Advances in Spatial Econometrics

In the introduction to New Directions in Spatial Econometrics (Anselin and Florax, 1995b), the precursor to the current volume, we set out by arguing that “it would be an overstatement to suggest that spatial econometrics has become accepted practice in current empirical research in regional science and regional economics.” However, we also pointed out that “there is evidence of an increased awareness of the importance of space in recent empirical work in ‘mainstream’ economics” (Anselin and Florax, 1995a, p. 3). In the few years since New Directions appeared, the latter observation has been confirmed by a tremendous growth in the number of publications in which spatial econometric techniques are applied, not only within regional science and economic geography, but also increasingly in the leading journals of economics, sociology and political science. This has not gone unnoticed, and the wealth of new publications has resulted in a separate classification in the Journal of Economic Literature devoted solely to cross-sectional and spatial models.¹ Parallelling the growth in applications, several new methods have been introduced as well, yielding a spatial econometric toolbox that is becoming ever more sophisticated.

In cross sectional regression models the possibility of spill-overs between neighboring units is increasingly being recognized in both the theoretical and applied literature.¹ Within a regression framework, typically recognized forms of such spill-overs relate to the model’s dependent and independent variables, as well as to the error terms. General issues relating to spill-overs suggest that the model's error terms may be spatially correlated. Because the statistical properties of the regression parameter estimators depend upon whether or not the error terms are indeed spatially correlated, tests for such correlation are frequently considered.²

The spatial econometric literature has developed a large number of approaches that can handle spatial dependence and heterogeneity, yet almost all of these approaches are single equation techniques. For many regional economic problems there are both multiple endogenous variables and data on observations that interact across space. To date, researchers have often been in the undesirable position of having to choose between modeling spatial interactions in a single equation framework, or using multiple equations but losing the advantages of a spatial econometric approach. This chapter establishes a framework for applying spatial econometrics within the context of multi-equation systems. Specifically, we discuss the need for multi-equation spatial econometric models and we develop a general model that can subsume many interesting special cases. We also examine the small sample properties of common estimators for specific cases of the general model.

It is widely acknowledged that one of the impediments to a broader acceptance of techniques for spatial data analysis is that handling spatial data involves more insight and possibly the use of additional applications than other forms of data (Anselin, 2000, p. 217). We are perhaps more familiar with the potential difficulties caused by the inadequate mapping of data into temporal reference frameworks, such as the predicted complications attributed to the year 2000 problem, when a circular measure (99 + 1 = 0) was treated as linear. Spatial data come with many assumptions about their reference frameworks, including projection metadata, and are often derived from geographical information systems or other archives of spatial position data. Some of these are also time-specific, where boundary segments are introduced to or removed from maps of polygon representations of spatial objects.

Data are often observed in a binary form: vote for or vote against; buy or don’t buy; build or don’t build; move or don’t move, etc. In classical econometrics this situation has been extensively studied and appropriate procedures developed to handle the nature of the data. The standard model however does not allow for spatial processes to drive the choices made by decision makers. For example, whether one city increases its sales tax may depend the actions of neighboring cities. Whether one jurisdiction subsidizes the construction of a new sports arena depends on the options that are offered to the sports enterprise by other jurisdictions — which has been occurring with increasing frequency in the United States, at the threat of the team moving elsewhere. In both of these cases, the conventional probit model fails to account for interdependencies.

Technological advances such as the global positioning system (GPS) and low-cost, high-quality geographic information systems (GIS) have led to an explosion in the volume of large data sets with locational coordinates for each observation. For example, the Census provides large amounts of data for over 250,000 locations in the US (block groups). Moreover, geographic information systems can often provide approximate locational coordinates for street addresses (geocoding). Given the volume of business information, which contains a street address field, this allows the creation of extremely large spatial data sets. Such data, as well as other types of spatial data, often exhibit spatial dependence and thus require spatial statistical methods for efficient estimation, valid inference, and optimal prediction.

Even small cities have complicated spatial patterns that are difficult to model adequately with a small number of explanatory variables. Shopping centers, parks, lakes, and the like have local effects on variables such as housing prices, land values, and population density. Proximity to such sites can be included as explanatory variables, but the number of potential sites is large and some may be unknown beforehand. Coefficient estimates are biased when relevant sites are omitted, but are inefficient when unimportant ones are included. Moreover, functional forms are often complex for urban spatial patterns even in the absence of local peaks and valleys.

In 1967, Ronald Ridker and John Henning conducted the first study that linked air pollution to property values. Using census level data, they found that, for St. Louis, air pollution had a negative and significant affect on median housing prices. Research since has verified, modified, and redefined the economic interpretation of this relationship. In summarizing twenty-five years of property value/air pollution literature, Smith and Huang (1993, 1995) reported that approximately 74 percent of the studies found at least one significant air pollution variable. Even allowing for a publication bias toward significant findings, there seems to be a preponderance of evidence that air pollution is negatively related to housing prices. This is important because it reveals information about the willingness to pay for air quality — a nonmarket commodity. Moreover, to the extent that policymakers use the results from air pollution/property value studies, the findings are socially relevant. The South Coast Air Quality Management District, for example, uses a property value based model in formulating their Air Quality Management Plans.

The econometrics of spatial models have focused mainly on estimation and testing of hypotheses, see Anselin (1988b), Anselin et al. (1996) and Anselin and Bera (1998) to mention a few. In this chapter we focus on prediction in spatial models based on panel data. In particular, we consider a simple demand equation for cigarettes based on a panel of 46 states over the period 1963–1992. The spatial autocorrelation due to neighboring states and the individual heterogeneity across states is taken explicitly into account. In order to explain how spatial autocorrelation may arise in the demand for cigarettes, we note that cigarette prices vary among states, primarily due to variation in state taxes on cigarettes. For example, in 1988, state excise taxes ranged from 2 cents per pack in a producing state like North Carolina, to 38 cents per pack in the state of Minnesota. In 1997, these state taxes varied from a low of 2.5 cents per pack for Virginia to $1.00 per pack in Alaska and Hawaii. Since cigarettes can be stored and are easy to transport, these varying taxes result in casual smuggling across neighboring states. For example, while New Hampshire had a 12 cents per pack tax on cigarettes in 1988, neighboring Massachusetts and Maine had a 26 and 28 cents per pack tax. Border effect purchases not explained in the demand equation can cause spatial autocorrelation among the disturbances.¹

Recent studies (Romer, 1986; Lucas, 1988) have stressed the importance of factors external to the firm in the production process. Such externalities are assumed to have a direct effect on the level of production or to enhance the productivity of traditional inputs. Broadly speaking, we can identify two types of externalities. First, inputs that are not explicitly taken into account in the firm’s decision-making process although they contribute to the production process (for instance, the availability of human capital, public capital or infrastructure, and social capital). We will refer to these external effects as “external inputs.” Second, externalities that are relevant outside the economies giving rise to the externality, regardless whether these economies are understood as the economy of a specific industry or a specific country or region. This type of externality has recently been considered theoretically in growth models dealing with open economies.

A continuing interest of regional scientists is the development of econometric models for the identification of local characteristics associated with regional growth (e.g., Carlino and Mills, 1987; Thurston and Yezer, 1994; Boarnet, 1994a). Recent advances in spatial econometrics and geographic information systems (GIS) enhance the reliability of small region growth models by incorporating the influences of spatial linkages on the local development process (e.g., Anselin, 1988b; Anselin and Florax, 1995b). Modeling the influence of spatial linkages along with local characteristics appears most beneficial in studies of small area economic change where inter-area spillovers may be extensive. For example, economic and population change in the “edge cities” of urban complexes may affect development of nearby rural areas.

Questions pertaining to the location of economic activity, to the relative sizes of cities in different countries, and to changing roles for different geographical areas in the process of economic growth have attracted considerable interest recently. Work by several theorists who developed the so-called new economic geography, including recent contributions by several researchers, but in particular by Masahisa Fujita, Paul Krugman and Anthony Venables have added important new spatial insight to the established system of cities literature, represented most notably by research by Henderson (1974, 1988). The system of cities approach features powerful models of the intrametropolitan spatial structure, but lacks an explicit model of intermetropolitan spatial structure. Certain aspects of the intermetropolitan spatial structure have played a key role in the new economic geography literature, as, for example, in Krugman (199 lb). Krugman (1998) provides an excellent overview of this literature. Tabuchi (1998) proposes a step towards a synthesis of the older system of cities literature with the newer economic geography based theories by incorporating intrametropolitan commuting costs in addition to intermetropolitan transport costs.

The notion that “neighbors” may generate spatial externalities is well established in economics. In addition to textbook examples of externalities among firms, a significant body of empirical work in urban and environmental economics has provided evidence of the effects of neighboring, undesirable land uses on residential location decisions and housing values. The goal of this chapter is not to challenge or augment this literature, but rather to use it as a starting point in asking whether spatial externalities may influence actual land use conversion decisions by landowning agents. The basic thesis proposed here is that agents’ consideration of these spatial externalities may influence their land use decisions if the resulting change in a parcel’s relative values in alternative land uses is sufficiently strong. If so, then the presence of such spatial externalities creates an interdependence among neighboring agents’ land use decisions, which implies that land use conversion may be partially driven by a process of endogenous change.

This chapter explores the impact of openness to trade, and the size of trade flows, on the determination of environmental regulations. Some authors argue that as a result of global trade liberalization countries are likely to relax domestic environmental policy standards in order to increase (or maintain) “competitiveness” (see Esty, 1994; Dua and Esty, 1997; Esty and Geradin, 1997). This could potentially lead to a “race to the bottom,” where countries continually undercut the competitors’ regulations, or refrain from enacting new environmental policies altogether, a “regulatory chill.” Fredriksson (1999) shows in a political economy model that the effect of trade liberalization on politically determined pollution taxes depends on the size of the relative shifts in political power of producer and environmental lobby groups that occur as a result of the liberalization (see also Bommer and Schulze, 1999). Others argue that “ecological dumping” may occur, where environmental policies are set at suboptimally lax levels for strategic reasons (Barrett, 1994; Kennedy, 1994; Rauscher, 1994). Industry and union interests join the environmentalists in their fear that trade liberalization will create “pollution havens” with low stringency of environmental regulations and a comparative advantage in polluting sectors. These fears have given rise to calls for harmonization of environmental policies in regional free trade areas, e.g., across the EU or NAFTA members (Esty and Geradin, 1997).

Economists, economic geographers and regional scientists have suggested different and contrasting explanations of why regions grow at different rates, and what kind of convergence, if any, one might expect from a system of interacting regions. Despite significant differences of approach, there are nevertheless common themes arising from the literature which bring an element of cohesion to a diverse subject matter, namely the relevance for understanding of returns to scale, externalities and catch up mechanisms, and the role of exogenous shocks in real-world turbulence. The chapter first reviews the growth literature, emphasising the importance of these themes, and sets the modelling approach adopted in the chapter in the context of the wider literature. It then gives new expressions for the equilibrium implied by various related models, and an iterative approach is developed to accommodate turbulence leading to “stochastic equilibrium.” As an illustration of the potential of the general methodology, the chapter finally focuses on a preferred single equation spatial econometric model (Anselin, 1988b; Anselin and Florax, 1995b). This model leads to substantive empirical evidence regarding causes of productivity growth variations, and the parameter estimates are used to calculate steady-states and stochastic equilibrium for manufacturing productivity ratios for 178 regions of the European Union (EU) (Armstrong, 1995; Cheshire and Carbonaro, 1995).

Recent theoretical models of economic growth emphasize the importance of external effects for the accumulation of factors of production (Romer, 1986, 1990; Lucas, 1988). Externalities imply that an increase in the stock of reproducible factors leads to an improvement in the level of technology that cannot be fully appropriated by the agent making the investment. As a result, the aggregate or social return on the investment is greater than the private return obtained by the individual agent. A crucial assumption is usually that externalities spread over the entire economy, affecting the level of technology of each individual firm.