A COMPANION TO Theoretical Econometrics

Spatial Econometrics

Luc Anselin*

1 Introduction

Spatial econometrics is a subfield of econometrics that deals with spatial interac­tion (spatial autocorrelation) and spatial structure (spatial heterogeneity) in regres­sion models for cross-sectional and panel data (Paelinck and Klaassen, 1979; Anselin, 1988a). Such a focus on location and spatial interaction has recently gained a more central place not only in applied but also in theoretical econometrics. In the past, models that explicitly incorporated "space" (or geography) were primarily found in specialized fields such as regional science, urban, and real estate economics and economic geography (e. g. recent reviews in Anselin, 1992a; Anselin and Florax, 1995a; Anselin and Rey, 1997; Pace et al., 1998). However, more recently, spatial econometric methods have increasingly been applied in a wide range of empirical investigations in more traditional fields of economics as well, including, among others, studies in demand analysis, international eco­nomics, labor economics, public economics and local public finance, and agricul­tural and environmental economics.1

This new attention to specifying, estimating, and testing for the presence of spatial interaction in the mainstream of applied and theoretical econometrics can be attributed to two major factors. One is a growing interest within theoretical economics in models that move towards an explicit accounting for the interaction of an economic agent with other heterogeneous agents in the system. These new theoretical frameworks of "interacting agents" model strategic interaction, social norms, neighborhood effects, copy-catting, and other peer group effects, and raise interesting questions about how the individual interactions can lead to emergent collective behavior and aggregate patterns. Models used to estimate such phenomena require the specification of how the magnitude of a variable of interest (say crime) at a given location (say a census tract) is determined by the values of the same variable at other locations in the system (such as neighbor­ing census tracts). If such a dependence exists, it is referred to as spatial auto­correlation. A second driver behind the increased interest in spatial econometric

techniques is the need to handle spatial data. This has been stimulated by the explosive diffusion of geographic information systems (GIS) and the associated availability of geocoded data (i. e. data sets that contain the location of the obser­vational units). There is a growing recognition that standard econometric tech­niques often fail in the presence of spatial autocorrelation, which is commonplace in geographic (cross-sectional) data sets.2

Historically, spatial econometrics originated as an identifiable field in Europe in the early 1970s because of the need to deal with sub-country data in regional econometric models (e. g. Paelinck and Klaassen, 1979). In general terms, spatial econometrics can be characterized as the set of techniques to deal with meth­odological concerns that follow from the explicit consideration of spatial effects, specifically spatial autocorrelation and spatial heterogeneity. This yields four broad areas of interest: (i) the formal specification of spatial effects in econometric models; (ii) the estimation of models that incorporate spatial effects; (iii) speci­fication tests and diagnostics for the presence of spatial effects; and (iv) spatial prediction (interpolation). In this brief review chapter, I will focus on the first three concerns, since they fall within the central preoccupation of econometric methodology.

The remainder of the chapter is organized as follows. In Section 2, I out­line some foundations and definitions. In Section 3, the specification of spatial regression models is treated, including the incorporation of spatial dependence in panel data models and models with qualitative variables. Section 4 focuses on estimation and Section 5 on specification testing. In Section 6, some practical implementation and software issues are addressed. Concluding remarks are formulated in Section 7.

2 Foundations