SPATIAL ECONOMETRIC DATA ANALYSIS: MOVING BEYOND TRADITIONAL MODELS

Transcription

1 INTERNATIONAL REGIONAL SCIENCE REVIEW 26, 3: (July 2003) / Florax, van der Vlist / SPATIAL INTERNATIONAL ECONOMETRIC REGIONAL DATA ANALYSIS SCIENCE REVIEW (Vol. 26, No. 3, 2003) ARTICLE SPATIAL ECONOMETRIC DATA ANALYSIS: MOVING BEYOND TRADITIONAL MODELS RAYMOND J. G. M. FLORAX Department of Spatial Economics, Free University, Amsterdam, The Netherlands, and Regional Economics Applications Laboratory (REAL), University of Illinois at Urbana-Champaign, Urbana, [email protected] ARNO J. VAN DER VLIST Department of Spatial Economics, Free University, Amsterdam, The Netherlands, [email protected] This article appraises recent advances in the spatial econometric literature. It serves as the introduction to a collection of new papers on spatial econometric data analysis brought together in this special issue, dealing specifically with new extensions to the spatial econometric modeling perspective. Although the initial development of the field of spatial econometrics has been rather slow, the Dixit-Stiglitz revolution and the emergence of the New Economy Geography have been instrumental in uplifting the significance and the use of spatial data analysis techniques. Concurrent developments in other social sciences parallel this situation in economics. The upsurge in spatial econometrics is, among other things, driven by the recognition that traditional spatial econometric models are insufficient to capture modern theoretical developments. Therefore, this issue brings together a collection of articles on space-time and discrete choice modeling, spatial nonstationarity, and the methodology and empirics of regional economic growth models. Keywords: spatial econometrics; data analysis; spatial regression models It is difficult not to notice the upsurge in the advancement of econometric theory for spatial cross-section models, the availability of easy-to-use software for spatial data, and the use of spatial econometric techniques in applied research. In 1988, Anselin and Griffith pointed out the negligence of regional science scholars toward incorporating spatial data analysis techniques in applied research. In the early 1990s, Anselin and Rey (1991) reiterated this point, but they had already observed indications of a gradual change. Ever since, the situation has altered radically, and it is fair to say that nowadays, spatial data analysis techniques abound. Recent conferences of constituent organizations of the Regional Science Association International (RSAI) have programmed special sessions on spatial econometrics. This was the case at the Western Regional Science Association meeting in Palm Springs, California, in 2001; the North American meeting in San Juan, Puerto DOI: / Sage Publications

2 224 INTERNATIONAL REGIONAL SCIENCE REVIEW (Vol. 26, No. 3, 2003) Rico, in 2002; and the European meeting in Dortmund, Germany, in A series of special issues of journals and edited volumes reveals the progress that is being made in the area of spatial econometrics (Anselin 1992a; Anselin and Florax 1995a; Anselin and Rey 1997; Pace 1998; Nelson 2002; Getis, Mur, and Zoller forthcoming; Pace, Tiefelsdorf, and LeSage forthcoming). Theoretical advances with respect to spatial econometric modeling are increasingly also published in some of the topnotch journals in economics and econometrics (Dubin 1988; Pinkse and Slade 1998; Conley 1999; Kelejian and Prucha 2001; Lee 2002). Funding organizations, such as the American National Science Foundation, finance programs in which the integration of the spatial dimension in social science research forms essentially the core of the program (i.e., the initiative to establish the Center for Spatially Integrated Social Sciences [CSISS]) (see Goodchild et al. 2000; As we will show below, the number of applied papers using spatial statistical and econometric techniques is rapidly increasing as well. We continue this article by discussing some of the history of spatial econometrics. Although the history dates back to the 1940s and 1950s, with subsequent sizable pushes in the 1970s and 1980s, the path of development remains rather flat until the 1990s. We argue that recent theoretical developments in economics and other social sciences induce a reorientation that includes spatial effects among the main determinants of real-world processes. The reorientation is accompanied by an increase in available spatially referenced data, which are usually easy to attain through the Internet. We discuss several consequences of changes in data availability, such as lowerspatial scale, computational aspects, and visualization. Apart from theory and data, the accessibility of appropriate software definitely goes a long way in explaining the current upsurge in the use of spatial econometric techniques. Subsequently, we provide an overview of the main methodological contributions to spatial econometrics, and we review applications of spatial econometric techniques according to areas demarcated in the subject index of the International Regional Science Review (IRSR). 2 We go on to argue that the above-mentioned theoretical developments and the increased data availability are starting to drive the field of spatial econometrics away from the traditional spatial error and spatial lag model and toward different and much broader directions now (see also Anselin 2002). The proliferation of spatial econometrics into different directions motivated the first author of this article to organize special sessions on spatial econometrics for the 42nd European conference of the RSAI, which took place in Dortmund (Germany) from August Some fifteen papers, organized in six special sessions, were presented. 3 After the conference, we invited the participants to submit their papers for this special issue. Two external reviewers per manuscript scrutinized the papers, following standard peer review procedures of IRSR. We now have a series of articles that illustrates the recent proliferation of spatial econometrics to very diverse areas of methodological concern and application. The articles cover

3 Florax, van der Vlist / SPATIAL ECONOMETRIC DATA ANALYSIS 225 the areas of space-time models, spatial hazard modeling, vector autoregressive models with spatial interaction effects, and spatial nonstationarity. The issue concludes with contributions to the empirics of regional economic growth using exploratory spatial data analysis techniques, Markov chain modeling, and a simultaneous dynamic least squares estimator for a generalized spatial convergence model. More detail about the individual contributions and promising avenues for future research on spatial econometrics conclude our contribution. SOME HISTORY The history of spatial statistical and econometric data analysis goes back to the work of statisticians such as Moran, Geary, and Whittle in the late 1940s and early 1950s. Initially, developments were rather slow, but they were decisively influenced by the publication of three seminal books (Florax and Nijkamp forthcoming). In 1973, Cliff and Ord devoted a monograph to spatial autocorrelation. Their book primarily focuses on the statistical analysis of spatial data series, although there is some attention for modeling as well. The modeling context is much more pronounced in the work of the Dutch-Belgian economist Jean Paelinck, who coined the term spatial econometrics in the early 1970s. Paelinck and Klaassen jointly wrote the first monograph on spatial econometrics in 1979, stressing the need to explicitly model spatial relations, epitomizing the asymmetry in spatial interrelations and the role of spatial interdependence. The field was in those days pushed ahead mainly by Dutch regional economists and British geographers and economists (e.g., Bartels, Brandsma, Hordijk, Ketellapper, and Nijkamp, in The Netherlands, and Fingleton, Haining, Ord, and Upton, in the United Kingdom). Later, the center of activity shifted to the United States, where both economists and geographers concentrated on introducing new statistical tests and specifying and estimating spatial regression models. The modeling perspective was pondered and comprehensively treated in Luc Anselin s (1988) book on methods and models in spatial econometrics. He defined spatial econometrics as the collection of techniques that deal with the peculiarities caused by space in the statistical analysis of regional science models (p. 7). The modeling perspective distinguishes spatial econometrics from the broader field of spatial statistics, the progress of which is documented in, for instance, Cressie (1993). Several reasons come to mind when trying to explain the initial lack of consideration of spatial effects and the subsequent upsurge in the development and use of spatial analysis tools. First, going back to classical economists such as Marshall, economists have been preoccupied with the temporal rather than the spatial dimension of economic phenomena. This was a majornuisance pushing WalterIsard to establish the interdisciplinary field of regional science, maintaining that (neo)classical economists are confined to analyzing a wonderland of no spatial dimensions (Isard 1956, 24-25). This did contribute to the establishment of spatial econometrics some twenty years later but, in itself, was not sufficient to lead to a widespread

4 226 INTERNATIONAL REGIONAL SCIENCE REVIEW (Vol. 26, No. 3, 2003) use of spatial econometric techniques. Although spatial econometrics is definitely one of the perks of the Isard push for a regional science, the Dixit-Stiglitz revolution has had a pervasive influence as well (Florax and Nijkamp forthcoming). It raised attention for imperfect competition and increasing returns to scale, which later became prominent elements in the New Economic Geography, next to the concept of spatial externalities (Fujita, Krugman, and Venables 1999; Fujita and Krugman forthcoming). In other social sciences, similar attention shifts have occurred. Increasingly, the popularity of neighborhood effects in sociology, associated with the Chicago school, and the revival of social interaction theory have caused researchers to think about spatial interaction, spatial spillovers, and spatial dependence (see Anselin 2003 and the references therein). Second, the availability of georeferenced data has increased considerably over the past two decades. The Internet obviously contributes to easy access and thus stimulates the use of spatial data with concurrent use of specialized technology, such as Geographic Information Systems (GIS) and Global Positioning Systems (GPS) and remote sensing technology (Goodchild et al. 2000; see also the examples in Nelson 2002). The increased availability of geographical data has several implications for the substance of spatial econometric techniques. First, the restriction to one spatial scale determined by data availability is relaxed. This creates the opportunity to experiment with models at different levels of spatial aggregation. The relevance of the scale aspect is well known. Straightforward aggregation over space is only warranted if the phenomenon at stake is homogeneously distributed over space (Anselin 1988, 26-27) and the effect of spatial scale on test statistics is pervasive (Griffith, Wong, and Whitfield forthcoming). The aspects of spatial scale and identification come together in the modifiable areal unit problem (Arbia 1989; Amrhein 1995; Amrhein and Reynolds 1996). Identification issues are particularly severe if limited data are available, and this is one of the reasons why spatial process models, which provide exogenous spatial structure through the spatial weights matrix to avoid the incidental parameter problem, have been used so intensively. With more data, it becomes feasible to use direct representation models, which are characterized by estimable distance decay functions rather than exogenously provided spatial structure. 4 The latter type of models provides a much more detailed and data-driven approach to model specification. An additional advantage is that direct representation models circumvent the computational problems associated with large-scale spatial process models, such as computational efficiency, accuracy, and storage, although progress has been made to solve these computational problems (Pace 1997; Pace and Barry 1997a, 1997b; Smirnov and Anselin 2001). Third, for a long time, the freestanding SpaceStat computer program (Anselin 1992b, 2000) was the only full-blown package forspatial econometric analysis. It was complemented by computercode documenting routines to estimate spatial models in mainstream software packages, such as Limdep and Shazam (Griffith 1988; Anselin and Hudak 1992). Slightly later, extensions such as S+SpatialStats (Kaluzny et al. 1997), INFO-MAP (Bailey and Gatrell 1995), and SAGE (Haining,

5 Florax, van der Vlist / SPATIAL ECONOMETRIC DATA ANALYSIS 227 Wise, and Signoretta 2000) were introduced. The improvement in the availability of easy-to-use software obviously contributes to the proliferation of spatial econometric applications. Nowadays, the two most complete software packages are SpaceStat (Anselin 1992b, 2000; see specs.html) and James LeSage s extensive spatial econometrics toolkit developed in MATLAB (see Anselin s package stands out for its combination of exploratory tools, linked to ESRI s ArcView software through a freely available extension, and misspecification tests and estimators for spatial models. LeSage s toolkit is slightly more oriented toward modeling and contains an array of Bayesian routines in addition to the classical tests and estimators. 5 The development of software tools has been very rapid over the past decade. On the CSISS Web site, Luc Anselin presents a spatial tools search engine that indexes a list of URLs and software archives of already more than 700 individual software titles. A spatial tool listing of links to portals (i.e., collections of links) is available as well. The development of software is expected to continue to proceed rapidly now. So-called open-source projects are promising. These projects are typically Web based, and they essentially constitute a platform and a common language for anybody who can credibly contribute to the development of software tools. Platform-independent software that is currently being developed in the context of the CSISS project (see Goodchild et al. 2000) will further facilitate and boost the application of spatial data analysis techniques. HIGHLIGHTS AND THE PROLIFERATION OF SPATIAL ECONOMETRIC TECHNIQUES It is virtually impossible to give a detailed account of the development and the achievements of spatial econometrics in the space-constrained context of a single section of an article. What follows is therefore by far not comprehensive but instead deals with some highlights of the methodological spatial econometric literature as well as a series of examples showing the proliferation of applying spatial econometric techniques to different areas in regional science. The consideration of spatial effects in applied research involves a series of logical steps in the analysis. We highlight some of the important methodological developments by means of these steps, distinguishing exploratory data analysis, misspecification testing in spatial regression models, and the estimation of spatial regression models. 6 Spatial effects is a catchall term referring to both spatial dependence and spatial heterogeneity. Spatial dependence (or autocorrelation) and heterogeneity are usually not easily discernable in an empirical sense (Anselin 2001b). They compete as meaningful but mutually exclusive interpretations of the spatial distribution of realworld phenomena. In the spatial statistical and econometric literature, however, substantially more attention has been given to testing for spatial autocorrelation as compared to spatial heterogeneity because the extent of heterogeneity can be

6 228 INTERNATIONAL REGIONAL SCIENCE REVIEW (Vol. 26, No. 3, 2003) assessed using standard statistical tools (Cliff and Ord 1981). Currently, several statistics measuring the extent of spatial autocorrelation are available, and their asymptotics and small sample behavior are well documented. Moran s I and the G statistic of Getis and Ord (1992) are the most commonly used statistics. The statistics have been disaggregated to investigate heterogeneity by means of local versions of the statistics. 7 The payoff of exploiting the above cross-correlation statistics is maximized if theiruse is embedded in a more extensive exploratory spatial data analysis, typically referred to as ESDA. A proper ESDA tool uses generally available statistical functionalities, such as box plots, charts, and histograms, but it typically focuses in particular on the detection of spatial patterns through maps and scatterplots (specifically, the Moran scatterplot) (see Anselin 1996), preferably in a setting with dynamically linked windows. The visualization of spatial relations is the subject of a voluminous literature and obviously bears close ties to geographic information systems (see Haining, Wise, and Ma 1998; Wise, Haining, and Signoretta 1999). Typically, the next step in applied spatial data analysis focuses on confirmatory orexplanatory modeling 8 and starts with misspecification testing in a regression context. Except for a limited number of direct representation cases, most spatial econometric models are spatial process models. The development of misspecification tests in a maximum likelihood framework, the derivation of their asymptotic properties, and the associated small sample properties have been a longstanding interest of various researchers in the field. The toolbox of misspecification tests includes the regression variant of Moran s I (see Cliff and Ord 1981; Kelejian and Prucha 2001) and large sample tests derived by Kelejian and Robinson (1992, 1998). Furthermore, a battery of unidirectional, multidirectional, and robust Lagrange multiplier (LM) tests is on hand (see Anselin and Griffith 1988; Anselin 1988, 2001c; Anselin and Rey 1991; Anselin and Florax 1995b; Anselin et al. 1996; Kelejian and Robinson 1998; de Graaff et al. 2001; Anselin and Moreno forthcoming; Florax and de Graaff forthcoming; Saavedra 2003). 9 The tests focus on detecting spatially correlated residuals due to any cause (i.e., a spatially autoregressive or moving average error structure, erroneously omitted spatially correlated variables, ora nonlinearrelationship), orthey test forwell-defined misspecifications such as a spatial autoregressive error process or an erroneously omitted spatially lagged dependent variable. It may be difficult to reconcile potentially conflicting results of a series of tests. The results of simulation experiments on specification searches indicate, however, that the classical approach, relying on the probability values of the different tests in a model without spatial effects, performs well in terms of finding the correct model (see Florax and Folmer 1992; Florax, Folmer, and Rey forthcoming). Once spatial effects are discovered, there is obviously a need to specify a spatial regression model accounting for such spatial effects and to use an appropriately spatially adapted estimator. A first approach, which recently regained attention, centers on spatial filtering of the existing variables in such a way that one can, in the

7 Florax, van der Vlist / SPATIAL ECONOMETRIC DATA ANALYSIS 229 end, resort to the use of ordinary least squares (see Getis 1995; and, more recently, Griffith and Tiefelsdorf 2002; Getis and Aldstadt forthcoming). A second approach builds on the work by Casetti (1997) and focuses primarily on the specification of spatial heterogeneity by means of geographically weighted regression (Fotheringham, Brunsdon, and Charlton 1998). Most of the work in this area, however, deals with the derivation of maximum likelihood, instrumental variables, and general methods of moments estimators for the model with spatially autoregressive errors, the so-called spatial lag model that contains a spatially lagged dependent variable, or the spatial error component model introduced by Kelejian and Robinson (1995). The use of Bayesian approaches is advocated and applied in LeSage (1997). The early work dealing with the derivation of properties of estimators is reviewed in Cliff and Ord (1981) and Anselin (1988). More recently, Kelejian and Prucha (1998, 1999), Bell and Bockstael (2000), and Lee (2001a, 2001b, 2002) have provided further theoretical results. Results of simulation experiments revealing the small sample properties of various estimators are scarce (see Anselin 1980; Florax 1992; Das, Kelejian, and Prucha 2003), but they invariably show that relying on ordinary least squares is not an adequate estimation procedure. Where do these theoretical advances in spatial econometrics lead us? Does the theoretical work translate into applications of spatial econometric techniques in diverse areas of regional science? To show the proliferation of the use of spatial econometric techniques in applied research, we tie on to the subject index published in each winteredition of the IRSR. The subject index, covering more than sixty major journals in regional science, indicates a broad array of topics, ranging from natural resources, human resources, economic growth and development, and urban and regional issues to social and political issues, as well as other policy and applications. Without aiming to be comprehensive, the review below shows that, particularly in the areas of housing and real estate, as well as economic growth and development, the utilization of spatial econometric data analysis diffuses rapidly. The area of environmental economics and natural resource management is a major growth area that has been catching up recently. Fora long time, the use of spatial data analysis techniques was underused in applications dealing with agricultural, environmental, and natural resource topics. Many of the subjects in this area are, however, inherently spatial. The spread of contaminated water, the diffusion of air pollution (both point- and non-point-source pollution), the location of waste management and otherhazardous facilities, the effect of environmental policy on foreign direct investment and the potential of environmental dumping, contamination patterns of animal disease, land use, and the valuation of nature areas and pollution all constitute subjects to which spatial econometric techniques can be fruitfully applied. Following, among others, the pleas of Bockstael (1996) and Anselin (2001a) to explicitly incorporate space in the analysis of environmental and agricultural topics, a small literature is now emerging. Lark (2000) is one of the first to use spatial econometric techniques dealing with soil organic matter, and recently, Nelson (2002, 197) has brought together a

8 230 INTERNATIONAL REGIONAL SCIENCE REVIEW (Vol. 26, No. 3, 2003) collection of articles to introduce agricultural economists to new analytical approaches involving spatial data. Florax, Voortman, and Brouwer (2002) apply the traditional spatial econometric models to precision agriculture and review the fast-growing literature dealing with variable rate application. Fewer works are available that deal with environmental issues. Rupasingha and Goetz (2001) incorporate space in the analysis of the environmental Kuznets curve, and Eliste and Fredriksson (forthcoming) pay attention to environmental stringency. The spatial econometric analysis of natural resources is gradually starting off by considering deforestation (e.g., Nelson and Hellerstein 1997) and air quality (Arbia and Lafratta 1997; Murdoch, Sandler, and Sargent 1997; Guldman and Kim 2001; Kim, Phipps, and Anselin forthcoming). It should be noted that the spatial econometric techniques used in agri-environmental applications typically boil down to rather straightforward applications of misspecification testing using LM tests and subsequent estimation of the traditional spatial error or spatial lag model. The same applies to the field of human resources. This is a broad area of studies, among other things, including studies on labor markets and unemployment. Molho (1995), Buettner(1999), and Haughton et al. (forthcoming) are good examples of studies dealing with the traditional spatial econometric modeling perspective, although Buettner (1999) adds an interesting example of block bootstrapping for statistical inference in a space-time context. The literature on population-employment dynamics is a second example of studies belonging to the field of human resources. Boarnet s (1994) well-known contribution to this literature broadens the traditional Carlino-Mills model by including spatial spillover effects. Many replications for different regions and time periods are subsequently published. Henry et al. (1999) include an interesting application because it also allows for spatial heterogeneity, and Rey and Boarnet (forthcoming) supply a taxonomic framework to classify different types of spatial simultaneous equation models and discuss problems of identification. Finally, we like to mention the area considering knowledge spillovers of academic institutions as an area where traditional spatial econometric models have been applied. Interesting examples of studies using spatial econometric techniques to model local spatial spillovers of knowledge production include Florax (1992); Anselin, Varga, and Acs (1997); Varga (1998); and Acs (2002), among others. Departures from the more traditional models are more frequent in the areas of economic growth and development, as well as urban and regional issues. Initially, the regional analysis of economic growth and development began by merely incorporating spatial effects (heterogeneity in the form of so-called spatial clubs, as well as spatial dependence) using traditional spatial econometric modeling techniques in a neoclassical theoretical setup (Chatterji and Dewhurst 1996; Rey and Montouri 1999; Fingleton 2003). Subsequently, exploratory spatial data analysis techniques have gained popularity (Rey and Montouri 1999; Le Gallo and Ertur 2003; Mossi et al [this issue]). Interestingly enough, however, considerable effort is now being put into adapting Markov chain analysis to a setting that includes spatial

9 Florax, van der Vlist / SPATIAL ECONOMETRIC DATA ANALYSIS 231 interaction effects (Fingleton 1999a; Rey 2001; Bickenbach and Bode 2003 [this issue]). Finally, the last area for which we note some interesting applications is concerned with the analysis of urban and regional issues. The application of spatial econometric techniques is not limited to one specific topic but again extends to a whole range of topics. First, some studies deal with the inclusion of neighborhood effects in explaining the spatial distribution of indicators related to, for instance, wages (Ioannides forthcoming), crime (Messner and Anselin 2003), health (Ellen, Mijanovich, and Dillman 2001), or schooling (Fotheringham, Charlton, and Brunsdon 2001). Second, there is an extensive literature on housing and real estate. It is obvious that for the assessment of price variation, neighborhood spillovers in prices or rents are likely to be relevant. The empirical analysis of this type goes back to Can (1992) and shows clear evidence of substantial spatial autocorrelation in transaction prices across housing markets, mainly because neighborhoods tend to have similar structural characteristics and share location amenities (see Basu and Thibodeau 1998). Employing spatially referenced estimators in housing and real estate substantially improves the quality of predictions and statistical inferences (Dubin 1998; Gelfand 1998; Clapp, Kim, and Gelfand 2002). The special issue on spatial statistics and real estate (Pace 1998) particularly the articles by Pace, Barry, and Sirmans (1998); Pace, Barry, Clapp, et al. (1998); and Dubin, Pace, and Thibodeau (1999) provides useful overviews of this literature. Recently, Hwang and Quigley (2003) analyzed the time course development of condominium prices in Singapore. Their approach is different from the habitual hedonic pricing model considered almost throughout the literature, in the sense that they use a wideranging time series of georeferenced data to explain the temporal development of prices, taking into account spatial spillovers in an intricate econometric model. Their model has an explicit link to theory. Linking up theory with spatial econometric specifications is also at the heart of the final area that we like to mention. This is the area dealing with interacting agents (Anselin 2002). The interaction among agents is modeled using spatial correlation across jurisdictions. For instance, Bivand and Szymanski (2000) specify the competition among municipalities in a compulsory competitive tendering system for waste management, and Case, Rosen, and Hines (1993) and Brueckner (1998) test for strategic interaction among governments with respect to budget spillovers and fiscal policy interdependence, respectively. The above concise review of applications evidently shows the rapid proliferation of spatial econometric techniques in various subject areas. Many of these applications are still strongly data driven rather than theory driven (Anselin 2002) and commonly use a relatively simple framework of exploratory spatial data analysis, followed by spatial regression modeling extended with misspecification tests. Gradually, however, things are changing, and we are moving beyond the stage where the traditional spatial modeling approach suffices.

10 232 INTERNATIONAL REGIONAL SCIENCE REVIEW (Vol. 26, No. 3, 2003) MOVING BEYOND TRADITIONAL MODELS The articles brought together in this special issue go beyond applying the traditional spatial econometric framework consisting of exploratory spatial data analysis and subsequent model fitting using spatial misspecification tests. They deal with several interesting extensions and new modeling approaches. In this section, we provide some detail on the relevant context for each contribution, and we summarize some of the main results of the articles. The contribution by Paul Elhorst (2003 [this issue]) offers a comprehensive treatment of the specification and estimation of four spatial panel data models that are developed by adapting the familiar traditional panel data specifications. 10 Relatively little work is available on spatial panel data models (Anselin 1988, 2001b; Elhorst 2001), although the relevance of these models is getting more and more evident because of increased data availability as well as the greater potential to model interaction behavior of agents with a firm theoretical basis. The increasing use of panel data sets in applied research in spatial settings necessitates the incorporation of spatial dependence and/or spatial heterogeneity. Elhorst discusses four widely used models: the spatial fixed and random effect models, as well as the fixed and random coefficient spatial error models. He summarizes what can be learned from the general econometric literature on panel data models and adapts the general models to the spatial context. He presents the respective likelihoods and discusses estimation strategies that are useful in applied research. Moreover, he treats potential problems of the spatially adapted versions of the traditional panel data models and suggests workable solutions to these problems. The literature on spatial effects in limited dependent variable models is getting increasingly rich. Kelejian and Prucha (2001), Fleming (forthcoming), and Pinkse (forthcoming) cover misspecification testing in spatial discrete choice models, and McMillen (1992, 1995), Dubin (1995), Pinkse and Slade (1998), Beron and Vijverberg (forthcoming), and LeSage (2000) present classical as well as Bayesian solutions to the estimation of spatial probit and logit models. A model that has received attention in applications rather than in the theoretical spatial econometric literature is the spatial counterpart of the hazard model. Brigitte Waldorf (2003 [this issue]) opens up this area by considering the spatial hazard model from a conceptual point of view. She explores the analogy between duration in time and space and concludes that, notwithstanding the mathematical analogy between time orduration and space ordistance, conceptual problems evoke substantial difficulties in the interpretation of spatial duration models. Following a concise introduction to duration models, she carries out limited experiments demonstrating how spatial hazard models can be used in empirical spatial research. She concludes that the modeling perspective should change from the static to the dynamic perspective to be able to fruitfully analyze spatial phenomena in a hazard framework. Jesús Murand JavierTrívez (2003 [this issue]) take up the discussion on spatial unit roots and spatial cointegration originally initiated by Fingleton (1999b). They

11 Florax, van der Vlist / SPATIAL ECONOMETRIC DATA ANALYSIS 233 argue that spatial dynamics are so much different from temporal dynamics that it is difficult to implement the notions of integration and unit roots in the multivariate spatial case as compared to the univariate time context. For example, the spatial data-generating process that allows for the inclusion of a unit root bears little resemblance to a mechanism of accumulating shocks in time series. The relevance of integration in a spatial setting is therefore still in need of further theoretical guidance and conceptual development. Mur and Trívez use Monte Carlo experiments to show that the risk of obtaining spurious regression results when using integrated variables remains. The symptoms related to unit roots can be identified, but these symptoms may also be caused by other factors. Their experimental results show anomalies, such as unexpected loss of statistical power, for spatial autocorrelation tests. This leads the authors to suggest that much more emphasis should be put on exploratory spatial data analysis, and in applied research, one should be vigilantly aware of the risk of attaining spurious regressions in spatial econometric models. ValterDi Giacinto (2003 [this issue]) argues that measuring the output effect of monetary policy decisions in structural vector autoregression (SVAR) models that neglect spatial feedback orspillovereffects results in serious misspecification. Building on the earlier work by Carlino and DeFina (1999), he carefully treats spatial interdependencies arising through different spatial propagation mechanisms that smooth out across space. Three mechanisms, related to trade channels, financial transmissions, and what he calls other mechanisms (i.e., mainly driven by commuting), are considered. As an extension to existing modeling approaches, Di Giacinto argues that simultaneous propagation between regions occurs, and he therefore suggests accounting for spatial interaction effects in SVAR models by incorporating information on geographical proximity. He considers three different VAR approaches: a model with no interdependencies, a second model with a oneperiod time lag interaction, and a model with contemporaneous feedback allowing for simultaneous propagation of effects across regions. He derives the appropriate maximum likelihood estimators, and in an application using data that have been used before in this literature, he shows that contemporaneous feedback effects of monetary policy decisions should not be ignored. Giuseppe Arbia and Jean Paelinck (2003 [this issue]) present a new approach to the traditional neoclassical growth convergence modeling. In the preceding section, we already indicated various contributions that explicitly incorporate spatial effects in neoclassical growth models, but Arbia and Paelinck take a different route. They propose a Lotka-Volterra predator-prey system to model regional convergence in a continuous-time framework that also allows for the inclusion of geographical effects. They generalize the traditional predator-prey model to a multiregional system and show that the concept of convergence implied in such a model differs from the classical convergence concept. In particular, they demonstrate that each region or system may follow its own trajectory, leading to a series of distinct convergence paths. The classical β-convergence model can be seen as a special case of their Lotka-Volterra model. The parameters of a discrete analogue of

12 234 INTERNATIONAL REGIONAL SCIENCE REVIEW (Vol. 26, No. 3, 2003) the generalized model are estimated using a simultaneous dynamic least squares estimator. Arbia and Paelinck illustrate their approach with a comparison of the empirical results generated for a traditional convergence equation, a spatially conditioned convergence equation, and the Lotka-Volterra model for 119 European regions over the time period from 1980 to The empirical results are satisfactory and point in the same direction for all models considered. The obvious advantage of the Lotka-Volterra model is, however, that it allows for much more flexibility across space. Markov chain theory offers another approach to modeling income convergence. In a spatial setting, this approach has been explored in Fingleton (1999a) and Rey (2001). Bickenbach and Bode (2003) follow up on this work, but they focus on statistical testing. They propose tests of homogeneity and independence over time and across space to counteract the tendency in most Markov chain studies to ignore checking the validity of the statistical assumptions of homogeneity and independence of the transition probabilities underlying the approach. This is a serious omission because the estimated transition probabilities, and hence the limiting income distribution, will be misleading if regions follow different processes. Furthermore, if the income dynamics of one system depends on the dynamics of its neighbors, the transition probabilities should be estimated conditional upon the income class for neighboring regions. Bickenbach and Bode illustrate the importance of testing for the homogeneity and independence using panel data of relative per capita income of U.S. states during the period from 1929 to They find that for both the first half and the second half of the twentieth century, homogeneity over time, as well as spatial homogeneity, is rejected. Their test results also indicate the relevance of considering dependence over space and time. The contribution of Mossi et al. (2003) demonstrates the usefulness of using spatial exploratory techniques in analyzing the spatial distribution of economic growth and perfectly illustrates the value of the testing framework outlined by Bickenbach and Bode (2003). Mossi and his colleagues investigate regional growth dynamics in Brazil during the time period from 1939 to 1998 and empirically establish the relevance of spatial heterogeneity and spatial dependence. Initially, they follow the traditional spatial exploratory data analysis approach, using global and local Moran s I, scatterplots, and choropleth maps. This analysis reveals the existence of two spatial clusters: a low-income cluster in northeast Brazil and a high-income cluster in southeast Brazil. Subsequently, they investigate the dynamics of regional economic growth using Quah s transitional dynamics framework. Following Bickenbach and Bode s work on statistical testing, they assess whether the transition probabilities are constant over time and across space. Their results indicate that time stationarity cannot be rejected during the period from 1939 to 1998, but the transition probabilities are not constant over space.

13 Florax, van der Vlist / SPATIAL ECONOMETRIC DATA ANALYSIS 235 CONCLUSION In this introductory article to the special issue Spatial Econometric Data Analysis: Models, Extensions, and Applications, we have shown the upsurge in the theoretical development and the use of spatial econometric techniques. Arguably, this is related to an intensified interest in spatial dimensions in theoretical research and to the availability of easy-to-use software for visualization, exploratory data analysis, and the estimation of spatial econometric models. We have documented that numerous case studies using spatial econometric techniques are becoming available. They cover such diverse areas as environmental and natural resources (including agriculture), the functioning of labor markets and unemployment, populationemployment dynamics, spatial externalities of various kinds, economic growth models, housing and real estate, and interacting agents. Much of this work is still using rather traditional spatial econometric techniques, particularly exploratory spatial data analysis techniques (Moran s I, the G statistic, scatterplots, and maps), and model fitting with misspecification tests geared toward verifying whether a spatially correlated error structure is applicable or if spatially lagged variables have erroneously been omitted. Things are starting to change, however. The developments in theory and the desirability of having theory rather than data driving the modeling process are gradually steering spatial econometrics away from the traditional techniques. The contributions to this special issue illustrate this development. They focus on space-time modeling, spatial hazard models, structural vector autoregressive models, spatial nonstationarity, and new methods for the specification, testing, and estimation of regional economic growth processes. Most of the articles indicate elements for future research, but we would like to highlight some promising avenues for future research in this introduction as well. First, much more work is needed on space-time modeling. In particular, the extension to general models incorporating spatial, temporal, and space-time correlations would be useful. This holds forpanel data models in general but also formodels focusing on diffusion. Temporal and spatial diffusion models are well established, but their integration into one modeling framework still needs further work. Moreover, the development of misspecification tests is still lagging behind in this area. It would be interesting to bring together a toolbox of unidirectional and multidirectional misspecification tests along the spatial and temporal dimensions. Second, we have a better view now of the conceptual implications of transforming duration in temporal hazard models to distance in spatial hazard models. An interesting further development could be to derive the associated likelihoods with a subsequent focus on estimation issues. In particular, it may be useful to see whether the use of the traditional spatial weights matrix is feasible and simplifies the intricate specification problem. 11 Third, we are starting to better understand the translation of the unit root and cointegration concepts from the time-series literature to the spatial perspective. The concurrent chance of obtaining spurious spatial regressions has been

14 236 INTERNATIONAL REGIONAL SCIENCE REVIEW (Vol. 26, No. 3, 2003) demonstrated in experimental simulation work. Applied empirical work is still lagging behind and may be fruitful to further underpin and demonstrate the relevance of this topic. Fourth, the structural vector autoregressive approach deserves more application in a spatial setting as well. The derivation of the associated likelihoods in this special issue may contribute to increasing its future usage in applied work, but also in this case, further work on the development of misspecification tests is desirable (the only sources to date that deal with multiple-equation models are Anselin and Kelejian 1997; Rey and Boarnet forthcoming). Finally, the contributions focusing on economic growth show that interesting generalizations of the traditional convergence model, epitomizing the relevance of space, are possible. Obviously, further empirical work is necessary, particularly concentrating on conditioning the growth equation in a regional setting and hence solving some of the data availability problems at this spatial scale. Furthermore, in the growth literature, generalized methods of moments estimation is advocated to account for omitted variable bias and endogeneity, and it has been shown to have a substantial influence on the estimated convergence rates (Abreu, Florax, and de Groot forthcoming). Exploring the use of such an estimator in models accounting for spatial effects is an interesting avenue for further research, as is broadening the analysis of economic growth to space-time models, which may eventually help to circumvent the use of a spatial process specification. NOTES 1. See for an overview of Regional Science Association International (RSAI) conferences and access to local Web sites. The results of these special sessions are in Getis, Mur, and Zoller (forthcoming) and Pace, Tiefelsdorf, and LeSage (forthcoming). This special issue contains some of the papers presented at the Dortmund conference. Although this overview focuses on regional science, concurrent developments take place in (quantitative) geography, sociology, agricultural economics, real estate economics and housing, and slowly but steadily also in environmental and natural resource economics. 2. Details about the subject index of the International Regional Science Review (IRSR) ar e pr o- vided in issue number 4 of each volume (see also below). 3. See for an overview of the program. Two papers on spatial econometrics were presented in the Young Scientists session. 4. See, forinstance, Anselin and Bera (1998) and Anselin (2001c, 2003) foran explanation of the distinction between spatial process models and direct representation models. 5. Some of the more popular online spatial econometric software resources are the spatial statistical toolbox of Kelly Pace (see containing MATLAB routines and programs for large spatial samples; SPDEP Spatial Analysis Tools, designed by Roger Bivand (see with spatial autocorrelation and regression routines written in R; and the commercial package Winbugs-Geobugs (see comprising routines for spatial models using the Gibbs sampler and Markov chain Monte Carlo estimation.

15 Florax, van der Vlist / SPATIAL ECONOMETRIC DATA ANALYSIS We discard interesting but more specialized issues such as the specification of weights, edge effects and the modifiable areal unit problem, infill asymptotics, spatial nonstationarity, limited dependent variable models, and so forth. 7. Anselin (1995) refers to the disaggregated statistics as local indicators of spatial association (LISA, for short). Strictly speaking, the local G i statistic does not belong to the LISA class because the overall or global statistic is not equal to the (scaled) sum of the local statistics. 8. Unless the model specification is strongly guided by theory, the distinction between the exploratory and the explanatory phase is much more blurred in the actual research process, and the researcher usually iterates back and forth using tools from each realm (Haining, Wise, and Signoretta 2000). 9. Florax and de Graaff (forthcoming) give a taxonomy of the different misspecification tests and an assessment of their small sample performance in a comparative response surface setting. 10. The term panel data is not used in a strict sense here. It would be more precise to use the term time series of spatial cross-section data, but we want to avoid its wordiness. 11. This goes back to an observation of Jim LeSage, who discussed a conference presentation of the paper on spatial hazard models. REFERENCES Abreu, M., R. J. G. M. Florax, and H. L. F. de Groot A meta-analysis of the speed of convergence in growth regressions. Discussion paper, Tinbergen Institute, Amsterdam. Acs, Z. J Innovation and the growth of cities. Cheltenham, UK: Edward Elgar. Amrhein, C. G Searching for the elusive aggregation effect: Evidence from statistical simulation. Environment and Planning A 27: Amrhein, C. G., and H. Reynolds Using spatial statistics to assess aggregation effects. Geographical Systems 3: Anselin, L Estimation methods for spatial autoregressive structures. Regional Science Dissertation and Monograph Series No. 8. Ithaca, NY: Cornell University Press Spatial econometrics: Methods and models. Boston: Kluwer Academic., ed. 1992a. Space and applied econometrics [Special issue]. Regional Science and urban Economics b. SpaceStat: A program for the analysis of spatial data. Santa Barbara: National Center for Geographic Information and Analysis, University of California Local indicators of spatial association LISA. Geographical Analysis 27: The Moran scatterplot as an ESDA tool to assess local instability in spatial association. In Spatial analytical perspectives on GIS, edited by M. Fischer, H. Scholten, and D. Unwin, London: Taylor & Francis Computing environments for spatial data analysis. Journal of Geographical Systems 2: a. Spatial effects in econometric practice in environmental and resource economics. American Journal of Agricultural Economics 83: b. Spatial econometrics. In Companion to theoretical econometrics, edited by B. Baltagi, Oxford, UK: Blackwell Scientific c. Rao s score test in spatial econometrics. Journal of Statistical Planning and Inference 97: Under the hood: Issues in the specification and interpretation of spatial regression models. Agricultural Economics 27: Spatial externalities. International Regional Science Review 26:

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20 242 INTERNATIONAL REGIONAL SCIENCE REVIEW (Vol. 26, No. 3, 2003) Messner, S., and L. Anselin Spatial analyses of homicide with areal data. In Spatially integrated social science, edited by M. Goodchild and D. Janelle. New York: Oxford University Press. Molho, I Spatial autocorrelation in British unemployment. Journal of Regional Science 35: Mossi, M. B., P. Aroca, I. J. Fernandez, and C. R. Azzoni Growth dynamics and space in Brazil. International Regional Science Review 26: Mur, J., and F. J. Trívez Unit roots and deterministic trends in spatial econometric models. International Regional Science Review 26: Murdoch, J. C., T. Sandler, and K. Sargent A tale of two collectives: Sulfur versus nitrogen oxides emission reduction in Europe. Economica 64: Nelson, G. C., ed Spatial analysis for agricultural economists [Special issue]. Agricultural Economics 27. Nelson, G. C., and D. Hellerstein Do roads cause deforestation? Using satellite images in econometric analysis of land use. American Journal of Agricultural Economics 79: Pace, R. K Performing large spatial regressions and autoregressions. Economics Letters 54: , ed Spatial statistics and real estate [Special issue]. Journal of Real Estate Finance and Economics 17. Pace, R. K., and R. Barry. 1997a. Sparse spatial autoregressions. Statistics and Probability Letters 33: b. Quick computation of spatial autoregressive estimators. Geographical Analysis 29: Pace, R. K., R. Barry, J. M. Clapp, and M. Rodiquez Spatiotemporal autoregressive models of neighborhood effects. Journal of Real Estate Finance and Economics 17: Pace, R. K., R. Barry, and C. F. Sirmans Spatial statistics and real estate. Journal of Real Estate Finance and Economics 17: Pace, R. K., M. Tiefelsdorf, and J. P. LeSage, eds. Forthcoming. Spatial econometrics [Special issue]. Geographical Analysis 35. Paelinck, J. H. P., and L. H. Klaassen Spatial econometrics. Farnborough, UK: Saxon House. Pinkse, J. Forthcoming. Moran-flavored tests with nuisance parameter. In Advances in spatial econometrics: Methodology, tools and applications, edited by L. Anselin, R. J. G. M. Florax, and S. J. Rey. Berlin: Springer-Verlag. Pinkse, J., and M. E. Slade Contracting in space: An application of spatial statistics to discretechoice models. Journal of Econometrics 85: Rey, S. J Spatial empirics for economic growth and convergence. Geographical Analysis 33: Rey, S. J., and M. G. Boarnet. Forthcoming. A taxonomy of spatial econometric models for simultaneous equations systems. In Advances in spatial econometrics: Methodology, tools and applications, edited by L. Anselin, R. J. G. M. Florax, and S. J. Rey. Berlin: Springer-Verlag. Rey, S. J., and B. D. Montouri U.S. regional income convergence: A spatial econometric perspective. Regional Studies 33: Rupasingha, A., and S. J. Goetz The environmental Kuznets curve for US counties: A spatial analysis. Paper presented at the North American meetings of the Regional Science Association International, November, Charleston, SC. Saavedra, L. A Tests for spatial lag dependence based on method of moments estimation. Regional Science and Urban Economics 33: Smirnov, O., and L. Anselin Fast maximum likelihood estimation of very large spatial autoregressive models: A characteristic polynomial approach. Computational Statistics and Data Analysis 35: Varga, A University research and regional innovation: A spatial econometric analysis of academic technology transfers. Dordrecht, The Netherlands: Kluwer Academic.

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