers or non-constant variance.

Spatial Econometric Models

Spatial regression models allow us to account for dependence among observations, which often arises when observations are collected from points or regions located in space. The spatial sample of observations being analyzed could come from a number of sources. Examples of point-level observations would be individual homes, firms, or schools. Regional observations could reflect average regional household income, total employment or population levels, tax rates, and soon. Regions often have widely varying spatial scales (for example, European Unionregions, countries, or administrative regions such as postal zones or census tracts).