32  Applied Spatial Econometrics

Spatial econometrics has its origins in the early 1970s, when Jean Paelinck used the term to refer to methodological aspects associated with incorporating dependence in cross-sectional multiregional econometric models. Initially, the development and application of spatial econometrics was mostly driven by the interests of regional scientists and applied economists in Europe, and several of the early classics appeared in RSUE. In part stimulated by advances in theory (social and spatial interaction) and technology (geographic information systems), the interest in spatial analysis in economics and other social sciences has seen tremendous growth in recent years (Goodchild et al., 2000). This culminated in the formal establishment in May 2006 of an international “Spatial Econometrics Association” at the Fifth Workshop on Spatial Econometrics and Statistics in Rome, Italy.

– Anselin (2007)

Spatial econometrics is the branch of spatial statistics concerned primarily with inference over prediction. The focus of the models is to obtain consistent and efficient estimation of model coefficients in the presence of two spatial effects: spatial dependence and spatial heterogeneity (Anselin, 1988; Anselin, 1989). Spatial dependence arises when observations in nearby locations are related to one another (violating the independence condition necessary for regression analysis). This could be because (1) they are both affected by the same (possibly unobserved) process, (2) because they exert direct interactive pressure on one another, (3) they affect one another indirectly or endogenously, or (4) some combination thereof. Spatial heterogeneity arises when the relationship between two variables is non-constant over space. This is a special case of heteroskedasticity where the relationship between X and Y is spatially-patterned.

In the causal inference literature these issues are treated as “interference” that can confound causal estimates. While unbiased estimation of the model parameters is one longstanding goal, the spatial interaction mechanisms are also substantively interesting and important in spatial science. That is, the interaction between units is often viewed as a meaningful process like spatial spillover, rather than an interfering pathway between cause and effect. This means that in many cases we do not want to rid the model of spatial interaction, but specify its form and study its implications. We often have some idea what this interaction structure could look like, for example, we expect nearby units may interact with one another leading to a distance or connectivity-based notion of spatial interaction.

As such, what sets spatial econometric models apart from other models is the inclusion of neighborhood characteristics linked to each observation through a spatial connectivity graph, canonically called the spatial weights matrix \(W\) which describes how nearby observations might be expected to interact with one another. These potential interactions can take several forms leading to a variety of model specifications. The canonical citations for econometric model specification are Anselin & Griffith (1988), Anselin (1988), and (Anselin1988?); the modern reference texts today are LeSage & Pace (2009), and Elhorst (2014) with poignant summaries for specifying, estimating, and interpreting spatial econometric models given in Elhorst (2010), Elhorst et al. (2012), LeSage & Pace (2014), and LeSage (2014).

32.1 Motivation

The raison d’etre for spatial econometrics is simple. As we saw in Chapter 10 (and as Tobler’s refrain reminds us), empirical data often show high levels of spatial autocorrelation, and if that spatial structure is ignored it leads to problems in the analysis. So the first test in the toolbox was straightforward: take a standard OLS regression, then run a Moran’s I test on the residuals. If the test is significant, then there is evidence the observations interact with one another in space and the model has an obvious problem.

Spatial autocorrelation is not mentioned at all of in 12 currently used econometrics textbooks. …spatial econometrics has not yet appeared in any serious way in the econometrics literature. The recent textbooks in econometrics mentioned earlier contain virtually nothing on ways to handle spatial data. This implies that all economists being educated today must learn about dealing with spatial models and data outside of their curricula. At the same time, however, economists are more concerned than ever about environmental and urban problems. No wonder the literature on such subjects is only lightly sprinkled with analyses of spatial effects and the use of the spatial autocorrelation concept.

– Getis (2007)

The origins of spatial econometrics are arguably based on an experimentalist framework, where geographers and regional scientists have long recognized the ways that spatial dependence may bias traditional regression results (Anselin & Griffith, 1988; Cliff & Ord, 1969; Cliff & Ord, 1973; Cliff & Ord, 1970). This is a long precursor to more recent work on intervening variables and the “reflection problem” in the neighborhood effects and epidemiology literature (Halloran et al., 1991; Halloran & Struchiner, 1995; Manski, 1993; Sobel, 2006).

But theoretical spatial econometrics is also explicitly structural, as it attempts to codify what Anselin (1988) refers to as a “model based” approach (as differentiated from the “data-based” approach). Despite the primary statistical motivation to recover unbiased estimation techniques, the models are introduced and discussed via a formal DGP that motivates each model’s use, and derives its functional form (LeSage & Pace, 2009). Although spatial econometric models can be viewed as a method for dealing with spatially-correlated unobserved variables, a key motivator behind many early developments was estimation of the structural spillover terms, which are often the key variables of interest in spatial science.

In practice, however, most applied work adopts a data-driven approach that selects a preferred model based on fit criteria, and uses that selection to defend against criticisms of inefficiency/bias from OVB or autocorrelation that would otherwise plague an aspatial model. As McMillen (2012) and Gibbons & Overman (2012) describe, this approach trades one identification error for another, and often ascribes significance to spatial effects that may be spurious. Luckily, there are cases when both fully structural approaches and experimentalist approaches can lead to better, more appropriately-identified hedonic (and other) models, but constructing them requires considerable knowledge about housing markets, urban dynamics, and spatial relationships (Elhorst, 2010).

Thus, for applied spatial econometrics it is the best of times. And it is the worst of times. The vast majority of mainstream social science literature focused on causal inference still ignores any potential for spatial misspecification despite heavy reliance on georeferenced data. For example a recent stream of research by leading econometricians on the closure of abortion clinics—focused explicitly on spatial distances—fails to ever consider potential spatial effects (Lindo et al., 2017; Myers, 2021; Quast et al., 2017), while work on spillover effects in housing research fails to operationalize spatial spillover (Voith et al., 2022). Despite professional organizations and scholarly journals focused on spatial econometrics, Much of the mainstream literature in policy analysis and applied econometrics still fails to heed Isard (1949)’s warning, even today:

Theoreticians of today are chiefly preoccupied with introducing the time element in full into their analyses, and the literature abounds with models of a dynamic nature. Yet who can deny the spatial aspect of economic development:that all economic processes exist in space, as well as over time? Realistically, both time and space must be vital considerations in any theory of economy. Unfortunately, however, aside from those of the monopolistic competition school of thought, particularly Chamberlin, the architects of our finest theoretical structures have intensified the prejudice exhibited by Marshall. They continue to abstract from the element of space, and in doing so they are approaching a position of great imbalance.”

At the same time, however, applied spatial econometricians have been aptly criticized for treating every problem with a spatial component as a nail to be pounded with their proverbial spatial autoregressive hammer. This mechanical application of applied spatial econometric modeling without serious consideration of identification or structural estimation issues has led to a large volume of papers that ascribe causal spillover effects in research designs where these same effects are questionably identified (Gibbons & Overman, 2012). What’s more, misspecification and misinterpretation of spatial models and spillover effects is also rampant (LeSage, 2014; LeSage & Pace, 2014).

Paradoxically, we need more research that considers formal spatial relationships and we need less blind application of spatial econometric methods. In this chapter, we use the hedonic housing price model (Blomquist & Worley, 1981; Rosen, 1974; Witte et al., 1979) as a vehicle to explore these issues in depth.

32.2 Software

  • libpysal
  • statsmodels
  • linearmodels
  • spreg

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